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Orbital Lifetime Analyses of Pico- and Nano-Satellites

Permanent Link: http://ufdc.ufl.edu/UFE0020154/00001

Material Information

Title: Orbital Lifetime Analyses of Pico- and Nano-Satellites
Physical Description: 1 online resource (63 p.)
Language: english
Creator: Cojuangco, Ai-Ai Lumnay C
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2007

Subjects

Subjects / Keywords: lifetime, nano, orbital, pico, satellite
Mechanical and Aerospace Engineering -- Dissertations, Academic -- UF
Genre: Mechanical Engineering thesis, M.S.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: In recent years, orbital debris has been a growing concern for the space industry due to its potential risk of causing collisions. Several agencies and organizations, such as the National Aeronautics and Space Administration (NASA), and the United Nations Committee on the Peaceful Uses of Outer Space (UNCOPUOS), have been involved in studying orbital debris and developing mitigation guidelines. In 2004, the Federal Communications Commission (FCC) began requiring a debris mitigation plan for all non-government United States radio communication satellites to be launched into orbit. Orbital lifetime analysis of a satellite is important in its development and in complying with debris mitigation guidelines. Factors that must be taken into consideration include environmental perturbations, such as solar radiation pressure, the Earth?s oblateness, and atmospheric drag. Other factors that affect orbital lifetime prediction are the satellite's physical properties. In this research, these perturbations and their effects on orbital lifetime, for Earth-orbiting satellites, were investigated. In this study, orbital lifetimes were determined using the Lifetime analysis tool in Analytical Graphics? Satellite Tool Kit (STK) software, focusing on pico- and nano-satellites. The focus on these two classes of satellites is due to their perceived rapid growth and the potential difficulty of adhering to FCC requirements for debris mitigation. The effect of solar cycle and different atmospheric density models were also explored during the analyses. The results indicate that orbital lifetimes of pico-satellites can be significantly reduced by increasing their drag area. For instance, changing the drag area of a 1-kg satellite from 0.01 to 0.1 meters squared decreased its orbital lifetime from 22 to 3 years, an 86% reduction. At 600 km above the Earth?s surface, pico-satellites with drag areas of 0.1 meters squared had minimum orbital lifetimes during years of highest solar activity. Our analysis implies that passive de-orbiting devices such as drag chutes can be effective devices on pico-satellites for addressing orbital debris mitigation. Meanwhile, the nano-satellites used in our study were between 11 to 28 kg, with drag areas from 0.08 and 0.2 meters squared, which led to orbital lifetimes in centuries when launched at 750 km altitude. Values indicate that additions to the nano-satellites are needed to fulfill a 25 year orbital lifetime requirement set by the FCC.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Ai-Ai Lumnay C Cojuangco.
Thesis: Thesis (M.S.)--University of Florida, 2007.
Local: Adviser: Fitz-Coy, Norman G.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2007
System ID: UFE0020154:00001

Permanent Link: http://ufdc.ufl.edu/UFE0020154/00001

Material Information

Title: Orbital Lifetime Analyses of Pico- and Nano-Satellites
Physical Description: 1 online resource (63 p.)
Language: english
Creator: Cojuangco, Ai-Ai Lumnay C
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2007

Subjects

Subjects / Keywords: lifetime, nano, orbital, pico, satellite
Mechanical and Aerospace Engineering -- Dissertations, Academic -- UF
Genre: Mechanical Engineering thesis, M.S.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: In recent years, orbital debris has been a growing concern for the space industry due to its potential risk of causing collisions. Several agencies and organizations, such as the National Aeronautics and Space Administration (NASA), and the United Nations Committee on the Peaceful Uses of Outer Space (UNCOPUOS), have been involved in studying orbital debris and developing mitigation guidelines. In 2004, the Federal Communications Commission (FCC) began requiring a debris mitigation plan for all non-government United States radio communication satellites to be launched into orbit. Orbital lifetime analysis of a satellite is important in its development and in complying with debris mitigation guidelines. Factors that must be taken into consideration include environmental perturbations, such as solar radiation pressure, the Earth?s oblateness, and atmospheric drag. Other factors that affect orbital lifetime prediction are the satellite's physical properties. In this research, these perturbations and their effects on orbital lifetime, for Earth-orbiting satellites, were investigated. In this study, orbital lifetimes were determined using the Lifetime analysis tool in Analytical Graphics? Satellite Tool Kit (STK) software, focusing on pico- and nano-satellites. The focus on these two classes of satellites is due to their perceived rapid growth and the potential difficulty of adhering to FCC requirements for debris mitigation. The effect of solar cycle and different atmospheric density models were also explored during the analyses. The results indicate that orbital lifetimes of pico-satellites can be significantly reduced by increasing their drag area. For instance, changing the drag area of a 1-kg satellite from 0.01 to 0.1 meters squared decreased its orbital lifetime from 22 to 3 years, an 86% reduction. At 600 km above the Earth?s surface, pico-satellites with drag areas of 0.1 meters squared had minimum orbital lifetimes during years of highest solar activity. Our analysis implies that passive de-orbiting devices such as drag chutes can be effective devices on pico-satellites for addressing orbital debris mitigation. Meanwhile, the nano-satellites used in our study were between 11 to 28 kg, with drag areas from 0.08 and 0.2 meters squared, which led to orbital lifetimes in centuries when launched at 750 km altitude. Values indicate that additions to the nano-satellites are needed to fulfill a 25 year orbital lifetime requirement set by the FCC.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Ai-Ai Lumnay C Cojuangco.
Thesis: Thesis (M.S.)--University of Florida, 2007.
Local: Adviser: Fitz-Coy, Norman G.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2007
System ID: UFE0020154:00001


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ORBITAL LIFETIME ANALYSES OF PICO- AND NANO-SATELLITES


By

AI-AI LUMNAY C. COJUANGCO
















A THESIS PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE

UNIVERSITY OF FLORIDA

2007



































2007 Ai-Ai Lumnay C. Cojuangco

































To my mother and sister









ACKNOWLEDGMENTS

I extend my sincere gratitude to my advisor, Dr. Norman Fitz-Coy, for his generous

support, guidance and patience through my graduate studies at the University of Florida.

I acknowledge and give appreciation to my committee members Dr. John K. Schueller and

Dr. Carl Crane for providing valuable input to this work.

I acknowledge my colleagues in the AMAS lab, the Space Systems Group and SAMM

group, for their support, input, and company with research and graduate studies.

I express my appreciation to the women in my life group, Pascalie Belony, Jamie Cabug,

Ann Duong, Sunny Ho, Jenny Jose, Christine Moran, and Carrie Torbert for their continuous

encouragement, belief in me, words of wisdom, prayers, and for being such great inspirations to

my life since I arrived at University of Florida. Also, to all the wonderful people I have met and

befriended through Gator Christian Life.

I thank Cris Dancel for her time, guidance and support with this work. I also express my

appreciation to the rest of the Filipino community I have met here for making me feel at home. I

thank my friends in Illinois as well for keeping me in their thoughts.

I thank my family. I especially thank my mother, Evangeline Chongco, and sister,

Claudine Foronda, for their love, support, and for allowing me to pursue graduate studies.

Last, I express my deep gratitude to Jesus Christ, my Lord, my Savior and my God, it is

through Him I have faith and strength and it is He who has made all of this possible. I thank

Him for his beautiful creation that I have had the joy in living and learning about.










TABLE OF CONTENTS

page

A C K N O W L E D G M E N T S ..............................................................................................................4

LIST OF TABLES ...................................................................7

LIST OF FIGURES .................................. .. ..... ..... ................. .8

ABSTRAC T .........................................................................................

CHAPTER

1 INTRODUCTION AND BACKGROUND ............................. 11

D definition of O rbital D ebris.......................................................... .. ........... ......... 11
C concerns w ith O rbital D ebris ................................................... ...... ........................ 11
Development of Mitigation Guidelines ............................................................................15
M otivation of R research ........... ........................................................................ ........ .. .. 17

2 METHODS .........................................20

T w o -b o d y P ro b lem .................................................................................................................2 0
C o n ic S ectio n s ................................................................2 3
O rb ital E lem en ts .............................................................................2 5
P e rtu rb a tio n s ...........................................................................................................................2 6
Perturbation Techniques ................................. ...................................................30
O rb ital L ifetim e ................................................................3 3

3 SIMULATIONS USING SATELLITE TOOL KIT (STK) SOFTWARE .............................35

S satellite T o o l K it (S T K ) ................................................................................................... 3 5
S T K L ifetim e T o o l ........................................................................................................... 3 5
S T K S satellite P ro p ertie s .........................................................................................................3 9
P aram eter S en sitiv ity Stu dy .............................................................................................. 4 1

4 RESULTS AND DISCUSSION ...................................... .........46

P ic o -satellite R e su lts ...............................................................................................................4 6
N ano-satellites R esults................................................. 50

5 CONCLUSION AND RECOMMENDATIONS ........................... ....... ...............58

C onclu sions.......... ..........................................................58
R ecom m endations............................................................................................. 59









L IST O F R E F E R E N C E S .............................................................................. ...........................60

B IO G R A PH IC A L SK E T C H .............................................................................. .....................63





















































6









LIST OF TABLES


Table page

3-1 Satellite mass, drag area, and area exposed to Sun..................................37

3-2 Orbital lifetime sensitivity simulation parameters .............. ..........................................41

4-1 CubeSat sim ulation param eters............................................... ............................. 47

4-2 MR SAT and M RS SAT simulation parameters................................... ............... 51

4-3 FASTRAC simulation parameters ........... .. ..... .......... .................. 51

4-4 Akoya-B and Bandit-C simulation parameters............. ....... ...... .... ........... 52

4-5 MR SAT with different initial altitudes simulation parameters............... .......... 52









LIST OF FIGURES


Figure p e

1-1 Typical pico- and nano-class satellite mass, volume and power ratios .........................18

1-2 Computer generated image of orbital debris in LEO.....................................................19

2-1 R elative m otion of tw o-bodies .............................................................. .....................2 1

2-2 G eom etry of an elliptic conic section ........................................ ......................... 24

2-3 O rbital elem ents ............................................................... .... .... ......... 25

3-1 ST K L ifetim e tool G U I................................................................................. .......... 36

3-2 STK Lifetim e A advanced option GU I................................................................... ......39

3-3 ST K satellite properties G U I ........................................ .............................................40

3-4 Orbital lifetime e vs. reflection coefficient................................ ................................. 43

3-5 Orbital lifetime e vs. area exposed to Sun ........................................ ....... ............... 43

3-6 O rbital lifetime e vs. drag coefficient........................................................................ .. ...44

3-7 O rbital lifetime e v s. drag area ........................................ .............................................44

3-8 O rbital lifetime e vs. m ass .......................................... ................... ........ 45

4-1 Orbital lifetime results for satellite A using seven atmospheric density models............48

4-2 Orbital lifetime results for satellite C using seven atmospheric density models .............48

4-3 Orbital lifetime results for satellites A, B, C, and D at 600-km initial altitude...............49

4-4 Orbital lifetime for MR SAT and MRS SAT at 350-km initial altitude..........................54

4-5 Orbital lifetime for MR SAT and MRS SAT at 750-km initial altitude..........................55

4-6 Orbital lifetime for the FASTRAC satellites at 350-km initial altitude.........................55

4-7 Orbital lifetime for the FASTRAC satellites at 750-km initial altitude...........................56

4-8 Orbital lifetime for the Akoya-B and Bandit-C at 350-km initial altitude ....................56

4-9 Orbital lifetime for the Akoya-B and Bandit-C at 750-km initial altitude ......................57

4-10 Orbital lifetime for the MR SAT using different initial altitudes ..................................57









Abstract of Thesis Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Science

ORBITAL LIFETIME ANALYSES OF PICO- AND NANO-SATELLITES

By

Ai-Ai Lumnay C. Cojuangco

December 2007

Chair: Norman Fitz-Coy
Major: Mechanical Engineering

In recent years, orbital debris has been a growing concern for the space industry due to its

potential risk of causing collisions. Several agencies and organizations, such as the National

Aeronautics and Space Administration (NASA), and the United Nations Committee on the

Peaceful Uses of Outer Space (UNCOPUOS), have been involved in studying orbital debris and

developing mitigation guidelines. In 2004, the Federal Communications Commission (FCC)

began requiring a debris mitigation plan for all non-government United States radio

communication satellites to be launched into orbit.

Orbital lifetime analysis of a satellite is important in its development and in complying

with debris mitigation guidelines. Factors that must be taken into consideration include

environmental perturbations, such as solar radiation pressure, the Earth's oblateness, and

atmospheric drag. Other factors that affect orbital lifetime prediction are the satellite's physical

properties. In this research, these perturbations and their effects on orbital lifetime, for Earth-

orbiting satellites, were investigated.

In this study, orbital lifetimes were determined using the Lifetime analysis tool in

Analytical Graphics' Satellite Tool Kit (STK) software, focusing on pico- and nano-satellites.

The focus on these two classes of satellites is due to their perceived rapid growth and the









potential difficulty of adhering to FCC requirements for debris mitigation. The effect of solar

cycle and different atmospheric density models were also explored during the analyses.

The results indicate that orbital lifetimes of pico-satellites can be significantly reduced by

increasing their drag area. For instance, changing the drag area of a 1-kg satellite from 0.01 to

0.1 m2 decreased its orbital lifetime from 22 to 3 years, an 86% reduction. At 600 km above the

Earth's surface, pico-satellites with drag areas of 0.1 m2 had minimum orbital lifetimes during

years of highest solar activity. Our analysis implies that passive de-orbiting devices such as drag

chutes can be effective devices on pico-satellites for addressing orbital debris mitigation.

Meanwhile, the nano-satellites used in our study were between 11 to 28 kg, with drag areas from

0.08 and 0.2 m2, which led to orbital lifetimes in centuries when launched at 750 km altitude.

Values indicate that additions to the nano-satellites are needed to fulfill a 25 year orbital lifetime

requirement set by the FCC.









CHAPTER 1
INTRODUCTION AND BACKGROUND

Definition of Orbital Debris

The launch of Sputnik in 1957 was the dawn of space exploration and a significant

milestone in the advances in science and technology. Since that date, numerous missions and

manned spacecraft have been launched and continue to be launched for scientific, educational,

and technological purposes. A major effect not considered in the early years of space

exploration was the contribution of artificial bodies (i.e., spent satellites and spacecraft

components) to the debris population in space. Two categories of debris now exist, natural (i.e.,

meteoroids) and artificial (i.e., used rocket bodies). Artificial debris is also referred to as orbital

debris. Orbital debris refers to man made space objects that are no longer functioning or serve

any useful purpose. Prior practices and procedures have allowed unregulated growth of orbital

debris, however, in recent years, the issue of orbital debris has become extremely important

requiring that the space industry monitors debris orbiting the Earth and develop procedures to

curtail its growth in the future.1

Concerns with Orbital Debris

There are several factors that have and will contribute to the growth of orbital debris, the

primary contributors being (1) explosions, (2) prior practices and procedures that have involved

the abandonment of spacecraft and upper stages, (3) the deposition rate of objects being sent into

space, (4) collisions, and (5) future trends of small satellite usage by academia, government and

industry.

First, orbital debris growth's primary cause is explosions, which produce breakups or

fragments. Explosions can be accidental or intentional. Accidental explosions obtain energy

from on-board energy sources. Meanwhile, intentional explosions include tests (i.e., anti-









satellite testing) or spacecraft separation. For example, in low Earth orbit (LEO), altitudes up to

2,000 km above the Earth's surface, accidental explosions of spent upper stages have been the

main source of debris.2

Second, the next largest contributor to orbital debris has been prior practices and

procedures that involved the abandonment of spacecraft and upper stages in their current orbit

after the spacecraft has completed its mission or is no longer operational. The National

Aeronautics and Space Administration (NASA) reported in 1995 the accumulation of

approximately 1968 tons of orbital debris due to these practices.2

Third, assets are being launched into space at a rate that is higher than the rate at which

expired assets are being removed by natural and artificial means.3 This has led to an average

growth rate in debris population of 5% per annum in LEO.4

Fourth, a major concern to orbital debris growth is collisions. Collisions can occur

between varieties of satellite classes. Due to their large speeds, when space objects collide with

each other, they may become non-operational. These masses would spatially distribute

themselves producing debris fragments or debris clouds and thus add on to the total debris

population. The threat of these clouds is evident by the debris created from the recently

destroyed Chinese satellite, Fengyun 1-C, this past January 2007.

Last, research and trends in the past were focused on traditional large costly satellites, but

are now transitioning to smaller satellites. This trend is the result of these satellites potential

lower costs and advances in technology, which allows for miniaturization. The Defense

Advanced Research Projects Agency (DARPA) organization is exploring fractionated spacecraft

flying in formation as well as a collection of heterogeneous small satellite modules5 performing

various tasks. This trend is also seen in academia through projects such as the CubeSat and the









University Nano-satellite Program (UNP).

The CubeSat program was developed by the California Polytechnic State University in San

Luis Obispo, and Stanford University's Space Systems Development lab as a mechanism to

enable universities to participate in the design, launch, and operations of satellites at an

affordable cost.6 A one unit CubeSat is a 10x 10x 10 cm cube with a mass of 1 kg classified as a

pico- satellite. Currently, these satellites typically have short operational lifetimes as compared

to their orbital lifetimes and if not properly disposed after its primary mission will then

contribute orbital debris.

The UNP is a joint program composing of the Air Force Research Laboratory's Space

Vehicles Directorate (AFRL/VS), the Air Force Office of Scientific Research (AFOSR), and the

American Institute of Aeronautics and Astronautics (AIAA). The program is a national student

satellite design and fabrication competition. It also enables small satellite research and

development, integration, payload development, and flight tests.7 There are a growing number

of these satellite classes planned on being sent to space and the increase can potentially

contribute to the total amount in number and mass of the orbital debris population.

The growth of orbital debris has become an immediate issue as its presence in space

continues to have an impact with the utilization of space assets. It is continuously monitored and

modeled by agencies such as NASA and the United Nations Committee on the Peaceful Uses of

Outer Space (UNCOPUOS) for study and risk assessment to future space missions. The impact,

both immediate and lasting, of collisions and explosions on the orbital debris population and

resultant hazards to space operations are discussed.

Explosions can produce debris fragments in large number and cause an operating

spacecraft to fail, as well as produce smaller debris fragments that may degrade its performance.









Other spacecraft, hundreds of kilometers away, may also be at a great risk from these fragments

due to their high velocities that may set them in very long orbit lifetimes.2

According to NASA, collision between large objects follows this scenario:

First, once collisions begin to occur, it will be almost impossible to halt the process and
they will occur with increasing frequency-a process referred to as collisional cascading.
Second, the energies in collisional breakup are much larger than in explosive breakup, in
the megajoule (a few kilograms to TNT) to gigajoule (a few metric tons of TNT) range.
This energy comes from the very large amount of chemical energy used to get objects into
orbit. This large amount of expended energy creates many more debris fragments in all
size ranges and spreads the debris over many hundreds of kilometers of altitude. This
debris may hit other satellite surfaces, carrying impact energies of hundreds of megajoules
per kilogram of impactor mass. At these energies, debris less than 1 mm in diameter,
typically about 1 mg of mass, can penetrate an unshielded spacecraft surface and damage
sensitive surfaces such as optics or thermal radiators; debris less than 1 cm (1 gm) can
penetrate even a heavily shielded surface; and debris as small as 10 cm (1 kg) can cause a
spacecraft to break up into debris fragments.2

Consequently, the risk of collision between debris and another object has become a close

concern. Abandoned spacecraft and upper stages are cases of large non-operational objects

already in space for which this type of collision can occur. Computer modeling indicates that

collisions between large objects in orbit will become a major source of debris within the next 3

decades, even if spacecraft launches were limited at 5 launches per year. The orbital debris that

will be produced from these collisions will be small particles that are large in number and are

capable of damage to operational spacecraft.1,2

For the purpose of this research, collision of objects in LEO is the focus. In this orbit, the

standard impact velocity of medium-sized orbital debris with other objects is about 13 km/s, with

an explosive potential equal to 40 times its mass of TNT. For instance, a 1-cm-diameter

aluminum sphere, about 1.4 grams, has a kinetic energy equivalent to the energy released by the

explosion of 0.056 kg of TNT (about 0.24 MJ). A 10-cm aluminum sphere, on the other hand, is

equivalent to 56 kg of TNT (about 240 MJ). Therefore, in LEO, the energy released by small

debris pieces may severely damage or destroy many spacecraft systems.1









Development of Mitigation Guidelines

Assessments of potential risks involved with orbital debris have led to possible solutions

and abatement measures. Although removing abandoned spacecrafts, upper stages, and other

orbital debris may be the most effective means in avoiding future collisions, this is not cost

effective because it would require difficult maneuvering of objects in space.2'8

Several national and international agencies/organizations are involved in orbital debris

assessment and mitigation. In 1993, the Inter-Agency Space Debris Coordination Committee

(IADC) was founded "to enable space agencies to exchange information on space debris research

activities, to review the progress of ongoing cooperative activities, to facilitate opportunities for

cooperation in space debris research and to identify debris mitigation options"9. Members of the

IADC consists of NASA, the Italian Space Agency (ASI), the British National Space Centre

(BNSC), the Centre National d'Etudes Spatiales (CNES), the China National Space

Administration (CNSA), the Deutsches Zentrum fuer Luft-und Raumfahrt e.V. (DLR), the

European Space Agency (ESA), the Indian Space Research Organisation (ISRO), the Japan

Aerospace Exploration Agency (JAXA), the National Space Agency of Ukrain (NSAU), and the

Russian Aviation and Space Agency (Rosaviakosmos).

By February 1994, the United Nations (UN) Scientific and Technical Subcommittee

agreed that international cooperation was needed to minimize the potential impact of space

debris on future space missions.9 NASA issued a comprehensive set of orbital debris mitigation

guidelines in 1995.10 The U.S. Government along with NASA, the Federal Aviation

Administration (FAA), the Department of Defense (DoD), and the Federal Communications

Commission (FCC) presented a set of orbital debris mitigation standard practices in a 1998 U.S.

Government Orbital Debris Workshop for Industry.11 Japan, France, Russia, and the European

Space Agency (ESA) and other countries, have since followed suit with their own guidelines.10









President Reagan issued a directive on national space policy requiring the limitation of

orbital debris accumulation on February 11 of the same year. This directive initiated the

collaborative work of the U.S. and other nations to learn more about orbital debris hazards and

management. An International Technical Working Group was established through this, which

helped influence nations with space activities to take action in limiting orbital debris.2

By the year 2001, the United States Government adopted its own guideline, U. S.

Government Orbital Debris Mitigation Standard Practices. 10,12 The IADC reached a consensus

on a set of guidelines that were formally presented to the Scientific and Technical Subcommittee

of the UNCOPUOS on February 2003.10 In June 2004, the FCC issued its own set of mitigation

rules, Orbital Debris Notice, closely following the U. S. Government Orbital Debris Mitigation

Standard Practices.13

Several orbital debris mitigation guidelines have been in place after NASA's lead.

NASA's, the U.S. Government's, the IADC's and the FCC's guidelines are summarized here

with a focus on post mission disposal in LEO, for the purpose of this thesis. NASA's guideline

has three general options for post mission disposal in LEO which are (1) atmospheric re-entry,

(2) maneuvering to a storage orbit, and (3) direct retrieval. For option one, the guideline states to

maneuver a structure into an orbit where atmospheric drag, the main nongravitational force

acting on satellites in LEO,14 will cause its lifetime to decay within 25 years after the end of its

mission. The second option states to maneuver the spacecraft with final missions passing

through LEO to a disposal orbit defined to be between 2500 km to 35,288 km. The last option

states to perform a direct retrieval of the spacecraft from its orbit within 10 years after the end of

its mission.2

The U.S. Government guidelines has the same three options as NASA, but with the









inclusion of human casualty risk to be limited to no greater than 1 in 10,000 upon re-entry added

to option one; different disposal orbit definition for option two; and, the time period stated to be

"as soon as practical" given for option three.12 The IADC Space Debris Mitigation Guidelines

has a post mission disposal section for the LEO region. The guideline gives the option for space

systems to be disposed by de-orbiting, by direct re-entry, by maneuvering it to an orbit that

reduces its lifetime and by direct retrieval.15

The FCC, which has general authority over U.S. radio communications with the exception

of government radio stations, includes three methods for post mission disposal. One method is

direct retrieval, which the commission currently states little relevance for this option regarding

Commission-licensed space stations. Another method is to maneuver a spacecraft to a disposal

or storage orbit. The storage orbit is defined to be in perigee altitudes above 2000 km and apogee

altitudes below 19,700 as suggested for satellites in LEO. The FCC gives two procedures for the

atmospheric re-entry option: (1) to use the spacecraft's propulsion to bring it further into the

Earth's atmosphere and (2) to move the satellite to an orbit from which atmospheric drag will

cause its re-entry into the Earth's atmosphere and that it will decay within 25 years after the end

of its mission. For continued affordable access to space, the FCC ruled that a satellite system

operator must submit an orbital debris mitigation plan before requesting space station

authorization.13

Motivation of Research

This research, in response to the FCC ruling, investigates the different parameters that

affect the orbital lifetime of pico- and nano-class satellites. These classes of satellites are

increasingly gaining attention throughout the space industry due to their potential low cost and

technological advances. The University of Florida has been involved with small satellite

research, in particular the CubeSat, since the fall of 2004. The nano-satellites developed through









the UNP are another example of the trend in academia moving towards small satellites. The

increase in number of these satellites being sent to space is a concern. The typical size, mass,

and power ratios of these two classes of satellites are shown in Figure 1-1.

Power 20W
/-/


Power 2W 10 kg



*10 -- 30
cm cm
Pico Nano
Figure 1-1. Typical pico- and nano-class satellite mass, volume and power ratios

As of May 2007, there have been 17 of the pico-class satellites referred to as CubeSats

successfully launched in LEO and are namely:16'17

2003: AAU CubeSat by the Aalborg University, DTUSat by the Technical University of
Denmark, CanX-1 by the University of Toronto SFL, CubeSat XI-IV by the University of
Tokyo, Cute-1 by the Tokyo Institute of Technology Matunaga LSS

2005: NCube-2 by the University of Oslo (and others), UWE-1 by the University of
Wirzburg, CubeSat XI-V by the University of Tokyo

2006: Cute-1.7 by the Tokyo Institute of Technology Matunaga LSS, HITSat by the
Hokkaido Institute of Technology

2007: AeroCube-2 by the Aerospace Corporation, CAPE-1 by the University of
Louisiana, CP-3 and CP-4 by the California Polytechnic State University, CSTB-1 by the
Boeing company, Libertad-1 by the Sergio Arboleda University, MAST by Tethers
Unlimited

The CubeSat has a small mass and volume that can make a huge collision impact especially due

to both the high velocity rates and concentration of spacecrafts in LEO. Figure 1-2 shows a

computer generated image of the concentration of orbital debris that has been tracked in LEO

(2005) courtesy of NASA. As opportunities for CubeSats to access space continue to proliferate,

their contribution to the total mass may not seem substantial on a small scale. However, the









quantity of dispersed orbiting CubeSats would deter the grade of the orbit unless measures are

taken to prevent this by satellite developers. Also, there are currently no enforced mitigation

plans for CubeSats.














Figure 1-2. Computer generated image of orbital debris in LEO. Courtesy of NASA.18

The nano-satellites also have the potential to contribute to the total mass and number of

orbital debris in space. The number of these types of satellite planned on being launched is

increasing. Details of the properties of the nano-satellites chosen for this study are further

discussed in Chapter 3. The initiative to take the necessary measures to reduce the orbital

lifetime of these types of satellites, in order to prevent them from becoming orbital debris, is a

step towards being responsible users of the space environment and must be taken seriously.

In Chapter 2, the equations of motion for the two-body problem and the equations that lead

to orbital lifetime prediction are presented followed by some computer programs available for

predicting orbital lifetime. In Chapter 3, Satellite Tool Kit (STK), the software used in this study

for orbital lifetime prediction, is presented and the different parameters used for the simulation

scenarios are reported. Chapter 4 elaborates on the orbital lifetime prediction results for the

pico- and nano-satellites, while the conclusions and recommendations for this research are in

Chapter 5.









CHAPTER 2
METHODS

In this chapter the equation of motion for the two-body problem is discussed. Brief

summaries of conic sections and orbital elements are given. The equations of motion for the

two-body problem with perturbations are also presented. These equations are then used to

describe orbital lifetime. Some programs for orbital lifetime prediction are presented.

Two-body Problem

A model to describe a satellite's orbital motion can be developed from planetary motions.

The physical motions of each planet were first described by Johannes Kepler's three laws:19

First Law The orbit of each planet is an ellipse, with the sun at a focus.

Second Law The line joining the planet to the sun sweeps out equal areas in equal
times.

Third Law The square of the period of a planet is proportional to the cube of its mean
distance from the sun.

The first two laws of planetary motion were published in 1609, while the third in 1619. The

mathematical equations of planetary motions were not formulated until about 50 years later,

through Issac Newton's second law of motion and law of universal gravitation. Newton's

second law of motion states that "the rate of change of momentum is proportional to the force

impressed and is in the same direction as that force"19. Newton's law of universal gravitation

states that "any two bodies attract one another with a force proportional to the product of their

masses and inversely proportional to the square of the distance between them "19

The equation for the second law of motion can be written as


dF=m md (2.1)
T dt2 i dt

The notation .F represents the sum of all the forces acting on a body which is equal to its









d2F
mass, mi, times its acceleration, measured relative to an inertial frame, and i is the
dt2

velocity vector. Newton's law of universal gravitation can be written as


F = G -1 ( -) i= 1,...n (2.2)
J=- r


where Fg is the gravitational force on m, due to m and (r i) is the vector from m, to mn.

The symbol G represents the universal gravitational constant and has the value of 6.670 x 10-8

dyne cm2/gm2.19

The equations of motion for planets and satellites were developed from equations (2.1) and

(2.2). The equations of motion are applicable for a system of two bodies, referred to as the two-

body problem, where n = 2 in equation (2.2). An illustration of the system with bodies m, and

m2 is shown in Figure 2-1. Two assumptions are required to develop the equations of motion

and are as follows: (1) body 1 and body 2 are spherically symmetric (this allows for the bodies to

be treated as though the concentrations of their masses are at their centers) and (2) only

gravitational forces are acting on the system, which act along the line joining the centers of the

two bodies. An inertial reference frame is also defined to measure the motion. In Figure 2-1 the

set of inertial coordinates is defined by (X, Y, Z). The position vectors of m, and m2, with

respect to the inertial frame, are defined as F, and F, respectively, so that r = r .19


Z r m2
1Figure 2-1. Relative motion oftwo-bodies






x
Figure 2-1. Relative motion of two-bodies









Equating Newton's second law of motion and his law of universal gravitation, for i = 1 and

2, after some manipulations, the governing equations of motion of m, and m, are


d G-n(r2 ) (2.3)
dt2 r


SG (F1 r2) (2.4)
dt2 r

where r1 = r 2 = Ir r = r, which is the distance between the two bodies. Twelve constants are

required for a complete solution of these second order ordinary differential equations, but only

10 exist and thus the equations cannot be solved analytically. The two equations can be reduced

to find the relative motion of body 2 with respect to body 1 by subtracting equation (2.3) from

(2.4) which results in


d2 -G= r+ mr r /) (2.5)


where r is the position vector from m, to m2. Equation (2.5) may be rewritten as

d2r U
d + r= (2.6)
dt2 r

assuming that m, = mass of the Earth and is much greater than m2 = mass of the satellite so that

u = G (m, + m2 ) Gmn, which is called the Earth's gravitational constant. Equation (2.6) is the

equation for the relative motion of two-bodies with only gravitational forces acting upon the

system describing the motion of m2 with respect to m, .19 Equation (2.6) is a second order,

nonlinear, vector, differential equation, that can be solved analytically, which requires six

constants of integration for a complete solution from F, and fo or six other constants.

By conservation of angular momentum, the orbit of a satellite around the Earth can be









shown to lie on a plane. The angular momentum vector, h, is then perpendicular to the orbit

plane and is a constant vector. A partial solution to Equation (2.6) is easy to obtain, that tells the

size and shape of the orbit. Crossing h to Equation (2.6) leads to a form of equation that can be

integrated:

d2x Q F) (2.7)
dt r

The left side of Equation (2.7) equals d x t and the right side equals r and
dt dt r r2 dt

after some manipulations Equation (2.7) can be rewritten as

d(df d (iYF
d c--x/ d = F (2.8)
dt dt dt r

Integrating both sides results in

-xh = p -+ (2.9)
dt r

where B is a vector constant of integration. Dot multiplying Equation (2.9) by F results in a

scalar equation

h2 =,r + rBcosf (2.10)

where f is the angle between B and F. By solving for r, Equation (2.10) becomes

hZ / ,
r= (2.11)
1 + (B/) cosf

and is called the trajectory equation expressed in polar coordinates.19

Conic Sections

Equation (2.11) is similar to the equation of a conic section, where a conic section may be

defined as "a curve formed by the intersection of a plane passing through a right circular cone"14









The equation of a conic section can be written as


r= (2.12)
1+ecosf

and gives the magnitude of the position vector, II = r, in terms of its location in the orbit where

p is called the parameter or semi-latus rectum, e is the eccentricity, and f is the polar angle or

true anomaly. The type of conic section represented by equation (2.12) is determined by the

value of the eccentricity. When e = 0 the conic section is a circle, 0 < e < 1 produces an ellipse,

e = 1 generates a parabola, and e > 1 represents a hyperbola.

Figure 2-2 shows a geometric representation of an elliptic conic section. The figure shows

the conic section having two foci, where F is the primary focus (i.e., the Earth's center) and F'

is the secondary or vacant focus. C is the center of the ellipse. Half the distance between foci is

the dimension c'. The dimension a is the semi-major axis and b is the semi-minor axis of the

ellipse. The distance from the primary focus to the farthest point of the ellipse is called the

radius of apogee, ra, and to the closest point of the ellipse is called the radius of perigee, r .

From Kepler's Second Law, the time required to complete one orbit is called the orbital period,

TP, and is expressed as


TP = a3/2 (2.13)









r r
a p


a
Figure 2-2. Geometry of an elliptic conic section









Orbital Elements


The six other constants of integration possible, asides from position and velocity for the

solution of Equation (2.6), to describe the motion of a satellite around the Earth, are known as

orbital elements or Keplerian orbital elements as shown in Figure 2-3 and are defined below (See

reference 14).

Semi-major axis (a) Defines the size of the orbit.

Eccentricity (e) Defines the shape of the orbit.

Inclination (i) The angle between Z and angular momentum vector, h .

Right Ascension of Ascending Node (RAAN) ( Q) "The angle from the vernal equinox
to the ascending node. The ascending node is the point where the satellite passes through
the equatorial plane moving from south to north. Right ascension is measured as a right-
handed rotation about the pole, Z ."

Argument of Perigee (0 ) "The angle from the ascending node to the eccentricity
vector, e, measured in the direction of the satellite's motion. The eccentricity vector
points from the center of the Earth to perigee with a magnitude equal to the eccentricity
of the orbit."

Mean anomaly (M) "The fraction of an orbit period which has elapsed since perigee,
expressed as an angle. The mean anomaly equals the true anomaly for a circular orbit."

2

h J0 Periapsis
Direction





/ (~J ro


Line of Nodes f
Y x 9Y i c
Vernal Equinox Line of Nodes Periapsis
Direction Direction
Figure 2-3. Orbital elements









Perturbations

The amount of time a satellite remains in orbit before perturbations causes its reentry into

the Earth's atmosphere is the satellite's orbital lifetime and can be found from the sum of its

orbital period, TP. The orbital period is a function of the semi-major axis. When the semi-major

axis remains constant then the period is constant and the orbital lifetime is indefinite. Orbital

lifetime goes towards infinity as a increases because the period gets larger. Orbital lifetime

becomes finite when the semi-major axis decreases as this causes the period to decrease. The

duration of a satellite's orbit with respect to the Earth is indefinite when the only forces acting on

the system are gravitational forces. The orbital elements also remain constant. When other

forces act on the system, however, the relative motion equation becomes

+ F i= d (2.14)
dt2 r

where dd is the perturbing acceleration. This non-homogeneous differential equation implies

that the previous "constants of motion are no longer constant. Thus, orbital lifetime can be finite

when perturbations are considered. 20,21

Some of these perturbations are atmospheric drag, solar radiation pressure, the Earth's

oblateness, and other bodies (n-body effect). Factors to consider with these perturbations are

solar activity, geomagnetic activity, atmospheric density, and ballistic coefficient (a function of

the satellite's mass, mean cross sectional drag area, and drag coefficient). These perturbing

accelerations cause a satellite's orbit to decrease and no longer be indefinite. The orbit will

decay into the Earth's atmosphere and the time it takes for the decay to bring the satellite into the

Earth is the satellite's orbital lifetime. In predicting the orbital lifetime of satellites,

perturbations must be taken into consideration. These factors and uncertainties in the solar and









geomagnetic activities can make orbital lifetime prediction very challenging.20'21 Some of the

factors that affect lifetime are discussed here.

The Earth's upper atmosphere has a strong effect on satellites in space. The atmosphere is

dynamic and is affected mostly by the sun's radiation. This solar activity heats up the

atmosphere and it expands as a result. The expansion "produces a variation in density

proportional to the degree of heating, which in turn depends upon solar activity"22. Solar activity

and Sun spots vary periodically, which is commonly known as the 11-year solar cycle. The

radiation from the sun is measured as a mean daily flux in the 10.7 cm (F10.7) wavelength in

solar flux units (sfu).

A bulge is also created, as a result of the heating on the side of the Earth that is facing the

sun. This causes "the density at a given point above the Earth to vary diurnally, as the point

rotates through the bulge every 24 hours, and seasonally, as the bulge moves with the sun in

latitude from winter to summer"22. The atmosphere is influenced by geomagnetic activity as

well "through delayed heating of atmospheric particles from collisions with charged energetic

particles from the sun"23. Satellite lifetimes are affected most by the variation in the solar cycle

and the heat from radiation. Disturbances from geomagnetic activity are usually too short to

affect lifetimes significantly.14

Atmospheric drag is the main nongravitational force that acts on a satellite in LEO.14 Drag

is part of the total aerodynamic force that acts on a body moving through a fluid such as air.21 It

acts in the direction opposite of the velocity and takes away energy from the orbit. The decrease

in energy causes the orbit to decay until the satellite renters the atmosphere. The equation for

the acceleration of a spacecraft due to drag is


ad 2= 1 p v2 (2.15)
2m =









where p is the atmospheric density, Cd is the satellite's drag coefficient z 2.2, A is the average

cross-sectional area of the satellite normal to its direction of travel (drag area), m is the mass of

m
the satellite and v, is the satellite's velocity relative to the atmosphere. The term is the
CdA

ballistic coefficient and is used as a measure of a satellite's response to drag effects.14'23 The

drag area is directly related to the satellite's shape, dimensions and attitude motion.21 Mass is

usually taken to be constant during a satellite's lifetime. When there is a mass loss, drag

deceleration of the satellite increases and its lifetime is shortened.22 The ballistic coefficient can

indicate how fast a satellite will decay along with solar activity. Satellites with low ballistic

coefficients tend to decay more quickly in response to the atmosphere than those with high

ballistic coefficients, which progress through more solar cycles. During solar maxima satellites

tend to decay more quickly and during solar minima satellites tend to decay more slowly as well.

The effect of atmospheric drag is not significant to satellites with perigees below -120 km due to

the high density of the Earth's atmosphere so satellites already have such short lifetimes up to

this altitude. Atmospheric drag is weak at altitudes above 600 km and thus a satellite's orbital

lifetime is longer than its operational life.14

Solar radiation pressure influences the orbital elements by causing periodic variations to

them. Satellites with low ballistic coefficients feel strong effects from this.14 Solar radiation

pressure produces acceleration in a radial direction away from the sun. The equation for solar

radiation pressure may be written as


arp = (2.16)


where A, is the satellite's average area projected normal to the direction of the sun in m2, m is

the satellite's mass in kg, T is the solar flux (SF) near the Earth, c is the speed of light, and F is









the satellite's reflection coefficient with a value of 0
perfectly absorbing; F = 4/3 flat, specularly reflecting.) The value of Tic can be taken as 4.5 x

105 dynes/cm2.24 The acceleration from solar radiation pressure is less than the acceleration

from drag below 800 km altitude and greater than the acceleration from drag above 800 km, with

the exception of balloon-type satellites because of large area to mass ratio.14'21

For the two-body equations of motion the masses were assumed to be spherically

symmetric. The Earth, represented as ml, however is not spherically symmetric, but instead has

a bulge at the equator, is oblate, and is a pear shape. The Earth although can be modeled without

this asymmetry by using a potential function. The acceleration of a satellite due to the central

body can be found by taking the gradient of the gravitational potential function expressed as


D= 1--Jnr J(sinL) (2.17)


where R, is the Earth's equatorial radius, 1' are Legendre polynomials, L is geocentric latitude,

and J, are dimensionless geopotential coefficients also called zonal coefficients. Periodic

variations occur in all orbital elements as a result of the potential generated by the Earth. The J2

term represents the Earth's oblateness in the geopotential expansion. The J2 perturbation has

the most effect on satellites in Geosynchronous Earth Orbit (GEO), an orbit where a satellite

appears to remain stationary over one location above the Earth's equator defined to be centered

at an altitude of 35,788 km, and below GEO.14 The asymmetric mass distribution of the Earth

alone can not lead to orbital decay; however, it can bring about large oscillations in the

orientation and shape of the orbit. These oscillations coupled with drag alters orbital lifetime.21

Other bodies that can affect a satellite are the sun and moon, which exert gravitational

forces that also cause perturbations. Oscillations in all orbital elements and orbital plane









precession are caused by tidal forces created by the third-bodies. These forces have great effect

on satellites far away from the Earth's center. These perturbations are only significant for

satellites near the Earth with eccentricity greater than 0.5. The effects of the sun and moon

attraction are usually neglected since most satellites near the Earth are launched into orbits with

low eccentricity.21

Perturbation Techniques

Equation (2.14) is the general form for the relative motion of two bodies with

perturbations. There are three main methods to solving the equations of motion with

perturbations; special perturbation, general perturbation and semi-analytic. Special perturbation

uses straightforward numerical integration of the equations of motion that includes all the

essential perturbing accelerations. Two such approaches are Cowell's method and Encke's

method. The numerical approach uses the position and velocity vectors of the satellite. General

perturbation replaces "the original equations of motion with an analytical approximation that

captures the essential character of the motion over some limited interval and which also permits

analytical integration"23. The analytical approach usually uses the orbital elements for

integration. Semi-analytic methods use a combination of the special perturbation (numerical)

and general perturbation (analytic) techniques.14,23

Equation (2.14) is a non-homogeneous differential equation and may be solved using the

method of variation of parameters. The general solution of equation (2.14) involves the

homogenous solution, from equation (2.6). The homogenous solution is known and may be

expressed as

r = r(t,a) v =(t, a) (2.18)

where d = (a e i co Q M), the six constants of integration or orbital elements.









For the disturbed motion of two bodies the orbital elements are no longer constant and are

governed by

dd dda
= -ad (2.19)
dt df

where dd represents the perturbing accelerations. A detailed derivation on how to obtain

equation (2.19) can be found in reference.2

After substituting the orbital elements in equation (2.19), the following variational

equations, (2.20) to (2.25), are obtained:

da 2e sin f 2a e2
cit adr + ado (2.20)


7de 1-e2sinf 1a -e a2 -( ) rado (2.21)
dt na na2e r


da J1- e1cos f v e r dO
d) -- -fadr + -- 1+- rsinf/ d cosI- (2.22)
dt nae nae p dt

dQa r sinu .
dt na2 e sini dh

di rcosu
ct na2 1_2 adh (2.24)
dt na dh-e

--n + (pcosf -2re)adr-((p+r)sinf)ad (2.25)
dt a ne 2


The symbol p is the semi-latus rectum which may also be written as p = a(- e2), n = is
aa

the mean motion, u = f + c) is the argument of latitude, adr is the component of the perturbing

acceleration in the radial direction, ad, is the component in the orbital plane normal to the radial









direction, and adh is the component normal to the orbit plane, whose direction is determined

from the cross product of the unit vectors ad and dO .25,26

Following Belcher et. al.,26 only long-term changes of the orbital elements are of

importance in satellite lifetime analysis and so the short-term changes can be omitted or averaged

out. Considering only long-term effects in this study, the satellite's instantaneous location along

its orbit need not be included so that equation (2.25) can be omitted. A change of the

independent variable from t to f is convenient in order to avoid some of the problems related

with the solution of Kepler's equation, M = E -e sin E, where E is called the eccentric anomaly.

The change of variable equation is

dfJj 1 r r
dt +radr cos/ 1+ d sin f (2.26)
dt r 2 pe I p

Due to the atmosphere, the semi-latus rectum will decrease less quickly than the semi-major axis

and thus it is convenient to replace a by p so that equations (2.20) to (2.24) become

dp 2r3y
adO (2.27)
df p

de r y r



d- ad Cos f/ + ado 1+ sinf --- cos (2.29)
df fp p ) df

da r3ysinu
adhr (2.30)
df /up sin

di 3r
-= adh --cosu (2.31)
df pp

where










= 1+ adrcosf -a d 1+ sin f (2.32)


Orbital Lifetime

The previous section discussed the relative motion of two-bodies with perturbations that

must be taken into consideration for orbit lifetime prediction. The components of the perturbing

accelerations must be substituted into equations (2.27) to (2.32) in order to obtain orbital lifetime

calculations. Atmospheric drag, the main force affecting the satellites simulated in this study, is

presented here following Belcher et. al. 26


ad =- -P CdA (2.33)


jr is the satellite's velocity vector with respect to the atmosphere and may be expressed as


Vr = I esin f adr + +l+ecosf)-coercosi do +(crcosusini)adh (2.34)


where o) is the angular rate of rotation for the Earth and its atmosphere, adr, adO, and adh are

the unit vectors in the adr, ad,9 adh directions, respectively. Substituting equation (2.34) into

(2.33) yields

1 A 1 (2.35)
adrd d PVr -esinf
S2 m p

1 A
add ICd APVr (l+ecos/)-0,rcosi (2.35)

ar =-Cd- PVrcorcos(co + f)sini
2 m

and


Vr U Vl+e2+2ecosv-" p)ecos (2.36)
P 1+e2 + 2ecosf









The components obtained in equation (2.35) may now be substituted into equations (2.27) to

(2.31). The equations are then integrated to obtain the changes in the orbital elements.

There are several programs available to perform the integration for lifetime prediction.

SatLife, a stand alone software developed by Microcosm,27 uses the satellite's initial orbit state,

mass, and area as well as historical and predicted solar cycle values for its lifetime prediction.

SatEvo, a program developed by Alan Pickup,28 computes the decay of satellites from changes

based on their orbital elements. NASA's Orbital Lifetime Program24 uses the satellite's physical

characteristics, launch date, and initial orbit state. Satellite Tool Kit's (STK) lifetime tool, the

software used for this thesis, was developed by Analytical Graphics, Inc. (AGI) based on

NASA's program.

There are three perturbations that STK takes into consideration: atmospheric drag, solar

radiation pressure, and the Earth's oblateness. The drag perturbation is solved by semi-analytic

techniques and the others by analytic methods. To obtain the total disturbing effects, the

solutions for each differential equation obtained for each disturbing function is summed up.

Initial orbit parameters need to be specified within the program in order for calculations to be

performed. Integration of equations (2.27) to (2.31) is performed in order to obtain new orbital

elements and is integrated over a single orbit. Once the new orbital elements are obtained then

the period of the orbit can be found and used to predict lifetime. The process is repeated until a

maximum orbit number is reached, specified by the user, or it reaches the Earth. The predicted

lifetime result is then displayed on a pop up window by STK.24 The next chapter discusses the

lifetime program in STK in more detail.









CHAPTER 3
SIMULATIONS USING SATELLITE TOOL KIT (STK) SOFTWARE

Satellite Tool Kit (STK)

Satellite Tool Kit (STK) is a commercially available software, developed by Analytical

Graphics, Inc. (AGI), and is used by national security and space professionals to perform

analyses of complex mission scenarios involving land, sea, air, and space assets. STK includes

integrated 2-D and 3-D graphics for visualization of aerospace objects such as satellites, launch

vehicles, missiles, and aircraft. STK enables users to calculate position and orientation, evaluate

inter-visibility times, and determine quality of dynamic spatial relationships among groups of

objects. The software is capable of custom data product generation, including reports, graphs

and Visual Data Format (VDF) files. STK can perform orbit/trajectory ephemeris generation,

acquisition times, and sensor coverage analysis for any of the objects mentioned.2

STK Lifetime Tool

STK has a Lifetime analysis tool that estimates a satellite's orbital lifetime (i.e., the

amount of time a satellite remains in orbit before atmospheric drag and other perturbations

causes its reentry). The analysis tool is based on algorithms developed at NASA's Langley

Research Center and the equations discussed in Chapter 2.30 Utilization of STK's Lifetime

analysis tool requires the user to input the satellite's characteristics (i.e., launch date, initial orbit,

mass, cross-sectional area, and drag coefficient). The algorithm then computes drag effects by

applying the satellite characteristics along with an atmospheric density model and a solar flux

file (both selected by the user from a list of several options). Figure 3-1 shows the graphical user

interface (GUI) for the Lifetime analysis tool.

As shown in Figure 3-1, the input for Satellite Characteristics includes Drag Coefficient,

Reflection Coefficient, Drag Area, Area Exposed to Sun, and Mass. For these studies, a drag









coefficient (Cd) of 2.2 was used based on a flat plate model satellite. Typically, the Reflection

Coefficient (F) varies between 0 and 4/3, but was maintained at 0.01 for this study (see

additional discussion in the Parameter Sensitivity Study section).



Satellite Characteristics Solar Data
Drag Coefficient: 12.20000000 Solar Flux File: ISolFlx1006_Schatten.dat
Reflection Coefficient: 1: 1:i:11:ii:11:ii:i Solar Flux Sigma Level: 10
Drag Area: 10.01 m^2
Area Exposed to Sun: 0.01 m^2 Advanced... Compute Report...
Mass: I1 kg -j Show Graphics Graph ...

-Atmospheric Density
Model: IJacchia 1970


Close Apply Help

Figure 3-1. STK Lifetime tool GUI (image is courtesy of AGI).

The pico-satellite model analyzed in this study was the CubeSat with a dimension of

10x10x10 cm and a mass of 1 kg. The Drag Area of the CubeSat is 0.01 m2, the surface area of

a face of the satellite (i.e., it was assumed that one of the satellite's principal axis was aligned

with its velocity vector). To investigate the effects of drag inducing devices for de-orbiting, the

satellite's drag area was increased to values of 0.04 m2, 0.06 m2, and 0.1 m2 (see Chapter 4).

Since there is a wide variety of nano-satellites, the following satellites from the University

Nanosatellite Program (UNP) were randomly selected for the study: MR SAT and MRS SAT

(University of Missouri-Rolla), FASTRAC (University of Texas at Austin), Akoya-B and

Bandit-C (Washington University in St. Louis). MR SAT has a mass of 28.25 kg, hexagonal

side length of 20.4 cm and height of 31.6 cm. MRS SAT has a mass of 11.45 kg, hexagonal side

length of 17.6 cm and height of 19.0 cm.31 FASTRAC consists of top and bottom hexagonal

structures: the top structure of FASTRAC has a mass of 15.46392 kg, the bottom has a mass









12.5757 kg and both are 20.84 cm in height and 47.50 cm in width.32 Akoya-B is a hexagonal

structure that is 45 cm across, 45 cm tall and has a mass of about 25 kg. Bandit-C is a

12x 12x 18 cm cube with a mass of 2 kg 61.33 The calculated hexagonal surface area of each

satellite was used as the drag area with the exception of Bandit-C, which was calculated as its

length times its width. Each satellite's mass (m), drag area (A), area exposed to Sun (A), and

ballistic coefficient are summarized in Table 3-1.

Table 3-1. Satellite mass, drag area, and area exposed to Sun
2 Area Exposed to Sun* Ballistic Coefficient
Satellites Mass (kg) Drag Area* (m) (2) (kg/m2)
CubeSat 1 0.0100 (0.01) 0.0100 (0.01) 45.45
1 0.0400 (0.04) 0.0400 (0.04) 11.36
1 0.0600 (0.06) 0.0600 (0.06) 7.58
1 0.1000 (0.1) 0.1000 (0.1) 4.55
MRS SAT 11.45 0.0805 (0.080478) 0.0805 (0.080478) 65.06
MR SAT 28.25 0.1080 (0.108122) 0.1080 (0.108122) 116.74
FASTRAC 12.5757 0.1954 (0.195397) 0.1954 (0.195397) 28.59
bottom
FASTRAC top 15.4639 0.1954 (0.195397) 0.1954 (0.195397) 35.14
Bandit-C 2 0.0140 (0.0144) 0.0140 (0.0144) 63.13
Akoya-B 25 0.1800 (0.17537) 0.1800 (0.17537) 64.80
*Values of parameters used for analyses are in parenthesis.

Of the ten atmospheric models available in STK, only these seven were used: Jacchia

1970, Jacchia 1971, Jacchia-Roberts, CIRA 1972, MSIS 1986, MSISE 1990, and NRLMSISE

2000. Three other atmospheric models, 1976 Standard, Harris-Priester, and Jacchia 1970

Lifetime, were not used. Based on initial simulations, the 1976 Standard model is only

dependent on altitude and, therefore, shows a single orbital lifetime value. Meanwhile, the

Harris-Priester was found not to agree with the other models according to Woodburn and Lynch

(2005).20 The Jacchia 1970 Lifetime model was retained, in the STK version used for the

analyses, for backward compatibility to previous STK versions.34

The simulations were performed using the solar flux file model SolFlx1006_Schatten.dat,

the most recent file available during the time the simulations were performed. The numbers









associated with the flux file names represents the month and year of the data (i.e., 1006

represents October 2006 in this case). Old files are retained for regression analysis. These files

contain predictions of solar radiation flux and geomagnetic index values produced by K. H.

Schatten in ASCII format.34 Updated files can be downloaded at "ftp://ftp.agi.com/pub/

DynamicEarthData" and integrated into the software. The solar flux sigma level was maintained

at zero in order to use mean solar flux and weighted planetary geomagnetic index.

The accuracy and speed of the lifetime calculations are defined by selecting the Advanced

button, which produces the GUI shown in Figure 3-2. The runtime of the lifetime computation

can be limited by the maximum orbit duration (duration), the number of orbit revolutions (orbit

count) or both. The Limit Method was set to Orbit Count in this study. The orbit count limit

was adjusted to a sufficiently large value that allowed the tool to determine the lifetime of the

satellite prior to termination. The number of Orbits per Calculation and the number of Gaussian

Quadratures per orbit used were set at default values to provide a compromise between the

amount of computation time required and the precision of the computation. The Decay Altitude

is the altitude at which calculation of the satellite's orbit ceases. The default value, 65 km, and a

value of 80 km were used for this research. The default options of a checked 2nd order

oblateness correction and unchecked rotating atmosphere were used. The satellite's orbital

elements through the duration of its lifetime can be displayed by the report and graph pane.

After calculations are performed the predicted results are displayed in a popup window that

shows a date and time in Gregorian Universal Time Coordinated (UTCG), number of orbits, and

lifetime in days or years down to a tenth of a decimal. It should be emphasized that the results

are estimates due to atmospheric density variations and the difficulty in predicting solar activity

involved with calculating a satellite's orbital lifetime.34












Limit Method: Orbit Count
Duration Limit (Days): 36525
Orbit Count Limit: I
Orbits per Calculation: 10
Gaussian Quadratures: 1
Decay Altitude: 65 km
We Use 2nd Order Oblateness Correction
I Rotating Atmosphere

S OK j Cancel | Help |

Figure 3-2. STK Lifetime Advanced option GUI (image is courtesy of AGI).

STK Satellite Properties

Figure 3-3 shows the basic orbit page GUI used to input the orbit properties for a satellite.

On this page, the user chooses from a variety of analytic and numerical orbit propagators. Of the

ten propagators available only two were appropriate for this analysis: J4Perturbation and High-

Precision Orbit Propagator (HPOP). The J4Perturbation propagator is an analytic propagator.

This propagator simply evaluates a formula in order to generate a satellite's position as a

function of time in a table listing or ephemeris. The J4Perturbation considers the point mass

effect of the central body, the asymmetry in the central body's gravity field, and oblateness

effects. The HPOP is a numerical propagator. To generate ephemeris, HPOP uses numerical

integration of the satellite's differential equations of motion. The HPOP can consider a full

gravitational model, third-body gravity, solar radiation pressure, and atmospheric drag to be

included for analysis. A highly precise orbit ephemeris can be generated using HPOP because of

the many parameter settings available for the user. The J4Perturbation propagator was used first

for testing the orbital lifetime tool and HPOP was used for more accurate orbital lifetime

prediction. More detailed description of each propagator can be found in the help menu.35










.. S e :UaicObt I


-I


,. Tr -l 1 F"jil'u' liU lji
i- *LH 1, [Tlih l





I hI n I 'i, ,, ,I,
"-. .,:e "f--"-"

"f' Ed E- C- ', h'"




-1 l. in..l I .
F, _-., ;






' 1 ,1 t ,,,- H I


Ilr.'.'l, l :' '':'' '


| -.,rj r, i. r. I d:,, :,,, -

ln -:,, r, .:,:i j "I l,, r U.i,-. j +


Figure 3-3. STK satellite properties GUI (image is courtesy of AGI).

A simulation Start Time, Stop Time, Step Size, and Orbit Epoch was inputted. The values

for the start time, stop time, and orbit epoch are typed by the user in the format as shown in

Figure 3-3. The start time corresponds with the orbit epoch and was defined to start from the

default value of 1 Jul 2005 12:00:00.000 UTCG, chosen as a possible satellite launch date, and

incremented by one year until 2030 to see the effect of the solar cycle on orbital lifetime. The

step size was left at its default value. The stop time was defined to be a day after the start date.

The default classical (Keplerian) coordinate type and J2000 coordinate system were used

for the simulations. Different sets of orbital elements and their values can be specified. Orbital

elements obtained from the AeroCube-1 satellite's two line element (TLE) data from the failed

launch 1 of the DNEPR vehicle were used for the pico-satellite simulations, with the exception

of the eccentricity value changed to zero. The orbital elements from the mission constraint goals

of the MR SAT project were used for the nano-satellite simulations.


,,i I_ T, I: :


-I
_J.
EJilT:: -i
E ---


I ..lIjl jI jlc T I









Parameter Sensitivity Study

Simulations were performed varying different parameters such as the reflection coefficient

(T), area exposed to Sun (A), drag coefficient ( C), drag area (A), and mass (m) available

within the lifetime tool to evaluate their effect on orbital lifetime prediction. A summary of the

parameters that were constant for these scenarios is given in Table 3-2. The default epoch of

1 Jul 2005 12:00:00.000 UTCG was chosen as a launch date. The propagator J4Perturbation was

used. The orbital elements obtained from the AeroCube-1 two line element (TLE) were used.

The Jacchia-Roberts atmospheric density model and a decay altitude of 80 km were used.

Table 3-2. Orbital lifetime sensitivity simulation parameters
Parameters Figure 3-4 to 3-8
Altitude (km): 550
Epoch Start Date: 1 Jul 2005 12:00:00.000 UTCG
Propagator: J4Perturbation
Semimajor Axis (km): 6927.248793
Eccentricity: 0.0064
Inclination (deg): 97.43
Argument of Perigee (deg): 189.63
RAAN (deg): 115.67
Mean Anomaly (deg): 349.58
Atmospheric Density Models: Jacchia-Roberts

Two parameters were found not to have significant effect on orbital lifetime, namely the

reflection coefficient (Figure 3-4) and area exposed to Sun (Figure 3-5). As discussed in Chapter

2, these are directly proportional to the acceleration from solar radiation pressure, which was

stated as being less effective than drag below altitudes of 800 km. In this thesis, analyses were

performed at altitudes of 750 km and lower, where such parameters are expected not to affect

orbital lifetime. Consequently, the reflection coefficient was maintained at 0.01, while the area

exposed to Sun value was kept the same as the satellite's drag area. number of orbits, and

lifetime in days or years with one significant digit after the decimal of the value

Four curves are shown in Figure 3-4 representing drag coefficients of 2.0 (blue-diamond),









2.05 (pink-square), 2.1 (green-triangle), and 2.2 (aqua-cross). For each curve, the reflection

coefficient was varied to values of 0, 0.3, 1.0, and 1.8 while the other parameters were kept at a

constant value as seen in the legend. Three curves are shown in Figure 3-5 representing drag

coefficients of 2.0 (blue-diamond), 2.1 (pink-square), and 2.2 (green-triangle). The area exposed

to Sun was varied from 0.05, 0.5, and 1 m2 for each curve. The other parameters were kept at a

constant value as seen in the legend. Both graphs show slopes close to zero, indicating that

orbital lifetime is not affected by the reflection coefficient and the area exposed to Sun.

The results from varying the drag coefficient, drag area, and mass are shown in Figures 3-6

to 3-8. Figure 3-6 shows a graph of the orbital lifetime vs. drag coefficient. In this graph, the

drag coefficient was increased to values of 1.8 to 2.5 while the other parameters were kept at

constant values as seen in the legend. Figure 3-7 shows a graph of orbital lifetime vs. drag area.

In this graph, the drag area was increased to values of 0.05 tol m2. Three curves were obtained

using drag coefficients values of 2.0 (blue-diamond), 2.1 (pink-square), and 2.2 (green-triangle),

while holding the other parameters constant as seen in the legend. All three curves show a

decrease in orbital lifetime. Figure 3-6 shows the dependence of orbital lifetime on the drag

coefficient. Figure 3-7 shows a dependence of orbital lifetime on drag area.

Figure 3-8 shows orbital lifetime vs. mass. In this graph, the value of the mass was

increased to values of 1 to 5 kg while the other parameters were kept at constant values as seen

in the legend. The graph shows an increase in orbital lifetime as a result of the simulation. This

graph shows the dependence of orbital lifetime on mass. The three figures (Figure 3-6 to 3-8)

show the dependence of the orbital lifetime on the three parameters with the given scenario. The

three parameters Cd, A, and m make up the ballistic coefficient, which is expected to affect

orbital lifetime as defined in Chapter 2. For the studies performed in Chapter 4, 0.01 m2 as area










exposed to Sun and 0.01 as reflection coefficient value were used because the sensitivity studies


show them to be invariant.

5.8


5.7 -


S5.6


" 5.5


5.4


0 5.3


5.2


SCd-2.0 A=0.01 As=0.01 m=1
- Cd -2.05 A=0.01 As=0.01 m=1
-Cd-2.1 A=0.01 As=0.01 m=1
Cd 2.2 A=0.01 A =0.01 m=1


5.1
0 0.5 1.0
Reflection coefficient (F)
Figure 3-4. Orbital lifetime vs. reflection coefficient


5.7


S5.6
fi
S5.5


.E 5.4
O


Cd=-2.0 F=0.01 A=0.01 m=l

- Cd 2.1 F=0.01 A=0.01 m=1
Cd 2.2 F=0.01 A=0.01 m=1


5.2
0 0.2 0.4 0.6
Area exposed to Sun (m )
Figure 3-5. Orbital lifetime vs. area exposed to Sun













--F 0.01A=0.01A=0.01 m 1


6.0


5.8


S5.6


5 5.4

O


1.8 2.0 2.2 2.4
Drag coefficient (Cd)

Figure 3-6. Orbital lifetime vs. drag coefficient




3.0 -- --------------------------
C d=2.0 r=0.01 As=1.01 m=1


Cd-2.1 F=0.01 As

CCd-2.2 F=0.01 A -
d


1.01 m:

1.01 m:


1 0.6 0.8
Drag area (
Drag area (m )


Figure 3-7. Orbital lifetime vs. drag area


2.5 ----


S2.0-


S1.5


1.0 -


0.5 -
















20


.E 15


10
o


Cd=-2.2 F=0.01 A=0.01 A =0.01


Mass (kg)


Figure 3-8. Orbital lifetime vs. mass









CHAPTER 4
RESULTS AND DISCUSSION

Simulations of orbital lifetimes for pico- and nano-satellites were performed. The results,

which are presented here, were used to study the effects of different parameters have on their

lifetimes. The CubeSat volume and mass are constant parameters; in order to reduce its lifetime,

the impact of increasing its cross-sectional area was investigated. The volume and mass of the

nano-satellites in this study varied; thus, the impact of different launch altitudes on each nano-

satellites' lifetime was studied. For both analyses, different launch years were considered to see

the effect of the 11-year solar cycle. Different atmospheric density models were also explored to

determine maximum, minimum, and average orbital lifetime values per launch year.

Pico-satellite Results

Four scenarios were simulated for the CubeSat, with varying drag areas of 0.01, 0.04, 0.06,

and 0.1 m2, which will be referred to as satellite A, B, C, and D, respectively. The CubeSat

simulation parameters are summarized in Table 4-1. An epoch start date of "1 Jul 2007

12:00:00.000 UTCG" was chosen as initial launch date and incremented yearly until 2030 to

determine the effect of the solar cycle, with peaks, known as solar maxima, occurring around

2012 and 2023, and valleys, known as solar minima, at 2007, 2018, and 2029. From 2007 to

2030, a solar cycle is determined from one minimum to the next. These solar maxima and

minima correspond to the years of highest and lowest solar radiation flux values, respectively,

within the solar flux file "SolarFlx1006 Schatten.dat". The orbital elements for these

simulations closely follow the AeroCube-1 elements, with the exception of changing the

eccentricity to zero. A 600-km initial altitude was used since this value falls within the range at

which the CubeSats would have been released from the DNEPR launch vehicle. Meanwhile, a

decay altitude of 80 km was used for the pico-satellite analyses.









Table 4-1. CubeSat simulation parameters
Parameters Satellites A and C Satellites B and D
Altitude (km): 600 600
Epoch Date: 1 Jul 2007 12:00:00.000 UTCG to 1 Jul 2007 12:00:00.000 UTCG to
1 Jul 2030 12:00:00.000 UTCG 1 Jul 2030 12:00:00.000 UTCG
Propagator: HPOP HPOP
Semimajor Axis (km): 6978.137 6978.137
Eccentricity: 0 0
Inclination (deg): 97.43 97.43
Argument of Perigee (deg): 189.63 189.63
RAAN (deg): 115.67 115.67
Mean Anomaly (deg): 349.58 349.58
Drag Coefficient: 2.2 2.2
Reflection Coefficient: 0.01 0.01
Drag Area (m2): 0.01 and 0.06 see figures 0.04 and 0.1 see figures
Area Exposed to the Sun (m2): Same as drag area respectively Same as drag area respectively
Mass (kg): 1 1
Atmospheric Density Models: Jacchia 1970, Jacchia 1971, Jacchia 1970, Jacchia 1971,
Jacchia-Roberts, CIRA 1972, Jacchia-Roberts
NRLMSISE 2000, MSISE 1990,
MSIS 1986

Seven atmospheric density models were used for satellite A (Figure 4-1) and satellite C

(Figure 4-2). The data show trends for certain atmospheric density models, producing maxi-

mum, minimum and average orbital lifetime values per launch year. For the pico-satellites,

orbital lifetimes for four consequent years, starting at 2007, were analyzed for satellites B and D,

using the seven atmospheric density models. From these results, those models that produced

maximum, minimum and close to average orbital lifetime values were determined; these were

then used for the rest of the simulations in order to reduce the analysis time.

The results for satellites A, B, C, and D (Figure 4-3) were plotted using the average life-

time values as a curve, while maximum and minimum orbital lifetime values are shown as error

bars. The orbital lifetime for satellite A ranged from 17 to 27 years, with an average curve value

of 22 years, while that for satellite B is between 2.5 and 9 years, with a mean of 6 years. The

lifetime for satellite C varied from 1 to 8 years, with an average of 4 years, while that for satellite

D were 1 to 5.6 years, with a mean of 3 years. As expected, the orbital lifetimes for satellites B,









C, and D were shorter compared to satellite A due to their low ballistic coefficients.14


25



20 --



15

Jacchia 1970
Jacchia-Roberts
10
CIRA 1972
o NRLMSISE 2000
-5 MSISE 1990
MSIS 1986
Jacchia 1971
0
2005 2009 2013 2017 2021 2025 2029
Launch year
Figure 4-1. Orbital lifetime results for satellite A using seven atmospheric density models


25 Jacchia 1970
Jacchia 1971
SJacchia-Roberts
-20 CIRA 1972
NRLMSISE 2000
MSISE 1990
0 15
5 MSIS 1986

-o
10


5



0
2005 2009 2013 2017 2021 2025 2029
Launch year
Figure 4-2. Orbital lifetime results for satellite C using seven atmospheric density models










J3 satellite A
satellite B
30 ---- satellite C
~satellite D
R25












0
2005 2009 2013 2017 2021 2025 2029
Launch year
Figure 4-3. Orbital lifetime results for satellites A, B, C, and D at 600-km initial altitude

A 75% reduction in orbital lifetime can be seen as the drag area is enlarged from 0.01 to

0.06 m2, when comparing the values for satellites A and C. A reduction of at least 40% can be

seen by comparing the average orbital lifetime of satellite B to D, 30% from satellite B to C and

about 25% from satellite C to D. The orbital lifetime for the CubeSat is greatly minimized when

the drag area is increased to ten times its original size.

Orbital lifetime minima occur at about 2010 and 2021 for satellite A, at 2011 and 2022 for

satellites B and C, and at 2012 and 2023 for satellite D (corresponding to solar cycle maxima).

Analyses show orbital lifetimes of 23, 5.0, 2.4, and 1.4 years for satellite A, B, C and D,

respectively, for a launch at 2012. Varying orbital lifetimes results from differences in the

satellites' ballistic coefficients, the highest of which is observed for Satellite A (see Table 3-1),

followed by B, then C, and minimum for D. Due to the high ballistic coefficient of satellite A,

its orbit does not decay as rapidly4 as the others; moreover, it pushes through at least 2 solar

cycle minima at 2018 and 2029 and a maximum at 2023. Satellite B encounters a solar cycle









maximum at 2012 and renters the atmosphere a year before the next cycle minimum. Satellite

C and D experience a solar maximum only at 2012 and their orbits decays within the following 3

years. The orbits of satellites B, C, and D decay rapidly when launched during a solar maximum

due to their low ballistic coefficients.14

Nano-satellites Results

The nano-satellite simulation parameters are summarized in Table 4-2 for MR SAT and

MRS SAT, Table 4-3 for FASTRAC, and Table 4-4 for Akoya-B and Bandit-C. The epoch start

of "1 Jul 2007 12:00:00.000 UTCG" was chosen as a possible launch date and incremented by a

year until 2030 to see the effect of the solar cycle. For all the simulations, a default decay alti-

tude of 65 km was used. Each satellite's orbital lifetime was simulated at two different altitudes

and inclination: (1) at 350-km altitude and 51.60 inclination, similar to the orbit of a typical

international space shuttle mission; and, (2) 750-km altitude and 570 inclination, obtained from

the mission constraint goals of the MR SAT project. Atmospheric density models for the simu-

lations were selected by means of the same methods used for satellite B and D. The results were

plotted using the average lifetime values as the curve, and the maximum and minimum values as

error bars.

Simulations were also performed to obtain orbital lifetimes for MR SAT, studying the

effect of different initial altitudes. The parameters used are summarized in Table 4-5. An epoch

start date of"l Jul 2007 12:00:00.000 UTCG" was chosen as a possible launch date and incre-

mented by yearly until 2030 to see the effect of the solar cycle. The simulation begins at 350-km

initial altitude and is incremented by 50 km until 750 km. An inclination of 51.6 was used.

A decay altitude of 65 km was used. Atmospheric density models used for the simulations were

determined by the same method as for satellite B and D per launch altitude. For each launch

year, the maximum and minimum orbital lifetime values are represented as error bars and the










average lifetime values as a curve obtained from the atmospheric density model results. These

values were then used to plot the orbital lifetime versus altitude for MR SAT.


Table 4-2. MR SAT and MRS SAT simulation parameters


Parameters
Altitude (km):
Epoch Date:

Propagator:
Semimajor Axis (km):
Eccentricity:
Inclination (deg):
Argument of Perigee (deg):
RAAN (deg):
Mean Anomaly (deg):
Drag Coefficient:
Reflection Coefficient:
Drag Area (m2):

Area Exposed to the Sun (m2):

Mass (kg):

Atmospheric Density Models:


Figure 4-4


Figure 4-5


350
1 Jul 2007 12:00:00.000 UTCGto
1 Jul 2030 12:00:00.000 UTCG
HPOP
6728.137
0
51.6
0
0
0
2.2
0.01
MR SAT = 0.108122
MRS SAT = 0.080478
MR SAT = 0.108122
MRS SAT = 0.080478
MR SAT = 28.25
MRS SAT =11.45
Jacchia-Roberts, CIRA 1972,
NRLMSISE 2000


750
1 Jul 2007 12:00:00.000 UTCG to
1 Jul 2030 12:00:00.000 UTCG
HPOP
7128.137
0
57
0
0
0
2.2
0.01
MR SAT = 0.108122
MRS SAT = 0.080478
MR SAT = 0.108122
MRS SAT = 0.080478
MR SAT =28.25
MRS SAT =11.45
Jacchia 1970, Jacchia-Roberts,
MSIS 1986


Table 4-3. FASTRAC simulation parameters
Parameters Figure 4-6
Altitude (km): 350
Epoch Date: 1 Jul 2007 12:0(


Propagator:
Semimajor Axis (km):
Eccentricity:
Inclination (deg):
Argument of Perigee (deg):
RAAN (deg):
Mean Anomaly (deg):
Drag Coefficient:
Reflection Coefficient:
Drag Area (m2):

Area Exposed to the Sun (m2):

Mass (kg):

Atmospheric Density Models:


1 Jul 2030 12:0(
HPOP


0:00.000 UTCG to
0:00.000 UTCG


6728.137


51.6
0


2.2
0.01
top= 0.195397
bottom = 0.193597
top = 0.195397
bottom = 0.193597
top = 15.4639
bottom = 12.5757
Jacchia-Roberts, CIRA 1972,
NRLMSISE 2000


Figure 4-7
750
1 Jul 2007 12:00:00.000 UTCG to
1 Jul 2030 12:00:00.000 UTCG
HPOP
7128.137
0
57
0
0
0
2.2
0.01
top= 0.195397
bottom = 0.193597
top = 0.195397
bottom = 0.193597
top = 15.4639
bottom = 12.5757
Jacchia 1970, Jacchia-Roberts,
NRLMSISE 2000, MSIS 1986


Y Y










Table 4-4. Akoya-B and Bandit-C simulation parameters
Parameters Figure 4-8


Altitude (km):
Epoch Date:

Propagator:
Semimajor Axis (km):
Eccentricity:
Inclination (deg):
Argument of Perigee (deg):
RAAN (deg):
Mean Anomaly (deg):
Drag Coefficient:
Reflection Coefficient:
Drag Area (m2):

Area Exposed to the Sun (m2):

Mass (kg):

Atmospheric Density Models:


350
1 Jul 2007 12:00:00.000 UTCGto
1 Jul 2030 12:00:00.000 UTCG
HPOP
6728.137
0
51.6
0
0
0
2.2
0.01
Akoya-B = 0.17537
Bandit-C = 0.0144
Akoya-B = 0.17537
Bandit-C = 0.0144
Akoya-B = 25
Bandit-C = 2
Jacchia-Roberts, CIRA 1972,
NRLMSISE 2000


Figure 4-9
750
1 Jul 2007 12:00:00.000 UTCGto
1 Jul 2030 12:00:00.000 UTCG
HPOP
7128.137
0
57
0
0
0
2.2
0.01
Akoya-B = 0.17537
Bandit-C = 0.0144
Akoya-B = 0.17537
Bandit-C = 0.0144
Akoya-B = 25
Bandit-C = 2
Jacchia 1970, Jacchia-Roberts,
MSIS 1986


Table 4-5. MR SAT with different initial altitudes simulation parameters
Parameters Figure 4-10
Altitude (km): 350 to 750
Epoch Date: 1 Jul 2007 12:00:00.000 UTCG to
1 Jul 2030 12:00:00.000 UTCG
Propagator: HPOP
Semimaior Axis (km): 6728.137 to 7128.137


Eccentricity:
Inclination (deg):
Argument of Perigee (deg):
RAAN (deg):
Mean Anomaly (deg):
Drag Coefficient:
Reflection Coefficient:
Drag Area (m2):
Area Exposed to the Sun (m2):
Mass (kg):
Atmospheric Density Models:


0
51.6
0
0
0
2.2
0.01
0.108122
0.108122
28.25
Jacchia 1970, Jacchia 1971, Jacchia-Roberts, CIRA
1972, NRLMSISE 2000, MSISE 1990, MSIS 1986


The results for MR SAT and MRS SAT (Figure 4-4), with an initial altitude of 350 km,

show orbital lifetime values between 140 and 370 days for the former, with an average curve

value of 247 days, and between 80 and 210 days for the latter, with an average curve of









141 days. Orbital lifetime minima for the average curves in Figure 4-4 occur at 2012 and 2023

for both satellites. On the other hand, the results at 750-km initial altitude (Figure 4-5) show

orbital lifetime values between 460 and 540 years for MR SAT, with an average curve value of

495 years, and between 250 and 300 years for MRS SAT, with an average curve value of

269 years. The lifetime minima for the average curve in Figure 4-5 occur at 2011 and 2021 for

MR SAT, and at 2011 and 2020 for MRS SAT.

At an initial altitude of 350 km, the results for the FASTRAC top and the bottom satellites

(Figure 4-6), show orbital lifetime values for FASTRAC top is between 50 and 125 days, with an

average curve value of 86 days, and from 40 to 110 days for the bottom, with an average curve

value of 72 days. Orbital lifetime minima for the average curves in Figure 4-6 occur at 2012 and

2023 for both satellites. On the other hand, results at 750-km initial altitude (Figure

4-7) show orbital lifetime values between 140 and 165 years, with an average curve value of

151 years for the top satellite, and from 110 to 135 years for the bottom satellite, with an average

curve value of 122 years. Orbital lifetime minima for the average curves in Figure 4-7 occur at

about 2011 and 2021 for the top satellite and at about 2010 and 2020 for the bottom satellite.

The results for Akoya-B and Bandit-C at an initial altitude of 350 km (Figure 4-8) show

orbital lifetime values between 86 and 210 days with an average curve value of 141 days for both

satellites. Orbital lifetime minima for the average curves in Figure 4-8 occur at 2012 and 2023

for both satellites. Meanwhile, the results at 750-km initial altitude (Figure 4-9) show orbital

lifetime values between 255 and 295 years for Akoya-B, with average curve value 270 years, and

from 250 to 285 years for Bandit-C, with an average curve value of 263 years. Orbital lifetime

minima for the average curves in Figure 4-9 occur at 2011 and 2022 for Akoya-B, and at about

2010 and 2021 for Bandit-C.









The orbital lifetimes of the nano-satellites are in centuries at 750-km initial altitude, in

contrast to less than 400 days at 350-km initial altitude. For both initial altitudes, the FASTRAC

bottom satellite, having the lowest ballistic coefficient of the nano-satellites studied, had shortest

orbital lifetime values; meanwhile MR SAT has the longest as a result of having the highest

ballistic coefficient.

The orbital lifetimes for MR SAT at varying initial orbit is shown in Figure 4-10. Its

average lifetime at 500 km is 11 years, more than twice the lifetime at 450 km, and more than 5

times compared to that at 400 km. This pattern continues up to 750-km initial orbit. At about

550 km, the curves merge as they progress through several solar cycles, making the launch date

insignificant at higher altitudes.14 The pattern indicates orbital lifetimes greater than 25 years at

altitudes greater than 550-km.

400

350 T-T T-TTr

300

R 250\

200

.. 150-
-c~






0
100 ----==---

50 ---MR SAT
MRS SAT

2005 2009 2013 2017 2021 2025 2029
Launch year
Figure 4-4. Orbital lifetime for MR SAT and MRS SAT at 350-km initial altitude










550 1

500 -. .

450

b 400

350

3 300

250

200 MR SAT
MRS SAT
150
2005 2009 2013 2017 2021 2025 2029
Launch year
Figure 4-5. Orbital lifetime for MR SAT and MRS SAT at 750-km initial altitude












60





20 FASTRAC bottom sat
I I / I I II











2005 2009 2013 2017 2021 2025 2029
Launch year
Figure 4-6. Orbital lifetime for the FASTRAC satellites at 350-km initial altitude
Figure 4-6. Orbital lifetime for the FASTRAC satellites at 350-km initial altitude










170

160

150

b 140

- 130

S120

110


100 FASTRAC top sat
FASTRAC bottom sat
90
2005 2009 2013 2017 2021 2025 2029
Launch year
Figure 4-7. Orbital lifetime for the FASTRAC satellites at 750-km initial altitude


200

180

160

140

120

100


40
2005


2009 2013 2017 2021 2025 2029
Launch year


Figure 4-8. Orbital lifetime for the Akoya-B and Bandit-C at 350-km initial altitude











300


290


S280


0 270


260


0 250


Figure 4-9.


240 Akoya-B
Bandit-C
230
2005 2009 2013 2017 2021 2025 2029
Launch year
Orbital lifetime for the Akoya-B and Bandit-C at 750-km initial altitude

3
10 -


2










O
10
10


..7
/


-1
101
300 400 500 600 700
Altitude (km)
Figure 4-10. Orbital lifetime for the MR SAT using different initial altitudes


800


9









CHAPTER 5
CONCLUSION AND RECOMMENDATIONS

Conclusions

Lifetime analyses of pico- and nano-satellites were conducted using the Satellite Tool Kit

(STK) orbital Lifetime tool. The pico-satellite analyses were performed on the standard CubeSat

developed by CalPoly and Stanford, whereas the nano-satellite analyses were performed on three

randomly selected satellites from the University Nano-satellite Program (UNP). Typical mission

scenarios for these two classes of satellites were investigated. Since the prediction of orbital

lifetime is not an exact science, parameters which have an effect on the prediction were varied to

provide ranges of expected lifetimes for the different scenarios.

The results indicate that orbital lifetimes of pico-satellites can be significantly reduced by

increasing their drag area from 0.01, to 0.04, 0.06 or 0.1 m2. The longest that the CubeSat is

predicted to stay up in orbit at a 600 km altitude with a drag area of 0.01 m2 is approximately 27

years, which is slightly above the FCC debris mitigation guidelines. The longest that the

CubeSat is predicted to stay in orbit at a 600 km altitude with a drag area of 0.04 m2 is about 8.8

years, 0.06 m2 is about 7 years, and 0.1 m2 about 5.5 years. Changing the drag area of a 1-kg

satellite from 0.01 to 0.1 m2 decreased its orbital lifetime from an average of 22 to 3 years and

results in 86% reduction. The results show that changing the drag areas to 0.04 or 0.1 m2 did not

make a significant difference to the reduced total amount of lifetime of the satellite than the drag

area of 0.06 m2. At 600 km above the Earth's surface, a pico-satellite with drag area of 0.1 m2

had minimum orbital lifetimes during years of highest solar activity due to its low ballistic

coefficient. At this same altitude, pico-satellites with smaller drag areas, which results in higher

ballistic coefficient, responded more slowly to the solar activity and as a result the orbital

lifetime minimums appear shifted from solar maximum years. This analysis implies that passive









de-orbiting devices such as drag chutes can be effective devices for addressing orbital debris

mitigation. The analyses also imply that in order to obtain minimum orbital lifetimes to set the

launch year of the satellite corresponding with high solar activity that is at solar maximum.

The nano-satellites used in this study were between 11 to 28 kg, with drag areas from 0.08

and 0.2 m2. The results of the nano-satellites analyses, with a launch altitude of 350 km, show

that the orbital lifetimes are in number of days. At this altitude the satellites will reenter the

atmosphere in a short amount of time. These lifetime values will meet the FCC mitigation

guidelines. The results of the nano-satellites analyses, with an altitude of 750 km, show that the

orbital lifetimes are in centuries. At this high altitude the nano-satellites' orbital lifetime will not

meet the FCC mitigation guidelines. Values indicate that additions to the nano-satellites are

needed to fulfill the 25 year orbital lifetime requirements at this altitude. The nano-satellites in

high orbit, above 500 km, have a problem of potentially becoming a debris space. The nano-

satellites do not have a volume or mass requirement as the CubeSats, therefore these were kept

constant respectively per satellite and only the effect of a change in altitude on their orbital

lifetimes were investigated.

Recommendations

There are different parameters to consider with prediction of long-term orbital lifetime and

its reduction. Satellites properties (i.e., geometry, mass and the solar activity, have significant

effects on these. For mission operations the implementation of an aerobraking technique for

both CubeSats and nano-satellites, that is a change in their drag area, should be further

investigated. For mission planning the consideration of proposed satellites to be launched during

the solar maximum time period should be further investigated.









LIST OF REFERENCES


1.National Research Council (U.S) Committee on Space Debris, "Orbital Debris: A
Technical Assessment," National Academy Press, Washington, DC, 1995, Chaps. 4, 8.

2."NASA Safety Standard: Guidelines and Assessment Procedures for Limiting Orbital
Debris," NSS 1740.14, August 1995.

3.Flury, W., "Space Debris," Preparingfor the Future [online], Vol. 4, No. 4, 1994,
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4.Aerospace Corporation, Center for Orbital and Reentry Debris Studies, "Space Debris
Basics: What is the Future Trend?," http://www.aero.org/capabilities/cords/debris-future.html
[accessed 26 June 2007].

5.Walker, S. H., ""Responsive" Access and Infrastructure," Proceedings ofDarpaTech 2005,
Defense Advance Research Project Agency (DARPA), Anaheim, CA, August 2005,
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6.Calpoly, CubeSat, "Mission Statement", http://cubesat.atl.calpoly.edu/
pages/home/mission-statement.php [accessed on 30 June 2007].

7.AFOSR, AFRL Space Vehicles, AIAA, NASA, SMC Det 12, "About the University
Nanosatellite Program," http://www.vs.afrl.af.mil/UNP/About.html [accessed on 19 July 2007].

8.Orbital Debris Program Office, NASA Johnson Space Center, "Orbital Debris Education
Package," http://www.orbitaldebris.jsc.nasa.gov/library/EducationPackage.pdf [retrieved 11 July
2007].

9."Technical Report On Space Debris," United Nations, (A/AC. 105/720), New York, 1999.

10. Orbital Debris Program Office, NASA Johnson Space Center, "Orbital Debris
Mitigation," http://www.orbitaldebris.jsc.nasa.gov/mitigate/mitigation.html [accessed 27 June
2007].

11. "U.S. Government Begins Orbital Debris Meetings with Industry," The Orbital Debris
Quarterly News, Vol. 4, No. 4, 1999, p. 4.

12. "U. S. Government Orbital Debris Mitigation Standard Practices" at the Johnson Space
Center [online], 1997, http://www.orbitaldebris.jsc.nasa.gov/library/
USG OD_Standard_Practices.pdf [accessed 1 July 2007].

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FCC 04-130, Washington, DC, June 2004, p. 2.

14. Wertz, J. R., and Larson, W. J., Space Mission Analysis andDesign, 3rd ed., Microcosm
Press, Torrence, CA, 1999, Chaps. 5, 6, 8.









15. "IADC Space Debris Mitigation Guidelines," Inter-Agency Space Debris Coordination
Committee, IADC-02-01, October 2002.

16. Calpoly, CubeSat, "Dnepr Launch Vehicle Status Integrated for Launch",
http://cubesat.atl.calpoly.edu/pages/missions/dnepr-launch-2/satellite-status.php [accessed 30
June 2007].

17. AMSAT, "Cubesat Information," http://www.amsat.org/amsat-
new/satellites/cubesats.php [accessed 27 June 2007].

18. Orbital Debris Program Office, NASA Johnson Space Center, "Orbital Debris Graphics,"
http://www.orbitaldebris.jsc.nasa.gov/photogallery/beehives.html#leo [accessed 27 June 2007].

19. Bate, R. R., Mueller, D. D., and White, J. R., "Two-body Orbital Mechanics,"
Fundamentals ofAstrodynamics, Dover Publications, Inc., New York, 1971, Chap. 1.

20. Woodburn, J., and Lynch, S., "A Numerical Study of Orbital Lifetime (revised),"
Proceedings of the 2005 AAS/AIAA Astrodynamics Specialists Conference,
Paper No. AAS 05-297, Lake Tahoe, CA, August 2005.

21. De Lafontaine, J., and Garg, S. C., "A review of satellite lifetime and orbit decay
prediction," Proc. Indian Acad. Sci. (Engg. Sci.), Vol. 5, Pt. 3, September 1982, pp. 197-258.

22. Ladner, J. E., and Ragsdale, G. C., "Earth Orbital Satellite Lifetime," NASA TN D-1995,
January 1964.

23. Vallado, D. A., "Special Perturbation Techniques," Fundamentals ofAstrodynamics and
Applications, 2nd ed., Microcosm Press, El Segundo, CA, 2001, Chap. 8.

24. Orr, L.H., "User's Guide for Langley Research Center Orbital Lifetime Program,"
NASA TM-87587, September 1985.

25. Battin, R. H., "Variation of Parameters," An Introduction to the A A, /etiitik and
Methods ofAstrodynamics, Revised Edition, Revised ed., American Institute of Aeronautics and
Astronautics, Inc., Reston, VA, 1999, Chap. 10.

26. Belcher, S. J., Rowell, L. N., and Smith, M. C., "Satellite Lifetime Program," The Rand
Corporation, RM-4007-NASA, April 1964.

27. Space Mission Analysis and Design, "SatLife Stand-Alone Module vl.0,"
http://www.smad.com/software/agimo3.html [accessed 21 May 2007].

28. Alan Pickup, "Satellite tracking and decay information,"
http://www.wingar.demon.co.uk/
satevo [accessed 21 June 2007].

29. Analytical Graphics, Inc., "About AGI," http://www.agi.com/corporate [accessed 27 June
2007].









30. Analytical Graphics, Inc., "STK Editions," http://www.agi.com/products/desktopApp/
stkFamily/editions/index.cfm?tab=key [accessed 27 June 2007].

31. University of Missouri-Rolla, "Conceptual Design of the MR SAT Tethered Satellite
Project at the University of Missouri-Rolla: 1.0 Structures,"
http://web.umr.edu/-mrsat/docs.html [accessed 12 February 2007].

32. Holt, G., Stewart, S., Mauldin, J., Campbell, T., Eckhoff, P., Yeldell, S., Greenbaum, J.,
Linford, M., Diaz-Aguado, M., Wang, T., Berthold, T., Lightsey, E. G., Raja, L. L., Ebinuma, T.,
"FASTRAC Mission Plan: Formation Autonomy Spacecraft with Thrust, Rel-Nav, Attitude and
Crosslink," The University of Texas at Austin, Austin, TX, December 2005.

33. Washington University, "Welcome to the Washington University Nanosat Page,"
http://www.me.wustl.edu/faculty/mas/nanosat [accessed 12 February 2007].

34. Analytical Graphics, Inc., "Lifetime Tool," http://www.agi.com/resources/
help/stk613/helpSystem/stk/tools- 1 .htm [accessed 1 July 2007].

35. Analytical Graphics, Inc., "Satellite Orbits," http://www.agi.com/resources/
help/stk613/helpSystem/stk/vehSatorbitTab.htm [accessed 1 July 2007].









BIOGRAPHICAL SKETCH

The author was born in Quezon City, Philippines. She immigrated to the United States in

Illinois on October 15, 1988. She received her bachelor's degree in Electrical Engineering on

December 2002 from the University of Illinois at Chicago. In August 2007, she moved to

Florida to attend the University of Florida in Gainesville. She received her master's degree in

Mechanical Engineering in December 2007 with a concentration in dynamics and control.





PAGE 1

1 ORBITAL LIFETIME ANALYSES OF PICOAND NANO-SATELLITES By AI-AI LUMNAY C. COJUANGCO A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2007

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2 2007 Ai-Ai Lumnay C. Cojuangco

PAGE 3

3 To my mother and sister

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4 ACKNOWLEDGMENTS I extend my sincere gratitude to my adviso r, Dr. Norman Fitz-Coy, for his generous support, guidance and patience th rough my graduate studies at the University of Florida. I acknowledge and give appreciation to my committee members Dr. John K. Schueller and Dr. Carl Crane for providing va luable input to this work. I acknowledge my colleagues in the AMAS lab, the Space Systems Group and SAMM group, for their support, input, and company with research and graduate studies. I express my appreciation to the women in my life group, Pascalie Belony, Jamie Cabug, Ann Duong, Sunny Ho, Jenny Jose, Christine Mora n, and Carrie Torbert for their continuous encouragement, belief in me, word s of wisdom, prayers, and for be ing such great inspirations to my life since I arrived at Universi ty of Florida. Also, to all th e wonderful people I have met and befriended through Gator Christian Life. I thank Cris Dancel for her time, guidance and support with this work. I also express my appreciation to the rest of the Filipino community I have met here for making me feel at home. I thank my friends in Illinois as we ll for keeping me in their thoughts. I thank my family. I especially thank my mother, Evangeline Chongco, and sister, Claudine Foronda, for their love support, and for allowing me to pursue graduate studies. Last, I express my deep gratitude to Jesus Ch rist, my Lord, my Savi or and my God, it is through Him I have faith and streng th and it is He who has made all of this possible. I thank Him for his beautiful creation that I have had the joy in living and learning about.

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5 TABLE OF CONTENTS page ACKNOWLEDGMENTS...............................................................................................................4 LIST OF TABLES................................................................................................................. ..........7 LIST OF FIGURES................................................................................................................ .........8 ABSTRACT....................................................................................................................... ..............9 CHAPTER 1 INTRODUCTION AND BACKGROUND...........................................................................11 Definition of Orbital Debris................................................................................................... .11 Concerns with Orbital Debris.................................................................................................11 Development of Mitig ation Guidelines..................................................................................15 Motivation of Research......................................................................................................... ..17 2 METHODS........................................................................................................................ .....20 Two-body Problem............................................................................................................... ..20 Conic Sections................................................................................................................. .......23 Orbital Elements............................................................................................................... ......25 Perturbations.................................................................................................................. .........26 Perturbation Techniques........................................................................................................ .30 Orbital Lifetime............................................................................................................... .......33 3 SIMULATIONS USING SATELLITE TOOL KIT (STK) SOFTWARE.............................35 Satellite Tool Kit (STK)....................................................................................................... ..35 STK Lifetime Tool.............................................................................................................. ...35 STK Satellite Properties....................................................................................................... ..39 Parameter Sensitivity Study....................................................................................................41 4 RESULTS AND DISCUSSION.............................................................................................46 Pico-satellite Results......................................................................................................... ......46 Nano-satellites Results........................................................................................................ ....50 5 CONCLUSION AND RECOMMENDATIONS...................................................................58 Conclusions.................................................................................................................... .........58 Recommendations................................................................................................................ ...59

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6 LIST OF REFERENCES............................................................................................................. ..60 BIOGRAPHICAL SKETCH.........................................................................................................63

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7 LIST OF TABLES Table page 3-1 Satellite mass, drag area, and area exposed to Sun..........................................................37 3-2 Orbital lifetime sens itivity simulation parameters...........................................................41 4-1 CubeSat simulation parameters........................................................................................47 4-2 MR SAT and MRS SAT simulation parameters..............................................................51 4-3 FASTRAC simulation parameters...................................................................................51 4-4 Akoya-B and Bandit-C simulation parameters................................................................52 4-5 MR SAT with different ini tial altitudes simulation parameters.......................................52

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8 LIST OF FIGURES Figure page 1-1 Typical picoand nano-class sa tellite mass, volume and power ratios...........................18 1-2 Computer generated imag e of orbital debris in LEO.......................................................19 2-1 Relative motion of two-bodies.........................................................................................21 2-2 Geometry of an elliptic conic section..............................................................................24 2-3 Orbital elements......................................................................................................... ......25 3-1 STK Lifetime tool GUI....................................................................................................36 3-2 STK Lifetime Advanced option GUI...............................................................................39 3-3 STK satellite properties GUI...........................................................................................40 3-4 Orbital lifetime vs. reflection coefficient.........................................................................43 3-5 Orbital lifetime vs. area exposed to Sun..........................................................................43 3-6 Orbital lifetime vs. drag coefficient.................................................................................44 3-7 Orbital lifetime vs. drag area...........................................................................................44 3-8 Orbital lifetime vs. mass................................................................................................ ..45 4-1 Orbital lifetime results for satellit e A using seven atmospheric density models.............48 4-2 Orbital lifetime results for satellit e C using seven atmospheric density models.............48 4-3 Orbital lifetime results for satellites A, B, C, and D at 600-km initial altitude...............49 4-4 Orbital lifetime for MR SAT a nd MRS SAT at 350-km initial altitude..........................54 4-5 Orbital lifetime for MR SAT a nd MRS SAT at 750-km initial altitude..........................55 4-6 Orbital lifetime for the FASTRAC satellites at 350-km initial altitude...........................55 4-7 Orbital lifetime for the FASTRAC satellites at 750-km initial altitude...........................56 4-8 Orbital lifetime for the Akoya-B and Bandit-C at 350-km initial altitude......................56 4-9 Orbital lifetime for the Akoya-B and Bandit-C at 750-km initial altitude......................57 4-10 Orbital lifetime for the MR SA T using different initial altitudes....................................57

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9 Abstract of Thesis Presen ted to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science ORBITAL LIFETIME ANALYSES OF PICOAND NANO-SATELLITES By Ai-Ai Lumnay C. Cojuangco December 2007 Chair: Norman Fitz-Coy Major: Mechanical Engineering In recent years, orbital debris has been a growing concern fo r the space industry due to its potential risk of causing collisi ons. Several agencies and orga nizations, such as the National Aeronautics and Space Administ ration (NASA), and the United Nations Committee on the Peaceful Uses of Outer Space (UNCOPUOS), have b een involved in studying orbital debris and developing mitigation guidelines. In 2004, th e Federal Communications Commission (FCC) began requiring a debris mitigation plan for all non-government United States radio communication satellites to be launched into orbit. Orbital lifetime analysis of a satellite is important in its development and in complying with debris mitigation guidelines. Factors th at must be taken into consideration include environmental perturbations, such as solar ra diation pressure, the Earths oblateness, and atmospheric drag. Other factors that affect orbital lif etime prediction are th e satellites physical properties. In this research, these perturbations and their effects on orbital lifetime, for Earthorbiting satellites, were investigated. In this study, orbital lifetimes were determ ined using the Lifetime analysis tool in Analytical Graphics Satellite Tool Kit (STK) software, focusi ng on picoand nano-satellites. The focus on these two classes of satellites is due to their perceived rapid growth and the

PAGE 10

10 potential difficulty of adhering to FCC requirement s for debris mitigation. The effect of solar cycle and different atmospheric density models were also explored during the analyses. The results indicate that orbital lifetimes of pico-satellites can be significantly reduced by increasing their drag area. For instance, changi ng the drag area of a 1kg satellite from 0.01 to 0.1 m2 decreased its orbital lifetime from 22 to 3 y ears, an 86% reduction. At 600 km above the Earths surface, pico-satellite s with drag areas of 0.1 m2 had minimum orbital lifetimes during years of highest solar activity. Our analysis implie s that passive de-orbiting devices such as drag chutes can be effective devices on pico-satellit es for addressing orbital debris mitigation. Meanwhile, the nano-satellites used in our study we re between 11 to 28 kg, with drag areas from 0.08 and 0.2 m2, which led to orbital lifetimes in centu ries when launched at 750 km altitude. Values indicate that additions to the nano-satellit es are needed to fulfill a 25 year orbital lifetime requirement set by the FCC.

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11 CHAPTER 1 INTRODUCTION AND BACKGROUND Definition of Orbital Debris The launch of Sputnik in 1957 was the dawn of space exploration and a significant milestone in the advances in science and techno logy. Since that date, numerous missions and manned spacecraft have been launched and continue to be launched for scientific, educational, and technological purposes. A major effect not considered in th e early years of space exploration was the contributi on of artificial bodies (i.e., sp ent satellites and spacecraft components) to the debris population in space. Tw o categories of debris now exist, natural (i.e., meteoroids) and artificial (i.e., used rocket bodies). Artif icial debris is also referred to as orbital debris. Orbital debris refers to man made sp ace objects that are no longer functioning or serve any useful purpose. Prior practic es and procedures have allowed unregulated growth of orbital debris, however, in recent years, the issue of orbital debris has become extremely important requiring that the space industry monitors debris orbiting the Earth and develop procedures to curtail its growth in the future.1 Concerns with Orbital Debris There are several factors that have and will co ntribute to the growth of orbital debris, the primary contributors being (1) explosions, (2) pr ior practices and procedur es that have involved the abandonment of spacecraft and upper stages, (3) the deposition rate of objects being sent into space, (4) collisions, and (5) future trends of small satellite usage by academia, government and industry. First, orbital debris growths primary cau se is explosions, which produce breakups or fragments. Explosions can be accidental or intentional. Acci dental explosions obtain energy from on-board energy sources. Meanwhile, inten tional explosions include tests (i.e., anti-

PAGE 12

12 satellite testing) or spacecraft separation. For ex ample, in low Earth orbit (LEO), altitudes up to 2,000 km above the Earths surface, accidental expl osions of spent upper stages have been the main source of debris.2 Second, the next largest contri butor to orbital debris ha s been prior practices and procedures that involved the ab andonment of spacecraft and upper stages in their current orbit after the spacecraft ha s completed its mission or is no longer operational. The National Aeronautics and Space Admini stration (NASA) reported in 1995 the accumulation of approximately 1968 tons of orbita l debris due to these practices.2 Third, assets are being launched into space at a ra te that is higher than the rate at which expired assets are being removed by natural and artificial means.3 This has led to an average growth rate in debris population of 5% per annum in LEO.4 Fourth, a major concern to orbital debris gr owth is collisions. Collisions can occur between varieties of satellite classes. Due to th eir large speeds, when space objects collide with each other, they may become non-operational. These masses would spatially distribute themselves producing debris fragments or debris clouds and thus add on to the total debris population. The threat of these clouds is evid ent by the debris created from the recently destroyed Chinese satellite, Fengyun 1-C, this past January 2007. Last, research and trends in the past were focused on traditional large costly satellites, but are now transitioning to smaller satellites. This trend is the result of these satellites potential lower costs and advances in technology, whic h allows for miniaturization. The Defense Advanced Research Projects Agency (DARPA) or ganization is exploring fractionated spacecraft flying in formation as well as a collecti on of heterogeneous small satellite modules5 performing various tasks. This trend is also seen in acad emia through projects such as the CubeSat and the

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13 University Nano-satellite Program (UNP). The CubeSat program was developed by the Califo rnia Polytechnic State University in San Luis Obispo, and Stanford Universitys Space Systems Development lab as a mechanism to enable universities to particip ate in the design, launch, and ope rations of satellites at an affordable cost.6 A one unit CubeSat is a 10 cm cube with a mass of 1 kg classified as a picosatellite. Currently, these satellites typica lly have short operational lifetimes as compared to their orbital lifetimes and if not properl y disposed after its primary mission will then contribute orbital debris. The UNP is a joint program composing of the Air Force Research Laboratorys Space Vehicles Directorate (AFRL/VS), the Air Force Office of Scientific Research (AFOSR), and the American Institute of Aeronautics and Astronautics (AIAA). The program is a national student satellite design and fabrication competition. It also enables small sa tellite research and development, integration, payloa d development, and flight tests.7 There are a growing number of these satellite classes pl anned on being sent to space a nd the increase can potentially contribute to the total amount in number and mass of the orbital debris population. The growth of orbital debris has become an immediate issue as its presence in space continues to have an impact with the utilization of space assets. It is continuously monitored and modeled by agencies such as NASA and the Unit ed Nations Committee on the Peaceful Uses of Outer Space (UNCOPUOS) for study and risk asse ssment to future space missions. The impact, both immediate and lasting, of collisions and e xplosions on the orbital debris population and resultant hazards to space operations are discussed. Explosions can produce debris fragments in large number and cause an operating spacecraft to fail, as well as produce smaller debr is fragments that may degrade its performance.

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14 Other spacecraft, hundreds of kilometers away, may also be at a great risk from these fragments due to their high velocities that may set them in very long orbit lifetimes.2 According to NASA, collision between large objects follows this scenario: First, once collisions begin to occur, it will be almost impossible to halt the process and they will occur with increasing frequencya pr ocess referred to as collisional cascading. Second, the energies in collisional breakup are much larger than in explosive breakup, in the megajoule (a few kilograms to TNT) to gi gajoule (a few metric tons of TNT) range. This energy comes from the very large amount of chemical energy used to get objects into orbit. This large amount of expended energy creates many more debris fragments in all size ranges and spreads the debris over many hundreds of kilometers of altitude. This debris may hit other satellite surfaces, carrying imp act energies of hundreds of megajoules per kilogram of impactor mass. At these energies, debris less than 1 mm in diameter, typically about 1 mg of mass, can penetrat e an unshielded spacecraft surface and damage sensitive surfaces such as optics or thermal radiators; debris less than 1 cm (1 gm) can penetrate even a heavily shielded surface; and debris as small as 10 cm (1 kg) can cause a spacecraft to break up into debris fragments.2 Consequently, the risk of collision between debris and another object has become a close concern. Abandoned spacecraft and upper stages are cases of large non-operational objects already in space for which this type of collision can occur. Computer modeling indicates that collisions between large objects in orbit will beco me a major source of debr is within the next 3 decades, even if spacecraft launches were limited at 5 launches per year. The orbital debris that will be produced from these collisions will be small particles that are large in number and are capable of damage to operational spacecraft1.1,2 For the purpose of this research, collision of objec ts in LEO is the focus. In this orbit, the standard impact velocity of medi um-sized orbital debris with other objects is about 13 km/s, with an explosive potential equal to 40 times its mass of TNT. For instance, a 1-cm-diameter aluminum sphere, about 1.4 grams, has a kinetic energy equivalent to the energy released by the explosion of 0.056 kg of TNT (about 0.24 MJ). A 10cm aluminum sphere, on the other hand, is equivalent to 56 kg of TNT (about 240 MJ). Ther efore, in LEO, the energy released by small debris pieces may severely damage or destroy many spacecraft systems.1

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15 Development of Mitigation Guidelines Assessments of potential risks i nvolved with orbital debris have led to possible solutions and abatement measures. Although removing ab andoned spacecrafts, upper stages, and other orbital debris may be the most effective means in avoiding future collisions, this is not cost effective because it would require di fficult maneuvering of objects in space7.2,8 Several national and internati onal agencies/organizations ar e involved in or bital debris assessment and mitigation. In 1993, the InterAgency Space Debris Coordination Committee (IADC) was founded to enable space agencies to exchange information on space debris research activities, to review th e progress of ongoing cooperative activiti es, to facilitate opportunities for cooperation in space debris research and to identify debris mitigation options8F9. Members of the IADC consists of NASA, the Italian Space Agen cy (ASI), the British National Space Centre (BNSC), the Centre National dEtudes Sp atiales (CNES), the China National Space Administration (CNSA), the Deut sches Zentrum fuer Luft-und Raumfahrt e.V. (DLR), the European Space Agency (ESA), the Indian Spac e Research Organisation (ISRO), the Japan Aerospace Exploration Agency (JAXA), the Nationa l Space Agency of Ukrain (NSAU), and the Russian Aviation and Space Agency (Rosaviakosmos). By February 1994, the United Nations (UN) Scientific and Tec hnical Subcommittee agreed that international c ooperation was needed to minimi ze the potential impact of space debris on future space missions125H.9 NASA issued a comprehensive set of orbital debris mitigation guidelines in 19959F.10 The U.S. Government along with NASA, the Federal Aviation Administration (FAA), the Department of Defe nse (DoD), and the Federal Communications Commission (FCC) presented a set of orbital debr is mitigation standard practices in a 1998 U.S. Government Orbital Debris Workshop for Industry10F.11 Japan, France, Russia, and the European Space Agency (ESA) and other countries, have since followed suit with their own guidelines126H.10

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16 President Reagan issued a directive on na tional space policy requiring the limitation of orbital debris accumulation on February 11 of th e same year. This directive initiated the collaborative work of the U.S. and other nations to learn more about orbital debris hazards and management. An International Technical Wo rking Group was established through this, which helped influence nations with space activitie s to take action in limiting orbital debris127H.2 By the year 2001, the United States Govern ment adopted its own guideline, U. S. Government Orbital Debris Mitigation Standard Practices128H11F. 10,12 The IADC reached a consensus on a set of guidelines that were formally presented to the Scientific and Technical Subcommittee of the UNCOPUOS on February 2003129H.10 In June 2004, the FCC issued its own set of mitigation rules, Orbital Debris Notice, closely following th e U. S. Government Or bital Debris Mitigation Standard Practices12F.13 Several orbital debris mitigation guidelines have been in place after NASAs lead. NASAs, the U.S. Governments, the IADCs a nd the FCCs guidelines are summarized here with a focus on post mission disposal in LEO, for the purpose of this thesis. NASAs guideline has three general options for post mission disposal in LEO which are (1) atmospheric re-entry, (2) maneuvering to a storage orbit, and (3) direct re trieval. For option one, the guideline states to maneuver a structure into an orbit where atmo spheric drag, the main nongravitational force acting on satellites in LEO13F,14 will cause its lifetime to decay w ithin 25 years afte r the end of its mission. The second option states to maneuve r the spacecraft with final missions passing through LEO to a disposal orbit defined to be between 2500 km to 35,288 km. The last option states to perform a direct retrieva l of the spacecraft from its orbit within 10 years after the end of its mission130H.2 The U.S. Government guidelines has the sa me three options as NASA, but with the

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17 inclusion of human casualty risk to be limited to no greater than 1 in 10,000 upon re-entry added to option one; different disposal orbit definition for option two; and, the time period stated to be as soon as practical given for option three131H.12 The IADC Space Debris Mitigation Guidelines has a post mission disposal section for the LEO re gion. The guideline gives the option for space systems to be disposed by de-orbiting, by dire ct re-entry, by maneuveri ng it to an orbit that reduces its lifetime and by direct retrieval14F.15 The FCC, which has general authority over U. S. radio communications with the exception of government radio stations, includes three me thods for post mission disposal. One method is direct retrieval, which the commission currently st ates little relevance for this option regarding Commission-licensed space stations. Another met hod is to maneuver a spacecraft to a disposal or storage orbit. The storage orbit is defined to be in perigee altitudes above 2000 km and apogee altitudes below 19,700 as suggested for satellites in LEO. The FCC gives two procedures for the atmospheric re-entry option: (1) to use the spac ecrafts propulsion to br ing it further into the Earths atmosphere and (2) to m ove the satellite to an orbit from which atmospheric drag will cause its re-entry into the Earths atmosphere an d that it will decay within 25 years after the end of its mission. For continued affordable access to space, the FCC ruled that a satellite system operator must submit an orbital debris mitigation plan before requesting space station authorization132H.13 Motivation of Research This research, in response to the FCC ruling, investigates the different parameters that affect the orbital lifetime of pi coand nano-class satellites. These classes of satellites are increasingly gaining attention th roughout the space indus try due to their poten tial low cost and technological advances. The University of Fl orida has been involved with small satellite research, in particular the CubeSat, since th e fall of 2004. The nano-satellites developed through

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18 the UNP are another example of the trend in a cademia moving towards small satellites. The increase in number of these sa tellites being sent to space is a concern. The typical size, mass, and power ratios of these two classes of satellites are shown in Figure 1-1. Power ~ 2W Power ~ 20W 30 cm 30 cm 10 cm 10 cm 1 kg 10 kgPico Nano Figure 1-1. Typical picoa nd nano-class satellite mass, volume and power ratios As of May 2007, there have been 17 of the pi co-class satellites refe rred to as CubeSats successfully launched in LEO and are namely15F 16F:16,17 2003: AAU CubeSat by the Aalborg University, DTUSat by the Technical University of Denmark, CanX-1 by the University of Toront o SFL, CubeSat XI-IV by the University of Tokyo, Cute-1 by the Tokyo Institute of Technology Matunaga LSS 2005: NCube-2 by the University of Oslo (a nd others), UWE-1 by the University of Wrzburg, CubeSat XI-V by the University of Tokyo 2006: Cute-1.7 by the Tokyo Institute of Technology Matunaga LSS, HITSat by the Hokkaido Institute of Technology 2007: AeroCube-2 by the Aerospace Corpor ation, CAPE-1 by th e University of Louisiana, CP-3 and CP-4 by the California Polytechnic State Univ ersity, CSTB-1 by the Boeing company, Libertad-1 by the Sergio Arboleda University, MAST by Tethers Unlimited The CubeSat has a small mass and volume that can make a huge collision impact especially due to both the high velocity rates and concentra tion of spacecrafts in LEO. Figure 1-2 shows a computer generated image of the concentration of orbital debris that ha s been tracked in LEO (2005) courtesy of NASA. As opportunities for Cube Sats to access space con tinue to proliferate, their contribution to the total mass may not seem substantial on a small scale. However, the

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19 quantity of dispersed orbiting CubeSats would de ter the grade of the orbit unless measures are taken to prevent this by satellite developers. Also, there are currently no enforced mitigation plans for CubeSats. Figure 1-2. Computer generated image of or bital debris in LEO. Courtesy of NASA17F.18 The nano-satellites also have the potential to contribute to the total mass and number of orbital debris in space. The number of these t ypes of satellite planne d on being launched is increasing. Details of the prope rties of the nano-sate llites chosen for this study are further discussed in Chapter 3. The initiative to take the necessary measures to reduce the orbital lifetime of these types of satellites, in order to prevent them from becoming orbital debris, is a step towards being responsible users of the space environment and must be taken seriously. In Chapter 2, the equations of motion for th e two-body problem and the equations that lead to orbital lifetime prediction are presented fo llowed by some computer programs available for predicting orbital lifetime. In Chapter 3, Satellite Tool Kit (STK), the software used in this study for orbital lifetime prediction, is presented and the different para meters used for the simulation scenarios are reported. Chapter 4 elaborates on the orbital lifetime prediction results for the picoand nano-satellites, while the conclusions and recommendati ons for this research are in Chapter 5.

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20 CHAPTER 2 METHODS In this chapter the equation of motion fo r the two-body problem is discussed. Brief summaries of conic sections and orbital elemen ts are given. The equations of motion for the two-body problem with perturbations are also pr esented. These equations are then used to describe orbital lifetime. Some programs for orbital lifetime prediction are presented. Two-body Problem A model to describe a satellites orbital moti on can be developed from planetary motions. The physical motions of each planet were fi rst described by Johannes Keplers three laws18F:19 First Law The orbit of each planet is an ellipse, with the sun at a focus. Second Law The line joining the planet to the sun sweeps out e qual areas in equal times. Third Law The square of the period of a planet is proportional to the cube of its mean distance from the sun. The first two laws of planetary motion were published in 1609, while th e third in 1619. The mathematical equations of planetary motions we re not formulated until about 50 years later, through Issac Newtons second la w of motion and law of unive rsal gravitation. Newtons second law of motion states that the rate of change of momentum is proportional to the force impressed and is in the same direction as that force133H19. Newtons law of universal gravitation states that any two bodies attr act one another with a force pr oportional to the product of their masses and inversely proportional to the square of the distance between them 134H19. The equation for the second law of motion can be written as 2 2 ii iidrdv Fmm dtdt (2.1) The notation F represents the sum of all the forces acting on a body which is equal to its

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21 mass, im times its acceleration, 2 2 idr dt measured relative to an inertial frame, and iv is the velocity vector. Newtons law of uni versal gravitation can be written as 3 1()1,...n ij gji j ij jimm FGrrin r (2.2) where g F is the gravitational force on im due to jm and ()jirr is the vector from im to jm. The symbol G represents the universal gravitational constant and has the value of 6.670 10-8 dyne cm2/gm2135H.19 The equations of motion for planets and sa tellites were developed from equations 136H(2.1) and 137H(2.2). The equations of motion are applicable for a system of two bodies, referred to as the twobody problem, where n = 2 in equation 138H(2.2). An illustration of the system with bodies 1m and 2m is shown in Figure 2-1. Tw o assumptions are required to develop the equations of motion and are as follows: (1) body 1 and body 2 are spheri cally symmetric (this allows for the bodies to be treated as though the concentr ations of their masses are at their centers) and (2) only gravitational forces are acting on the system, which act along the li ne joining the centers of the two bodies. An inertial reference frame is also defined to measure the motion. In Figure 2-1 the set of inertial coordinates is defined by (,, X YZ). The position vectors of 1m and 2m, with respect to the inertial frame, are defined as 1r and 2r respectively, so that 21rrr 139H.19 2m1mr 1r 2r X Z Y 2m1m r 1r 2r X Z Y Figure 2-1. Relative motion of two-bodies

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22 Equating Newtons second law of motion and his law of universal gravitation, for i = 1 and 2, after some manipulations, the governing equations of motion of 1m and 2m are 2 12 21 23 12() drm Grr dtr (2.3) 2 21 12 23 21() drm Grr dtr (2.4) where 122121rrrrr which is the distance between the two bodies. Twelve constants are required for a complete solution of these second order ordinary differen tial equations, but only 10 exist and thus the equations ca nnot be solved analytically. Th e two equations can be reduced to find the relative motion of body 2 with respect to body 1 by subtracting equation 140H(2.3) from 141H(2.4) which results in 2 12 23mm dr Gr dtr (2.5) where r is the position vector from 1m to 2m142H. Equation 143H(2.5) may be rewritten as 2 230 dr r dtr (2.6) assuming that 1m = mass of the Earth and is much greater than 2m = mass of the satellite so that 121GmmGm, which is called the Earths gravitational constant. Equation 144H(2.6) is the equation for the relative motion of two-bodies with only gravitationa l forces acting upon the system describing the motion of 2m with respect to 1m145H.19 Equation 146H(2.6) is a second order, nonlinear, vector, differential equation, that ca n be solved analytical ly, which requires six constants of integration for a complete solution from 0r and 0v or six other constants. By conservation of angular momentum, the or bit of a satellite ar ound the Earth can be

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23 shown to lie on a plane. Th e angular momentum vector, h is then perpendicular to the orbit plane and is a constant vector. A partial solution to Equation 147H(2.6) is easy to obtain, that tells the size and shape of the orbit. Crossing h to Equation 148H(2.6) leads to a form of equation that can be integrated: 2 23dr hhr dtr (2.7) The left side of Equation 149H(2.7) equals ddr h dtdt and the right side equals 2dr vr rrdt and after some manipulations Equation 150H(2.7) can be rewritten as ddrdr h dtdtdtr (2.8) Integrating both sides results in drr hB dtr (2.9) where B is a vector constant of integration. Dot multiplying Equation 151H(2.9) by r results in a scalar equation 2coshrrBf (2.10) where f is the angle between B and r By solving for r, Equation 152H(2.10) becomes 2/ 1/cos h r B f (2.11) and is called the trajectory equati on expressed in polar coordinates153H.19 Conic Sections Equation 154H(2.11) is similar to the equation of a co nic section, where a conic section may be defined as a curve formed by the intersection of a plane passing through a right circular cone14.

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24 The equation of a conic sect ion can be written as 1cos p r ef (2.12) and gives the magnitude of the position vector, rr in terms of its location in the orbit where p is called the parameter or semi-latus rectum, e is the eccentricity, and f is the polar angle or true anomaly. The type of c onic section represented by equation 155H(2.12) is determined by the value of the eccentricity. When 0 e the conic section is a circle, 01 e produces an ellipse, 1 e generates a parabola, and 1 e represents a hyperbola. Figure 2-2 shows a geometric representation of an elliptic conic secti on. The figure shows the conic section having two foci, where F is the primary focus (i.e., the Earths center) and 'F is the secondary or vacant focus. C is the center of the ellipse. Ha lf the distance between foci is the dimension c. The dimension a is the semi-major axis and b is the semi-minor axis of the ellipse. The distance from the primary focus to the farthest point of the ellipse is called the radius of apogee, ar and to the closest point of the elli pse is called the radius of perigee, pr From Keplers Second Law, the time required to co mplete one orbit is called the orbital period, TP and is expressed as 3/22 TPa (2.13) cCF Far p r bpa f r cCF Far p r bpa f r Figure 2-2. Geometry of an elliptic conic section

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25 Orbital Elements The six other constants of integration possible, asides from position and velocity for the solution of Equation 156H(2.6), to describe the motion of a satellite around the Earth, are known as orbital elements or Keplerian orbital elements as shown in Figure 2-3 an d are defined below (See reference 14). Semi-major axis (a) Defines the size of the orbit. Eccentricity (e) Defines the shape of the orbit. Inclination ( i ) The angle between Z and angular momentum vector, h. Right Ascension of Ascending Node (RAAN) ( ) The angle from the vernal equinox to the ascending node. The ascending node is the point where the sa tellite passes through the equatorial plane moving from south to north Right ascension is measured as a righthanded rotation about the pole, Z Argument of Perigee ( ) The angle from the asce nding node to the eccentricity vector, e, measured in the direction of the sate llites motion. The eccentricity vector points from the center of the Earth to perige e with a magnitude equal to the eccentricity of the orbit. Mean anomaly ( M ) The fraction of an orbit period which has elapsed since perigee, expressed as an angle. The mean anomaly equals the true anomaly for a circular orbit. Vernal Equinox Direction Line of Nodes Periapsis Direction i 0 f X Y Z h 0re Line of Nodes( A l w a y s D e f i n e d )Periapsis Direction 0 f ( A l w a y s D e f i n e d )0r Figure 2-3. Orbital elements

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26 Perturbations The amount of time a satellite remains in orbit before perturbations causes its reentry into the Earths atmosphere is the satellites orbi tal lifetime and can be found from the sum of its orbital period, TP. The orbital period is a function of the semi-major axis. When the semi-major axis remains constant then the period is constant and the orbital lifetime is indefinite. Orbital lifetime goes towards infinity as a increases because the period ge ts larger. Orbital lifetime becomes finite when the semi-major axis decreases as this causes the pe riod to decrease. The duration of a satellites orbit with respect to the Earth is indefinite when the only forces acting on the system are gravitational forces. The orbital elements also remain constant. When other forces act on the system, however, the relative motion equation becomes 2 23ddr ra dtr (2.14) where da is the perturbing acceleration. This non-homogeneous differential equation implies that the previous consta nts of motion are no longer constant. Thus, orbital lifetime can be finite when perturbations are considered. 20,21 Some of these perturbations are atmospheric drag, solar radiation pressure, the Earths oblateness, and other bodie s (n-body effect). Factors to cons ider with these perturbations are solar activity, geomagnetic activity, atmospheric de nsity, and ballistic coefficient (a function of the satellites mass, mean cross sectional drag area, and dr ag coefficient). These perturbing accelerations cause a satellites or bit to decrease and no longer be indefinite. The orbit will decay into the Earths atmosphere and the time it ta kes for the decay to bring the satellite into the Earth is the satellites orbital lifetime. In predicting the orbital lifetime of satellites, perturbations must be taken into consideration. These factors and uncertainties in the solar and

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27 geomagnetic activities can make orbita l lifetime prediction very challenging19F 20F.20,21 Some of the factors that affect lifetime are discussed here. The Earths upper atmosphere has a strong effect on satellites in space. The atmosphere is dynamic and is affected mostly by the suns ra diation. This solar activity heats up the atmosphere and it expands as a result. The expansion produces a variation in density proportional to the degree of heating, wh ich in turn depends upon solar activity21F22. Solar activity and Sun spots vary periodically, which is commonly known as the 11-year solar cycle. The radiation from the sun is measured as a mean daily flux in the 10.7 cm (F10.7) wavelength in solar flux units (sfu). A bulge is also created, as a result of the hea ting on the side of the Earth that is facing the sun. This causes the density at a given point above the Earth to vary diurnally, as the point rotates through the bulge every 24 hours, and seasonally, as the bulge moves with the sun in latitude from winter to summer157H22. The atmosphere is influenced by geomagnetic activity as well through delayed heating of atmospheric particles from collisions with charged energetic particles from the sun22F23. Satellite lifetimes are affected mo st by the variation in the solar cycle and the heat from radiation. Disturbances from geomagnetic ac tivity are usually too short to affect lifetimes significantly.14 Atmospheric drag is the main nongravitationa l force that acts on a satellite in LEO.14 Drag is part of the total aerodynamic force that acts on a body moving through a fluid such as air158H.21 It acts in the direction opposite of th e velocity and takes away energy from the orbit. The decrease in energy causes the orbit to decay until the sate llite reenters the atmosphere. The equation for the acceleration of a spac ecraft due to drag is 21 2d drCA av m (2.15)

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28 where is the atmospheric density, dC is the satellites drag coefficient 2.2, A is the average cross-sectional area of the sa tellite normal to its direction of travel (drag area) m is the mass of the satellite and rv is the satellites velocity relative to the atmosphere. The term dm CA is the ballistic coefficient and is used as a measur e of a satellites res ponse to drag effects159H.14,23 The drag area is directly related to the satell ites shape, dimensions and attitude motion160H.21 Mass is usually taken to be constant dur ing a satellites lifetime. Wh en there is a mass loss, drag deceleration of the satellite increa ses and its lifetime is shortened161H.22 The ballistic coefficient can indicate how fast a satellite will decay along with solar activity. Satellites with low ballistic coefficients tend to decay more quickly in resp onse to the atmosphere than those with high ballistic coefficients, which progress through more solar cycles. During solar maxima satellites tend to decay more quickly and during solar minima satellites tend to decay more slowly as well. The effect of atmospheric drag is not significant to satellites with perigees below ~120 km due to the high density of the Earths atmosphere so sa tellites already have such short lifetimes up to this altitude. Atmospheric drag is weak at alti tudes above 600 km and t hus a satellites orbital lifetime is longer than its operational life.14 Solar radiation pressure influences the orbita l elements by causing periodic variations to them. Satellites with low ballistic coeffi cients feel strong effects from this.14 Solar radiation pressure produces acceleration in a radial direc tion away from the sun. The equation for solar radiation pressure may be written as s rpA T a cm (2.16) where s A is the satellites average area projected normal to the direction of the sun in m2, m is the satellites mass in kg, T is the solar flux (SF) near the Earth, c is the speed of light, and is

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29 the satellites reflection co efficient with a value of 04/3 (0 transparent; 1 perfectly absorbing; 4/3 flat, specularly reflect ing.) The value of T / c can be taken as 4.5 105 dynes/cm223F.24 The acceleration from solar radiation pressure is less than the acceleration from drag below 800 km altitude and greater than the acceleration from drag above 800 km, with the exception of balloon-type satellites because of large area to mass ratio162H.14,21 For the two-body equations of motion the masses were assumed to be spherically symmetric. The Earth, represented as 1m however is not spherically symmetric, but instead has a bulge at the equator, is oblate, and is a pear shape. The Ea rth although can be modeled without this asymmetry by using a potential function. Th e acceleration of a satell ite due to the central body can be found by taking the gradient of the gravitational potential function expressed as 21sine nn nR JPL rr (2.17) where e R is the Earths equatorial radius, nP are Legendre polynomials, L is geocentric latitude, and nJ are dimensionless geopotential coefficients also called z onal coefficients. Periodic variations occur in all orbital elements as a result of the potential generated by the Earth. The 2J term represents the Earths oblateness in the geopotential expansion. The 2J perturbation has the most effect on satellites in Geosynchronous Earth Orbit (GEO), an orbit where a satellite appears to remain stationary over one location ab ove the Earths equator defined to be centered at an altitude of 35,788 km, and below GEO.14 The asymmetric mass distribution of the Earth alone can not lead to orbital decay; however, it can bring abou t large oscillations in the orientation and shape of the orbit. These oscillations coupled w ith drag alters orbital lifetime163H.21 Other bodies that can affect a satellite are the sun and moon, which exert gravitational forces that also cause perturbations. Oscilla tions in all orbital elements and orbital plane

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30 precession are caused by tidal forces created by the third-bodies. These forces have great effect on satellites far away from the Earths center. These perturbations are only significant for satellites near the Eart h with eccentricity greater than 0.5. The effects of the sun and moon attraction are usually neglected sinc e most satellites near the Earth are launched into orbits with low eccentricity164H.21 Perturbation Techniques Equation 165H(2.14) is the general form for th e relative motion of two bodies with perturbations. There are three main methods to solving the equa tions of motion with perturbations; special perturbati on, general perturbation and semi-a nalytic. Special perturbation uses straightforward numerical integration of the equations of motion that includes all the essential perturbing accelerations. Two such approaches are Cowells method and Enckes method. The numerical approach uses the position and velocity ve ctors of the satellite. General perturbation replaces the orig inal equations of motion with an analytical approximation that captures the essential character of the motion over some limited interval and which also permits analytical integration166H23. The analytical approach usually uses the orbital elements for integration. Semi-analytic methods use a comb ination of the special perturbation (numerical) and general perturbation (analytic) techniques167H.14,23 Equation 168H(2.14) is a non-homogeneous differential equation and may be solved using the method of variation of parameters. The general solution of equation 169H(2.14) involves the homogenous solution, from equation 170H(2.6). The homogenous solution is known and may be expressed as (,)(,)rrtvvt (2.18) where aeiM the six constants of integr ation or orbital elements.

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31 For the disturbed motion of two bodies the orb ital elements are no longer constant and are governed by ddd a dtdv (2.19) where da represents the perturbing accelerations. A detailed derivation on how to obtain equation 171H(2.19) can be found in reference24F.25 After substituting the orbital elements in equation 172H(2.19), the following variational equations, 173H(2.20) to 174H(2.25), are obtained: 2 22sin21 1drddaefae aa dtnr ne (2.20) 22 22 21 1sin1drdae deefe ara dtnar nae (2.21) 221cos1 1sincosdrddeferd afai dtnaenaepdt (2.22) 22sin 1sindhdru a dt naei (2.23) 22cos 1dhdiru a dt nae (2.24) 21 (cos2)sindrddM npfreaprfa dt ane (2.25) The symbol p is the semi-latus rectum wh ich may also be written as 21 p ae 3n a is the mean motion, uf is the argument of latitude, dra is the component of the perturbing acceleration in the radial direction, da is the component in the orbital plane normal to the radial

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32 direction, and dha is the component normal to the orbit plane, whose direction is determined from the cross product of the unit vectors dra and da 175H25F.25,26 Following Belcher et. al.176H,26 only long-term changes of the orbital elements are of importance in satellite lifetime analysis and so the short-term changes can be omitted or averaged out. Considering only long-term effects in this study, the sate llites instantaneous location along its orbit need not be included so that equation 177H(2.25) can be omitted. A change of the independent variable from t to f is convenient in order to avoid some of the problems related with the solution of Keplers equation, sin M EeE where E is called the eccentric anomaly. The change of variable equation is 2 21cos1sindrdp dfrr afaf dtep r (2.26) Due to the atmosphere, the semi-latus rectum will decrease less quickly than the semi-major axis and thus it is convenient to replace a by p so that equations 178H(2.20) to 179H(2.24) become 32ddpr a df (2.27) 2 2sin2cos1cosdrdderr afafef dfp (2.28) 2cos1sincosdrd edrrd afafi dfpdf (2.29) 3sin sindhdru a dfpi (2.30) 3cosdhdir au dfp (2.31) where

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33 1 21cos1sindrdrr afaf ep (2.32) Orbital Lifetime The previous section discussed the relative motion of two-bodies with perturbations that must be taken into considerati on for orbit lifetime pred iction. The components of the perturbing accelerations must be substituted into equations 180H(2.27) to 181H(2.32) in order to obtain orbital lifetime calculations. Atmospheric drag, th e main force affecting the satelli tes simulated in this study, is presented here following Belcher et. al.182H 26 1 2d drrCA avv m (2.33) rv is the satellites velocity vector with resp ect to the atmosphere and may be expressed as sin1coscoscossinrdrededhvefaefriaruia pp (2.34) where e is the angular rate of rotation for the Earth and its atmosphere, dra da and dha are the unit vectors in the dra da dha directions, respectively. Substituting equation 183H(2.34) into 184H(2.33) yields 1 sin 2 1 1coscos 2 1 cossin 2d d ddrdr ddre drdreA aCvef mp A aCvefri mp A aCvrfi m (2.35) and 2 2cos 12cos 12cose rpi veev p eef (2.36)

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34 The components obtained in equation 185H(2.35) may now be substituted into equations 186H(2.27) to 187H(2.31). The equations are then integrated to obtain the changes in the orbital elements. There are several programs available to perform the integration for lifetime prediction. SatLife, a stand alone software developed by Microcosm26F,27 uses the satellites initial orbit state, mass, and area as well as historical and predicte d solar cycle values for its lifetime prediction. SatEvo, a program developed by Alan Pickup27F,28 computes the decay of satellites from changes based on their orbital elements. NASAs Orbital Lifetime Program188H24 uses the satellites physical characteristics, launch date, and initial orbit stat e. Satellite Tool Kits (STK) lifetime tool, the software used for this thesis, was develope d by Analytical Graphics Inc. (AGI) based on NASAs program. There are three perturbations that STK takes in to consideration: atmospheric drag, solar radiation pressure, and the Earth s oblateness. The drag perturba tion is solved by semi-analytic techniques and the others by an alytic methods. To obtain the total disturbing effects, the solutions for each differential equation obtained for each disturbing function is summed up. Initial orbit parameters need to be specified wi thin the program in order for calculations to be performed. Integr ation of equations 189H(2.27) to 190H(2.31) is performed in or der to obtain new orbital elements and is integrated over a single orbit. Once the new orbital elements are obtained then the period of the orbit can be found and used to pr edict lifetime. The process is repeated until a maximum orbit number is reached, specified by the user, or it reaches the Earth. The predicted lifetime result is then disp layed on a pop up window by STK191H.24 The next chapter discusses the lifetime program in STK in more detail.

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35 CHAPTER 3 SIMULATIONS USING SATELLITE TOOL KIT (STK) SOFTWARE Satellite Tool Kit (STK) Satellite Tool Kit (STK) is a commercially available software, developed by Analytical Graphics, Inc. (AGI), and is used by nationa l security and space professionals to perform analyses of complex mission scenarios involving land, sea, air, and space assets. STK includes integrated 2-D and 3-D graphics for visualizati on of aerospace objects such as satellites, launch vehicles, missiles, and aircraft. STK enables user s to calculate position an d orientation, evaluate inter-visibility times, and determine quality of dynamic spatial relationships among groups of objects. The software is capable of custom da ta product generation, in cluding reports, graphs and Visual Data Format (VDF) files. STK can perform orbit/trajectory ephemeris generation, acquisition times, and sensor coverage an alysis for any of the objects mentioned28F.29 STK Lifetime Tool STK has a Lifetime analysis tool that estimat es a satellites orbital lifetime (i.e., the amount of time a satellite remains in orbit be fore atmospheric drag and other perturbations causes its reentry). The analysis tool is based on algorithms devel oped at NASAs Langley Research Center and the equations discussed in Chapter 229F.30 Utilization of STKs Lifetime analysis tool requires the user to input the satelli tes characteristics (i.e., launch date, initial orbit, mass, cross-sectional area, and drag coefficient) The algorithm then co mputes drag effects by applying the satellite characteris tics along with an atmospheric density model and a solar flux file (both selected by the user fr om a list of several options). Figure 3-1 shows the graphical user interface (GUI) for the Li fetime analysis tool. As shown in Figure 3-1, the input for Satellit e Characteristics includes Drag Coefficient, Reflection Coefficient, Drag Area, Area Exposed to Sun, and Mass. For these studies, a drag

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36 coefficient (dC ) of 2.2 was used based on a flat plate model satellite. Typically, the Reflection Coefficient ( ) varies between 0 and 4/3, but was ma intained at 0.01 for this study (see additional discussion in the Para meter Sensitivity Study section). Figure 3-1. STK Lifetime tool GUI (image is courtesy of AGI). The pico-satellite model analyzed in this study was the CubeSat with a dimension of 10 cm and a mass of 1 kg. The Drag Area of the CubeSat is 0.01 m2, the surface area of a face of the satellite (i.e., it was assumed that one of the satellites principal axis was aligned with its velocity vector). To investigate the e ffects of drag inducing devices for de-orbiting, the satellites drag area was increased to values of 0.04 m2, 0.06 m2, and 0.1 m2 (see Chapter 4). Since there is a wide variety of nano-satellite s, the following satellites from the University Nanosatellite Program (UNP) were randomly se lected for the study: MR SAT and MRS SAT (University of Missouri-Rolla), FASTRAC (University of Texas at Austin), Akoya-B and Bandit-C (Washington University in St. Louis) MR SAT has a mass of 28.25 kg, hexagonal side length of 20.4 cm and height of 31.6 cm MRS SAT has a mass of 11.45 kg, hexagonal side length of 17.6 cm and height of 19.0 cm30F.31 FASTRAC consists of top and bottom hexagonal structures: the top structure of FASTRAC ha s a mass of 15.46392 kg, the bottom has a mass

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37 12.5757 kg and both are 20.84 cm in height and 47.50 cm in width31F.32 Akoya-B is a hexagonal structure that is 45 cm across, 45 cm tall and has a mass of about 25 kg. Bandit-C is a 12 cm cube with a mass of 2 kg 32F61.33 The calculated hexagonal surface area of each satellite was used as the drag area with the exception of Bandit-C, which was calculated as its length times its width. Each satellites mass (m), drag area ( A ), area exposed to Sun ( s A ), and ballistic coefficient are summarized in Table 3-1. Table 3-1. Satellite mass, drag area, and area exposed to Sun Satellites Mass (kg) Drag Area* (m2) Area Exposed to Sun* (m2) Ballistic Coefficient (kg/m2) CubeSat 1 0.0100 (0.01) 0.0100 (0.01) 45.45 1 0.0400 (0.04) 0.0400 (0.04) 11.36 1 0.0600 (0.06) 0.0600 (0.06) 7.58 1 0.1000 (0.1) 0.1000 (0.1) 4.55 MRS SAT 11.45 0.0805 (0.080478) 0.0805 (0.080478) 65.06 MR SAT 28.25 0.1080 (0.108122) 0.1080 (0.108122) 116.74 FASTRAC bottom 12.5757 0.1954 (0.195397) 0.1954 (0.195397) 28.59 FASTRAC top 15.4639 0.1954 (0.195397) 0.1954 (0.195397) 35.14 Bandit-C 2 0.0140 (0.0144) 0.0140 (0.0144) 63.13 Akoya-B 25 0.1800 (0.17537) 0.1800 (0.17537) 64.80 *Values of parameters used for analyses are in parenthesis. Of the ten atmospheric models available in STK, only these seven were used: Jacchia 1970, Jacchia 1971, Jacchia-Roberts, CIRA 1972, MSIS 1986, MSISE 1990, and NRLMSISE 2000. Three other atmospheric models, 1976 St andard, Harris-Priester, and Jacchia 1970 Lifetime, were not used. Based on initial simulations, the 1976 Standard model is only dependent on altitude and, therefore, shows a single orbital lifetime value. Meanwhile, the Harris-Priester was found not to agree with th e other models according to Woodburn and Lynch (2005).20 The Jacchia 1970 Lifetime model was retained, in the STK version used for the analyses, for backward compatib ility to previous STK versions33F.34 The simulations were performed using the so lar flux file model SolFlx1006_Schatten.dat, the most recent file available during the time the simulations were performed. The numbers

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38 associated with the flux file names represents the month and year of the data (i.e., 1006 represents October 2006 in this case). Old files ar e retained for regression analysis. These files contain predictions of solar ra diation flux and geomagnetic i ndex values produced by K. H. Schatten in ASCII format192H.34 Updated files can be downloa ded at ftp://ftp.agi.com/pub/ DynamicEarthData and integrated into the softwa re. The solar flux sigma level was maintained at zero in order to use mean solar flux and weighted planetary geomagnetic index. The accuracy and speed of the lifetime calcula tions are defined by selecting the Advanced button, which produces the GUI shown in Figure 32. The runtime of the lifetime computation can be limited by the maximum orbit duration (dur ation), the number of or bit revolutions (orbit count) or both. The Limit Method was set to Or bit Count in this study. The orbit count limit was adjusted to a sufficiently large value that al lowed the tool to determine the lifetime of the satellite prior to termination. The number of Orbits per Calculation a nd the number of Gaussian Quadratures per orbit used were set at defau lt values to provide a compromise between the amount of computation time required and the prec ision of the computation. The Decay Altitude is the altitude at which calculation of the satellit es orbit ceases. The defa ult value, 65 km, and a value of 80 km were used for this resear ch. The default options of a checked 2nd order oblateness correction and unchecked rotating atmosphere were used. The satellites orbital elements through the duration of its lifetime can be displayed by the report and graph pane. After calculations are performe d the predicted results are di splayed in a popup window that shows a date and time in Gregorian Universal Ti me Coordinated (UTCG), number of orbits, and lifetime in days or years down to a tenth of a d ecimal. It should be emphasized that the results are estimates due to atmospheric density variatio ns and the difficulty in predicting solar activity involved with calculating a satellites or bital lifetime193H.34

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39 Figure 3-2. STK Lifetime Advanced opti on GUI (image is courtesy of AGI). STK Satellite Properties Figure 3-3 shows the basic orbit page GUI used to input the orbit properties for a satellite. On this page, the user chooses from a variety of analytic and numerical orb it propagators. Of the ten propagators available only two were appropria te for this analysis: J4Perturbation and HighPrecision Orbit Propagator (HPOP). The J4Perturba tion propagator is an analytic propagator. This propagator simply evaluates a formula in order to generate a satellites position as a function of time in a table listing or ephemeris. The J4Perturbation considers the point mass effect of the central body, the asymmetry in the central bodys gravity field, and oblateness effects. The HPOP is a numerical propagator. To generate ephemeris, HPOP uses numerical integration of the satellites differential equatio ns of motion. The HPOP can consider a full gravitational model, third-body gravity, solar radi ation pressure, and atmospheric drag to be included for analysis. A highly precise orbit ephe meris can be generated using HPOP because of the many parameter settings available for the us er. The J4Perturbation propagator was used first for testing the orbital lifetime tool and HPOP was used for more accurate orbital lifetime prediction. More detailed description of each propagator can be found in the help menu34F.35

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40 Figure 3-3. STK satellite properties GUI (image is courtesy of AGI). A simulation Start Time, Stop Time, Step Size, and Orbit Epoch was inputted. The values for the start time, stop time, and orbit epoch are typed by the user in the format as shown in Figure 3-3. The start time corresponds with th e orbit epoch and was defined to start from the default value of 1 Jul 2005 12:00: 00.000 UTCG, chosen as a possibl e satellite launch date, and incremented by one year until 2030 to see the effect of the solar cycle on orbital lifetime. The step size was left at its default value. The stop time was defined to be a day after the start date. The default classical (Keplerian ) coordinate type and J2000 c oordinate system were used for the simulations. Different sets of orbital elements and their va lues can be specified. Orbital elements obtained from the AeroCube-1 satellit es two line element (TLE) data from the failed launch 1 of the DNEPR vehicle were used for th e pico-satellite simulations, with the exception of the eccentricity value changed to zero. The orbital elements from the mission constraint goals of the MR SAT project were used for the nano-satellite simulations.

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41 Parameter Sensitivity Study Simulations were performed varying different pa rameters such as the reflection coefficient ( ), area exposed to Sun ( s A ), drag coefficient (dC ), drag area ( A ), and mass (m) available within the lifetime tool to evaluate their effect on orbital lifetime predic tion. A summary of the parameters that were constant for these scenarios is given in Table 3-2. The default epoch of 1 Jul 2005 12:00:00.000 UTCG was chosen as a la unch date. The propagator J4Perturbation was used. The orbital elements obtained from the AeroCube-1 two line element (TLE) were used. The Jacchia-Roberts atmospheric density model and a decay altitude of 80 km were used. Table 3-2. Orbital lifetime sensitivity simulation parameters Parameters Figure 3-4 to 3-8 Altitude (km): 550 Epoch Start Date: 1 Jul 2005 12:00:00.000 UTCG Propagator: J4Perturbation Semimajor Axis (km): 6927.248793 Eccentricity: 0.0064 Inclination (deg): 97.43 Argument of Perigee (deg): 189.63 RAAN (deg): 115.67 Mean Anomaly (deg): 349.58 Atmospheric Density Models: Jacchia-Roberts Two parameters were found not to have signif icant effect on orbital lifetime, namely the reflection coefficient (Figure 3-4) and area exposed to Sun (Figure 3-5). As discussed in Chapter 2, these are directly proportional to the acceler ation from solar radiation pressure, which was stated as being less effective than drag below alti tudes of 800 km. In this thesis, analyses were performed at altitudes of 750 km and lower, where such parameters are expected not to affect orbital lifetime. Consequently, the reflection coefficient was main tained at 0.01, while the area exposed to Sun value was kept the same as th e satellites drag area. number of orbits, and lifetime in days or years with one signif icant digit after the decimal of the value Four curves are shown in Figur e 3-4 representing drag coeffici ents of 2.0 (blue-diamond),

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42 2.05 (pink-square), 2.1 (green-triangle), and 2. 2 (aqua-cross). For each curve, the reflection coefficient was varied to values of 0, 0.3, 1.0, and 1.8 while the other parameters were kept at a constant value as seen in the legend. Three curves are shown in Figur e 3-5 representing drag coefficients of 2.0 (blue-diamond), 2.1 (pink-squa re), and 2.2 (green-trian gle). The area exposed to Sun was varied from 0.05, 0.5, and 1 m2 for each curve. The other parameters were kept at a constant value as seen in the legend. Both gr aphs show slopes close to zero, indicating that orbital lifetime is not affected by the reflect ion coefficient and the area exposed to Sun. The results from varying the drag coefficient, drag area, and mass are shown in Figures 3-6 to 3-8. Figure 3-6 shows a graph of the orbital lif etime vs. drag coefficient. In this graph, the drag coefficient was increased to values of 1.8 to 2.5 while the other parameters were kept at constant values as seen in the legend. Figure 37 shows a graph of orbital lifetime vs. drag area. In this graph, the drag area was increased to values of 0.05 to1 m2. Three curves were obtained using drag coefficients values of 2.0 (blue-diam ond), 2.1 (pink-square), and 2.2 (green-triangle), while holding the other parameters constant as seen in the legend. All three curves show a decrease in orbital lifetime. Figure 3-6 shows the dependence of orbital lifetime on the drag coefficient. Figure 3-7 shows a depende nce of orbital lifet ime on drag area. Figure 3-8 shows orbital lifetime vs. mass. In this graph, the value of the mass was increased to values of 1 to 5 kg while the other pa rameters were kept at constant values as seen in the legend. The graph shows an increase in orb ital lifetime as a result of the simulation. This graph shows the dependence of orb ital lifetime on mass. The thr ee figures (Figure 3-6 to 3-8) show the dependence of the orbita l lifetime on the three parameters with the given scenario. The three parameters Cd, A and m make up the ballistic coefficient, which is expected to affect orbital lifetime as defined in Chapter 2. For the studies performed in Chapter 4, 0.01 m2 as area

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43 exposed to Sun and 0.01 as reflection coefficient value were used because the sensitivity studies show them to be invariant. 0 0.5 1.0 1.5 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 Reflection coefficient ()Orbital lifetime (years) Cd=2.0 A=0.01 As=0.01 m=1 Cd=2.05 A=0.01 As=0.01 m=1 Cd=2.1 A=0.01 As=0.01 m=1 Cd=2.2 A=0.01 As=0.01 m=1 Figure 3-4. Orbital lifetime vs. reflection coefficient 0 0.2 0.4 0.6 0.8 1.0 5.2 5.3 5.4 5.5 5.6 5.7 Area exposed to Sun (m2)Orbital lifetime (years) Cd=2.0 =0.01 A=0.01 m=1 Cd=2.1 =0.01 A=0.01 m=1 Cd=2.2 =0.01 A=0.01 m=1 Figure 3-5. Orbital lifetime vs. area exposed to Sun

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44 1.8 2.0 2.2 2.4 2.6 5.0 5.2 5.4 5.6 5.8 6.0 6.2 Drag coefficient (Cd )Orbital lifetime (years) =0.01 A=0.01 As=0.01 m=1 Figure 3-6. Orbital lifetime vs. drag coefficient 0 0.2 0.4 0.6 0.8 1.0 0 0.5 1.0 1.5 2.0 2.5 3.0 Drag area (m2)Orbital lifetime (years) Cd=2.0 =0.01 As=1.01 m=1 Cd=2.1 =0.01 As=1.01 m=1 Cd=2.2 =0.01 As=1.01 m=1 Figure 3-7. Orbital lifetime vs. drag area

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45 0 1 2 3 4 5 6 0 5 10 15 20 25 30 Mass (kg)Orbital lifetime (years) Cd=2.2 =0.01 A=0.01 As=0.01 Figure 3-8. Orbital lifetime vs. mass

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46 CHAPTER 4 RESULTS AND DISCUSSION Simulations of orbital lifetimes for picoand nano-satellites were performed. The results, which are presented here, were used to study the effects of different parameters have on their lifetimes. The CubeSat volume and mass are constant parameters; in order to reduce its lifetime, the impact of increasing its cross-sectional area was investigated. The volume and mass of the nano-satellites in this study varied; thus, the im pact of different launch altitudes on each nanosatellites lifetime was studied. For both analyses different launch years were considered to see the effect of the 11-year solar cy cle. Different atmospheric density models were also explored to determine maximum, minimum, and average orbital lifetime values per launch year. Pico-satellite Results Four scenarios were simulated for the CubeSat, with varying drag areas of 0.01, 0.04, 0.06, and 0.1 m2, which will be referred to as satellite A, B, C, and D, respectively. The CubeSat simulation parameters are summarized in Table 4-1. An epoch start date of Jul 2007 12:00:00.000 UTCG was chosen as initial launch date and incr emented yearly until 2030 to determine the effect of the so lar cycle, with peaks, known as solar maxima, occurring around 2012 and 2023, and valleys, known as solar minima, at 2007, 2018, and 2029. From 2007 to 2030, a solar cycle is determined from one mi nimum to the next. These solar maxima and minima correspond to the years of highest and lo west solar radiation fl ux values, respectively, within the solar flux file S olarFlx1006_Schatten.dat. The orbital elements for these simulations closely follow the AeroCube-1 el ements, with the exception of changing the eccentricity to zero. A 600-km initial altitude was us ed since this value falls within the range at which the CubeSats would have been released from the DNEPR launch vehicle. Meanwhile, a decay altitude of 80 km was used for the pico-satellite analyses.

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47 Table 4-1. CubeSat simulation parameters Parameters Satellites A and C Satellites B and D Altitude (km): 600 600 Epoch Date: 1 Jul 2007 12:00:00.000 UTCG to 1 Jul 2030 12:00:00.000 UTCG 1 Jul 2007 12:00:00.000 UTCG to 1 Jul 2030 12:00:00.000 UTCG Propagator: HPOP HPOP Semimajor Axis (km): 6978.137 6978.137 Eccentricity: 0 0 Inclination (deg): 97.43 97.43 Argument of Perigee (deg): 189.63 189.63 RAAN (deg): 115.67 115.67 Mean Anomaly (deg): 349.58 349.58 Drag Coefficient: 2.2 2.2 Reflection Coefficient: 0.01 0.01 Drag Area (m2): 0.01 and 0.06 see figures 0.04 and 0.1 see figures Area Exposed to the Sun (m2): Same as drag area respectively Same as drag area respectively Mass (kg): 1 1 Atmospheric Density Models: Jacchia 1970, Jacchia 1971, Jacchia-Roberts, CIRA 1972, NRLMSISE 2000, MSISE 1990, MSIS 1986 Jacchia 1970, Jacchia 1971, Jacchia-Roberts Seven atmospheric density models were used for satellite A (Figure 4-1) and satellite C (Figure 4-2). The data show trends for certa in atmospheric density models, producing maximum, minimum and average orbita l lifetime values per launch year. For the pico-satellites, orbital lifetimes for four conseque nt years, starting at 2007, were an alyzed for satellites B and D, using the seven atmospheric density models. Fr om these results, those models that produced maximum, minimum and close to average orbital lifetime values were determined; these were then used for the rest of the simulations in order to reduce the analysis time. The results for satellites A, B, C, and D (Fi gure 4-3) were plotted using the average lifetime values as a curve, while maximum and mini mum orbital lifetime values are shown as error bars. The orbital lifetime for satellite A ranged fr om 17 to 27 years, with an average curve value of 22 years, while that for satellite B is between 2.5 and 9 years, with a mean of 6 years. The lifetime for satellite C varied from 1 to 8 years, w ith an average of 4 years, while that for satellite D were 1 to 5.6 years, with a mean of 3 years. As expected, the orbital lifetimes for satellites B,

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48 C, and D were shorter compared to satellit e A due to their low ballistic coefficients.14 2005 2009 2013 2017 2021 2025 2029 0 5 10 15 20 25 Launch yearOrbital lifetime (years) Jacchia 1970 Jacchia-Roberts CIRA 1972 NRLMSISE 2000 MSISE 1990 MSIS 1986 Jacchia 1971 Figure 4-1. Orbital lifetime results for satell ite A using seven atmos pheric density models 2005 2009 2013 2017 2021 2025 2029 0 5 10 15 20 25 Launch yearOrbital lifetime (years) Jacchia 1970 Jacchia 1971 Jacchia-Roberts CIRA 1972 NRLMSISE 2000 MSISE 1990 MSIS 1986 Figure 4-2. Orbital lifetime results for satell ite C using seven atmospheric density models

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49 2005 2009 2013 2017 2021 2025 2029 0 5 10 15 20 25 30 35 Launch yearOrbital lifetime (years) satellite A satellite B satellite C satellite D Figure 4-3. Orbital lifetime results for satell ites A, B, C, and D at 600-km initial altitude A 75% reduction in orbital lifetime can be seen as the drag area is enlarged from 0.01 to 0.06 m2, when comparing the values for satellites A and C. A reduction of at least 40% can be seen by comparing the average orbital lifetime of sa tellite B to D, 30% from satellite B to C and about 25% from satellite C to D. The orbital lif etime for the CubeSat is greatly minimized when the drag area is increased to ten times its original size. Orbital lifetime minima occur at about 2010 and 2021 for satellite A, at 2011 and 2022 for satellites B and C, and at 2012 and 2023 for satell ite D (corresponding to solar cycle maxima). Analyses show orbital lifetimes of 23, 5.0, 2. 4, and 1.4 years for satellite A, B, C and D, respectively, for a launch at 2012. Varying orbi tal lifetimes results from differences in the satellites ballistic coefficients, the highest of which is observed for Satellite A (see Table 3-1), followed by B, then C, and minimum for D. Due to the high ballistic coefficient of satellite A, its orbit does not decay as rapidly14 as the others; moreover, it pushes through at least 2 solar cycle minima at 2018 and 2029 and a maximum at 2023. Satellite B enco unters a solar cycle

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50 maximum at 2012 and reenters the atmosphere a year before the next cycle minimum. Satellite C and D experience a solar maximum only at 2012 and their orbits decays within the following 3 years. The orbits of satellites B, C, and D decay rapidly when launched during a solar maximum due to their low ballistic coefficients.14 Nano-satellites Results The nano-satellite simulation parameters ar e summarized in Table 4-2 for MR SAT and MRS SAT, Table 4-3 for FASTRAC, and Table 44 for Akoya-B and Bandit-C. The epoch start of Jul 2007 12:00:00.000 UTCG was chosen as a possible launch date and incremented by a year until 2030 to see the effect of the solar cycl e. For all the simulations, a default decay altitude of 65 km was used. Each satellites orbital lifetime was simulated at two different altitudes and inclination: (1) at 350-km altitude and 51.6 inclination, similar to the orbit of a typical international space shuttle mission; and, (2) 750-km altitude and 57 inclination, obtained from the mission constraint goals of the MR SAT proj ect. Atmospheric density models for the simulations were selected by means of the same method s used for satellite B and D. The results were plotted using the average lifetime values as the curve, and the maximum and minimum values as error bars. Simulations were also performed to obtain orbital lifetimes for MR SAT, studying the effect of different initial altitudes. The paramete rs used are summarized in Table 4-5. An epoch start date of Jul 2007 12:00: 00.000 UTCG was chosen as a possible launch date and incremented by yearly until 2030 to see the effect of the solar cycle. The simulation begins at 350-km initial altitude and is incremented by 50 km until 750 km. An inclination of 51.6 was used. A decay altitude of 65 km was used. Atmospheric density models used for the simulations were determined by the same method as for satellite B and D per launch altitude. For each launch year, the maximum and minimum orbital lifetime va lues are represented as error bars and the

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51 average lifetime values as a curve obtained from the atmospheric density model results. These values were then used to plot the orbi tal lifetime versus altitude for MR SAT. Table 4-2. MR SAT and MR S SAT simulation parameters Parameters Figure 4-4 Figure 4-5 Altitude (km): 350 750 Epoch Date: 1 Jul 2007 12:00:00.000 UTCG to 1 Jul 2030 12:00:00.000 UTCG 1 Jul 2007 12:00:00.000 UTCG to 1 Jul 2030 12:00:00.000 UTCG Propagator: HPOP HPOP Semimajor Axis (km): 6728.137 7128.137 Eccentricity: 0 0 Inclination (deg): 51.6 57 Argument of Perigee (deg): 0 0 RAAN (deg): 0 0 Mean Anomaly (deg): 0 0 Drag Coefficient: 2.2 2.2 Reflection Coefficient: 0.01 0.01 Drag Area (m2): MR SAT = 0.108122 MRS SAT = 0.080478 MR SAT = 0.108122 MRS SAT = 0.080478 Area Exposed to the Sun (m2): MR SAT = 0.108122 MRS SAT = 0.080478 MR SAT = 0.108122 MRS SAT = 0.080478 Mass (kg): MR SAT = 28.25 MRS SAT = 11.45 MR SAT = 28.25 MRS SAT = 11.45 Atmospheric Density Models: Jacchia-Roberts, CIRA 1972, NRLMSISE 2000 Jacchia 1970, Jacchia-Roberts, MSIS 1986 Table 4-3. FASTRAC simulation parameters Parameters Figure 4-6 Figure 4-7 Altitude (km): 350 750 Epoch Date: 1 Jul 2007 12:00:00.000 UTCG to 1 Jul 2030 12:00:00.000 UTCG 1 Jul 2007 12:00:00.000 UTCG to 1 Jul 2030 12:00:00.000 UTCG Propagator: HPOP HPOP Semimajor Axis (km): 6728.137 7128.137 Eccentricity: 0 0 Inclination (deg): 51.6 57 Argument of Perigee (deg): 0 0 RAAN (deg): 0 0 Mean Anomaly (deg): 0 0 Drag Coefficient: 2.2 2.2 Reflection Coefficient: 0.01 0.01 Drag Area (m2): top = 0.195397 bottom = 0.193597 top = 0.195397 bottom = 0.193597 Area Exposed to the Sun (m2): top = 0.195397 bottom = 0.193597 top = 0.195397 bottom = 0.193597 Mass (kg): top = 15.4639 bottom = 12.5757 top = 15.4639 bottom = 12.5757 Atmospheric Density Models: Jacchia-Roberts, CIRA 1972, NRLMSISE 2000 Jacchia 1970, Jacchia-Roberts, NRLMSISE 2000, MSIS 1986

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52 Table 4-4. Akoya-B and Bandit-C simulation parameters Parameters Figure 4-8 Figure 4-9 Altitude (km): 350 750 Epoch Date: 1 Jul 2007 12:00:00.000 UTCG to 1 Jul 2030 12:00:00.000 UTCG 1 Jul 2007 12:00:00.000 UTCG to 1 Jul 2030 12:00:00.000 UTCG Propagator: HPOP HPOP Semimajor Axis (km): 6728.137 7128.137 Eccentricity: 0 0 Inclination (deg): 51.6 57 Argument of Perigee (deg): 0 0 RAAN (deg): 0 0 Mean Anomaly (deg): 0 0 Drag Coefficient: 2.2 2.2 Reflection Coefficient: 0.01 0.01 Drag Area (m2): Akoya-B = 0.17537 Bandit-C = 0.0144 Akoya-B = 0.17537 Bandit-C = 0.0144 Area Exposed to the Sun (m2): Akoya-B = 0.17537 Bandit-C = 0.0144 Akoya-B = 0.17537 Bandit-C = 0.0144 Mass (kg): Akoya-B = 25 Bandit-C = 2 Akoya-B = 25 Bandit-C = 2 Atmospheric Density Models: Jacchia-Roberts, CIRA 1972, NRLMSISE 2000 Jacchia 1970, Jacchia-Roberts, MSIS 1986 Table 4-5. MR SAT with different in itial altitudes simulation parameters Parameters Figure 4-10 Altitude (km): 350 to 750 Epoch Date: 1 Jul 2007 12:00:00.000 UTCG to 1 Jul 2030 12:00:00.000 UTCG Propagator: HPOP Semimajor Axis (km): 6728.137 to 7128.137 Eccentricity: 0 Inclination (deg): 51.6 Argument of Perigee (deg): 0 RAAN (deg): 0 Mean Anomaly (deg): 0 Drag Coefficient: 2.2 Reflection Coefficient: 0.01 Drag Area (m2): 0.108122 Area Exposed to the Sun (m2): 0.108122 Mass (kg): 28.25 Atmospheric Density Models: Jacchia 1970, Jacchia 1971, Jacchia-Roberts, CIRA 1972, NRLMSISE 2000, MSISE 1990, MSIS 1986 The results for MR SAT and MRS SAT (Figure 4-4), with an initia l altitude of 350 km, show orbital lifetime values between 140 and 370 days for the former, with an average curve value of 247 days, and between 80 and 210 days fo r the latter, with an average curve of

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53 141 days. Orbital lifetime minima for the averag e curves in Figure 4-4 occur at 2012 and 2023 for both satellites. On the other hand, the resu lts at 750-km initial altitude (Figure 4-5) show orbital lifetime values between 460 and 540 years for MR SAT, with an average curve value of 495 years, and between 250 and 300 years for MRS SAT, with an averag e curve value of 269 years. The lifetime minima for the averag e curve in Figure 4-5 occur at 2011 and 2021 for MR SAT, and at 2011 and 2020 for MRS SAT. At an initial altitude of 350 km, the results for the FASTRAC top and the bottom satellites (Figure 4-6), show orbital lifetime values for FASTRAC top is between 50 and 125 days, with an average curve value of 86 days, and from 40 to 110 days for the bottom, with an average curve value of 72 days. Orbital lifetime minima for th e average curves in Figu re 4-6 occur at 2012 and 2023 for both satellites. On the other hand, results at 750-km initial altitude (Figure 4-7) show orbital lifet ime values between 140 and 165 years, with an average curve value of 151 years for the top satellite, and from 110 to 135 y ears for the bottom satell ite, with an average curve value of 122 years. Orbita l lifetime minima for the average curves in Figure 4-7 occur at about 2011 and 2021 for the top satellite and at about 2010 and 2020 for the bottom satellite. The results for Akoya-B and Bandit-C at an in itial altitude of 350 km (Figure 4-8) show orbital lifetime values between 86 and 210 days w ith an average curve value of 141 days for both satellites. Orbital lifetime minima for the av erage curves in Figure 4-8 occur at 2012 and 2023 for both satellites. Meanwhile, the results at 750km initial altitude (Fi gure 4-9) show orbital lifetime values between 255 and 295 years for Akoya -B, with average curve value 270 years, and from 250 to 285 years for Bandit-C, with an aver age curve value of 263 y ears. Orbital lifetime minima for the average curves in Figure 49 occur at 2011 and 2022 for Akoya-B, and at about 2010 and 2021 for Bandit-C.

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54 The orbital lifetimes of the nano-satellites are in centuries at 750-km initial altitude, in contrast to less than 400 days at 350-km initial altitude. For both initial altitudes, the FASTRAC bottom satellite, having the lowest ballistic coeffici ent of the nano-satellites studied, had shortest orbital lifetime values; meanwhile MR SAT has the longest as a result of having the highest ballistic coefficient. The orbital lifetimes for MR SAT at varying initial orbit is shown in Figure 4-10. Its average lifetime at 500 km is 11 y ears, more than twice the life time at 450 km, and more than 5 times compared to that at 400 km. This pattern continues up to 750-km initi al orbit. At about 550 km, the curves merge as they progress thr ough several solar cycles, making the launch date insignificant.at higher altitudes.14 The pattern indicates orbital lifetimes greater than 25 years at altitudes greater than 550-km. 2005 2009 2013 2017 2021 2025 2029 0 50 100 150 200 250 300 350 400 Launch yearOrbital lifetime (days) MR SAT MRS SAT Figure 4-4. Orbital lifetime for MR SA T and MRS SAT at 350-km initial altitude

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55 2005 2009 2013 2017 2021 2025 2029 150 200 250 300 350 400 450 500 550 Launch yearOrbital lifetime (years) MR SAT MRS SAT Figure 4-5. Orbital lifetime for MR SA T and MRS SAT at 750-km initial altitude 2005 2009 2013 2017 2021 2025 2029 20 40 60 80 100 120 Launch yearOrbital lifetime (days) FASTRAC top sat FASTRAC bottom sat Figure 4-6. Orbital lifetime for the FASTRA C satellites at 350-km initial altitude

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56 2005 2009 2013 2017 2021 2025 2029 90 100 110 120 130 140 150 160 170 Launch yearOrbital lifetime (years) FASTRAC top sat FASTRAC bottom sat Figure 4-7. Orbital lifetime for the FASTRA C satellites at 750-km initial altitude 2005 2009 2013 2017 2021 2025 2029 40 60 80 100 120 140 160 180 200 Launch yearOrbital lifetime (days) Akoya-B Bandit-C Figure 4-8. Orbital lifetime for the Akoya-B and Bandit-C at 350-km initial altitude

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57 2005 2009 2013 2017 2021 2025 2029 230 240 250 260 270 280 290 300 Launch yearOrbital lifetime (years) Akoya-B Bandit-C Figure 4-9. Orbital lifetime for the Akoya-B and Bandit-C at 750-km initial altitude 300 400 500 600 700 800 10-1 100 101 102 103 Altitude (km)Orbital lifetime (years) Figure 4-10. Orbital lifetime for the MR SAT using different initial altitudes

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58 CHAPTER 5 CONCLUSION AND RECOMMENDATIONS Conclusions Lifetime analyses of picoand nano-satellites were conducted using th e Satellite Tool Kit (STK) orbital Lifetime tool. The pico-satellite analyses were performed on the standard CubeSat developed by CalPoly and Stanford, whereas the nano-satellite analyses were performed on three randomly selected satellites from the University Nano-satellite Program (UNP). Typical mission scenarios for these two classes of satellites were investigated. Since the prediction of orbital lifetime is not an exact science, parameters which have an effect on the prediction were varied to provide ranges of expected lifetimes for the different scenarios. The results indicate that orbital lifetimes of pico-satellites can be significantly reduced by increasing their drag area from 0.01, to 0.04, 0.06 or 0.1 m2. The longest that the CubeSat is predicted to stay up in orbit at a 600 km altitude with a drag area of 0.01 m2 is approximately 27 years, which is slightly above the FCC debris mitigation guidelines. The longest that the CubeSat is predicted to stay in orbit at a 600 km altitude with a drag area of 0.04 m2 is about 8.8 years, 0.06 m2 is about 7 years, and 0.1 m2 about 5.5 years. Changi ng the drag area of a 1-kg satellite from 0.01 to 0.1 m2 decreased its orbital lifetime from an average of 22 to 3 years and results in 86% reduction. The results show th at changing the drag areas to 0.04 or 0.1 m2 did not make a significant difference to the reduced total am ount of lifetime of the sa tellite than the drag area of 0.06 m2. At 600 km above the Earths surface, a pico-satellite with drag area of 0.1 m2 had minimum orbital lifetimes during years of hi ghest solar activity due to its low ballistic coefficient. At this same altitude, pico-satell ites with smaller drag areas, which results in higher ballistic coefficient, responded more slowly to the solar activity and as a result the orbital lifetime minimums appear shifted from solar maximum years. This analysis implies that passive

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59 de-orbiting devices such as drag chutes can be effective devices for a ddressing orbital debris mitigation. The analyses also imply that in or der to obtain minimum orbital lifetimes to set the launch year of the satellite co rresponding with high solar activity that is at solar maximum. The nano-satellites used in this study were between 11 to 28 kg, with drag areas from 0.08 and 0.2 m2. The results of the nano-sa tellites analyses, with a la unch altitude of 350 km, show that the orbital lifetimes are in number of days. At this altitude the satellites will reenter the atmosphere in a short amount of time. Thes e lifetime values will meet the FCC mitigation guidelines. The results of the na no-satellites analyses, wi th an altitude of 750 km, show that the orbital lifetimes are in centuries. At this high a ltitude the nano-satellites orbital lifetime will not meet the FCC mitigation guidelines. Values indi cate that additions to the nano-satellites are needed to fulfill the 25 year orbital lifetime require ments at this altitude. The nano-satellites in high orbit, above 500 km, have a problem of pot entially becoming a debris space. The nanosatellites do not have a volume or mass requireme nt as the CubeSats, therefore these were kept constant respectively per satellite and only the effect of a change in altitude on their orbital lifetimes were investigated. Recommendations There are different parameters to consider with prediction of long-term orbital lifetime and its reduction. Satellites propert ies (i.e., geometry, mass and th e solar activity, have significant effects on these. For mission operations the implementation of an aerobraking technique for both CubeSats and nano-satellites, that is a change in their drag area, should be further investigated. For mission planning the consideration of proposed sa tellites to be launched during the solar maximum time period should be further investigated.

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60 LIST OF REFERENCES 1.National Research Council (U.S) Comm ittee on Space Debris, Orbital Debris: A Technical Assessment, National Academy Pres s, Washington, DC, 1995, Chaps. 4, 8. 2.NASA Safety Standard: Guidelines and A ssessment Procedures for Limiting Orbital Debris, NSS 1740.14, August 1995. 3.Flury, W., Space Debris, Preparing for the Future [online], Vol. 4, No. 4, 1994, http://esapub.esrin.esa.it/pff/pffv4n4/ ppfflunr4.htm [retrieved 26 June 2007]. 4.Aerospace Corporation, Center for Orbital and Reentry Debris Studies, Space Debris Basics: What is the Future Trend?, http:// www.aero.org/capabilities/cord s/debris-future.html [accessed 26 June 2007]. 5.Walker, S. H., Responsive A ccess and Infrastructure, Proceedings of DarpaTech 2005 Defense Advance Research Project Agency (DARPA), Anaheim, CA, August 2005, pp. 203-207. 6.Calpoly, CubeSat, Mission Statemen t, http://cubesat.atl.calpoly.edu/ pages/home/mission-statement.php [accessed on 30 June 2007]. 7.AFOSR, AFRL Space Vehicles, AIAA, NA SA, SMC Det 12, About the University Nanosatellite Program, http://www.vs.afrl. af.mil/UNP/About.html [accessed on 19 July 2007]. 8.Orbital Debris Program Office, NASA Johns on Space Center, Orbital Debris Education Package, http://www.orbitaldebris.jsc.nasa.gov/ library/EducationPackage.pdf [retrieved 11 July 2007]. 9.Technical Report On Space Debris, Un ited Nations, (A/AC.105/720), New York, 1999. 10. Orbital Debris Program Office, NASA Johnson Space Center, Orbital Debris Mitigation, http://www.orbitaldebris.jsc.nasa .gov/mitigate/mitigation. html [accessed 27 June 2007]. 11. U.S. Government Begins Orbital De bris Meetings with Industry, The Orbital Debris Quarterly News Vol. 4, No. 4, 1999, p. 4. 12. U. S. Government Orbital Debris Mitiga tion Standard Practices at the Johnson Space Center [online], 1997, http://www.orbitaldebris.jsc.nasa.gov/library/ USG_OD_Standard_Practices. pdf [accessed 1 July 2007]. 13. In the Matter of Mitigation of Orbital Debr is, Federal Communications Commission, FCC 04-130, Washington, DC, June 2004, p. 2. 14. Wertz, J. R., and Larson, W. J., Space Mission Analysis and Design 3rd ed., Microcosm Press, Torrence, CA, 1999, Chaps. 5, 6, 8.

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61 15. IADC Space Debris Mitigation Guidelines, Inter-Agency Space Debris Coordination Committee, IADC-02-01, October 2002. 16. Calpoly, CubeSat, Dnepr Launch Vehi cle Status Integrated for Launch, http://cubesat.atl.calpoly.edu/pages/missions/ dnepr-launch-2/satellite-status.php [accessed 30 June 2007]. 17. AMSAT, Cubesat Information, http://www.amsat.org/amsatnew/satellites/cubesats.p hp [accessed 27 June 2007]. 18. Orbital Debris Program Office, NASA Johnson Space Center, Orbital Debris Graphics, http://www.orbitaldebris.jsc.nasa.gov/photoga llery/beehives.html#leo [accessed 27 June 2007]. 19. Bate, R. R., Mueller, D. D., and White, J. R., Two-body Orbital Mechanics, Fundamentals of Astrodynamics Dover Publications, Inc., New York, 1971, Chap. 1. 20. Woodburn, J., and Lynch, S., A Numerical Study of Orbital Lifetime (revised), Proceedings of the 2005 AAS/AIAA As trodynamics Specialists Conference Paper No. AAS 05-297, Lake Tahoe, CA, August 2005. 21. De Lafontaine, J., and Garg, S. C., A revi ew of satellite lifetime and orbit decay prediction, Proc. Indian Acad. Sci. (Engg. Sci.) Vol. 5, Pt. 3, September 1982, pp. 197-258. 22. Ladner, J. E., and Ragsdale, G. C., Earth Orbital Satellite Life time, NASA TN D-1995, January 1964. 23. Vallado, D. A., Special Perturbation Techniques, Fundamentals of Astrodynamics and Applications 2nd ed., Microcosm Press, El Segundo, CA, 2001, Chap. 8. 24. Orr, L.H., Users Guide for Langley Res earch Center Orbital Lifetime Program, NASA TM-87587, September 1985. 25. Battin, R. H., Variation of Parameters, An Introduction to the Mathematics and Methods of Astrodynamics, Revised Edition Revised ed., American Ins titute of Aeronautics and Astronautics, Inc., Reston, VA, 1999, Chap. 10. 26. Belcher, S. J., Rowell, L. N., and Smith, M. C., Satellite Lifetime Program, The Rand Corporation, RM-4007-NASA, April 1964. 27. Space Mission Analysis and Design, SatLife Stand-Alone Module v1.0, http://www.smad.com/software/agimo3.html [accessed 21 May 2007]. 28. Alan Pickup, Satellite tracking and decay information, http://www.wingar.demon.co.uk/ satevo [accessed 21 June 2007]. 29. Analytical Graphics, Inc., About AGI, h ttp://www.agi.com/corporate [accessed 27 June 2007].

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62 30. Analytical Graphics, Inc., STK Editions http://www.agi.com/products/desktopApp/ stkFamily/editions/index.cfm?tab=key [accessed 27 June 2007]. 31. University of Missouri-Rolla, Conceptual Design of the MR SAT Tethered Satellite Project at the University of Missouri-Rolla: 1.0 Structures, http://web.umr.edu/~mrsat/docs.html [accessed 12 February 2007]. 32. Holt, G., Stewart, S., Mauldin, J., Campbell, T., Eckhoff, P., Yeldell, S., Greenbaum, J., Linford, M., Diaz-Aguado, M., Wang, T., Berthold, T., Lightsey, E. G., Raja, L. L., Ebinuma, T., FASTRAC Mission Plan: Formation Autonomy Sp acecraft with Thrust, Rel-Nav, Attitude and Crosslink, The University of Texas at Austin, Austin, TX, December 2005. 33. Washington University, Welcome to the Washington University Nanosat Page, http://www.me.wustl.edu/faculty/mas/n anosat [accessed 12 February 2007]. 34. Analytical Graphics, Inc., Lifetime Tool, http://www.agi.com/resources/ help/stk613/helpSystem/stk/tools11.htm [accessed 1 July 2007]. 35. Analytical Graphics, Inc ., Satellite Orbits, http://www.agi.com/resources/ help/stk613/helpSystem/stk/vehSat_or bitTab.htm [accessed 1 July 2007].

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63 BIOGRAPHICAL SKETCH The author was born in Quezon City, Philippines. She immigrated to the United States in Illinois on October 15, 1988. She received her bachelors degree in El ectrical Engineering on December 2002 from the University of Illinois at Chicago. In August 2007, she moved to Florida to attend the University of Florida in Ga inesville. She received her masters degree in Mechanical Engineering in D ecember 2007 with a concentration in dynamics and control.


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