Simplified Population Growth Modeling for Low Earth
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SIMPLIFIED POPULATION GROWTH MODELING FOR LOW EARTH ORBIT by THOMAS PERCY A DISSERTATION Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in The Department of Mechanical & Aerospace Engineering to The School of Graduate Studies of The University of Alabama in Huntsville HUNTSVILLE, ALABAMA 2015 i In presenting this dissertation in partial fulfillment of the requirements for a doctoral degree from The University of Alabama in Huntsville, I agree that the Library of this University shall make it freely available for inspection. I further agree that permission for extensive copying for scholarly purposes may be granted by my advisor or, in his/her absence, by the Chair of the Department or the Dean of the School of Graduate Studies. It is also understood that due recognition shall be given to me and to The University of Alabama in Huntsville in any scholarly use which may be made of any material in this dissertation. ____________________________ ___________ (student signature) (date) ii DISSERTATION APPROVAL FORM Submitted by Thomas Percy in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Aerospace Systems Engineering and accepted on behalf of the Faculty of the School of Graduate Studies by the dissertation committee. We, the undersigned members of the Graduate Faculty of The University of Alabama in Huntsville, certify that we have advised and/or supervised the candidate on the work described in this dissertation. We further certify that we have reviewed the dissertation manuscript and approve it in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Aerospace Systems Engineering. _________________________________________ Committee Chair (Date) _________________________________________ _________________________________________ _________________________________________ _________________________________________ _________________________________________ Department Chair _________________________________________ College Dean _________________________________________ Graduate Dean iii ABSTRACT The School of Graduate Studies The University of Alabama in Huntsville Degree Doctor of Philosophy College/Dept. Mechanical & Aerospace Engineering Name of Candidate Thomas Percy Title Simplified Population Growth Modeling For Low Earth Orbit_____________ The accumulation of 50 years’ worth of man-made space objects has increased the risk of catastrophic collisions. Continuing to operate in a business-as-usual manner will one day render regions of LEO unusable. The landscape of future LEO satellite operations is complicated by the evolving nature of space policy and the emergence of the CubeSat which has the potential to radically shift the current LEO satellite market. Long-term population modeling is required to predict population growth, support policy decisions, and inform industry best practices. Many space agencies around the world have high-fidelity analysis codes to serve this function but they are complex and computationally expensive. The Simplified LEO Orbital Object Population (SLOOP) model has been developed to provide a broader user base a simplified, reasonably accurate prediction tool for rapidly evaluation future scenarios. Expanding on previous simplified population models for LEO, new algorithms for evaluating fragment and intact object populations over time were developed. These algorithms add spatial fidelity and allow the evaluation of LEO as a series of layers rather than one large region of space. This addition enables more specific evaluations of LEO populations. Differential equations and coefficients that represent various contributors to iv the orbital object populations were investigated and modified. To support this development, a new comprehensive orbital object database was created, integrating several data sources. A new model of atmospheric density was created to fill a gap in available data and help quantify natural orbit decay times at high LEO altitudes. Comparisons of the SLOOP model with benchmark data from current high- fidelity models show only a +/- 5% error over a 100 year simulation. This level of agreement indicates that, for the first time, a simplified model can direct higher-fidelity studies by identifying trends with reasonably high accuracy in a fraction of the run time. A sample SLOOP analysis evaluating the impact of deploying large CubeSat constellations shows the power of the model to rapidly evaluate future operating scenarios. Overall, the data presented shows that with enhanced algorithms, improved use of demographic data, and faster simulations, the SLOOP model fills an important role in orbital debris analysis. Abstract Approval: Committee Chair _______________________________________ Department Chair _______________________________________ Graduate Dean _______________________________________ v ACKNOWLEDGEMENTS The work described in this dissertation would not have been possible without the support of several people who deserve recognition for their contributions. First I would like to thank my advisor, Dr. D. Brian Landrum, for his guidance throughout this process and his support on my publications. Second, the other members of my committee have provided excellent suggestions through the course of my research. I must also thank my managers at Science Applications International Corporation not only for their financial contribution to my education but for their support and encouragement along the way. I would further like to recognize the engineers and scientists at NASA’s Marshall Space Flight Center, and specifically those with whom I have the great pleasure of working at the Advanced Concepts Office, for their support and for initially involving me in the analysis work in orbital debris that inspired this research topic. Finally, I would like to dedicate this work to my children, Abby Rose, Brady, and Colin and to my wife, Erin. Your immense patience and unwavering encouragement and support have carried me through this long journey. I will be forever indebted to you for allowing me the time and energy to pursue this work and I cannot wait to rejoin our regularly scheduled life, already in progress. vi TABLE OF CONTENTS Page LIST OF FIGURES ………..………………………………………………………..……………x LIST OF TABLES ……….………………………………………….…………………………xv CHAPTER 1: INTRODUCTION ................................................................................................ 1 CHAPTER 2: BACKGROUND AND LITERATURE REVIEW .............................................. 6 2.1 Populations and Collisions ................................................................................... 7 2.1.1 It’s crowded up there ...................................................................................... 9 2.1.2 And even more crowded in the future ........................................................... 11 2.1.3 LEO crowd control ....................................................................................... 14 2.1.4 The Business of Space .................................................................................. 17 2.2 A Brief History of Orbital Object Population Modeling .................................... 19 2.2.1 Predicting Collisions ..................................................................................... 19 2.2.2 Simplified Approaches to Population Analysis ............................................ 22 2.2.3 The High-Fidelity Approach ......................................................................... 24 2.2.4 The Reemergence of the Simplified Model .................................................. 27 CHAPTER 3: DEVELOPMENT OF THE SLOOP MODEL ................................................... 32 3.1 Establishing a Baseline for Comparison ............................................................ 33 3.2 An Evaluation of the Lafleur Simplified LEO Population Model ..................... 37 3.3 The SLOOP Model Structure ............................................................................. 44 vii CHAPTER 4: CALCULATION OF COEFFICIENT VALUES FOR THE SLOOP MODEL 52 4.1 Combining Data Sources .................................................................................... 52 4.1.1 The Joint Space Operations Center Catalog ................................................. 53 4.1.2 The SATCAT Database ................................................................................ 55 4.1.3 The Union of Concerned Scientists Database ............................................... 57 4.1.4 The Satellite Tool Kit Database and Other Spacecraft References............... 58 4.1.5 MASTER2009 .............................................................................................. 58 4.2 Calculating Coefficients ..................................................................................... 60 4.2.1 The Launch Term .......................................................................................... 62 4.2.2 The Orbit Decay Terms ................................................................................ 73 4.2.3 The Object Collision Terms .......................................................................... 91 4.2.4 The Fragmentation Terms ........................................................................... 104 4.2.5 Post-Mission Disposal Rate ........................................................................ 111 4.3 Initial Population Data ..................................................................................... 111