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The Full Two-Body-Problem: Simulation, Analysis, and Application to the Dynamics, Characteristics, and Evolution of Binary Asteroid Systems

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The Full Two-Body-Problem: Simulation, Analysis, and Application to the Dynamics, Characteristics, and Evolution of Binary Asteroid Systems THE FULL TWO-BODY-PROBLEM: SIMULATION, ANALYSIS, AND APPLICATION TO THE DYNAMICS, CHARACTERISTICS, AND EVOLUTION OF BINARY ASTEROID SYSTEMS by Eugene Gregory Fahnestock A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy (Aerospace Engineering) in The University of Michigan 2009 Doctoral Committee: Professor Daniel J. Scheeres, Chair Professor Michael R. Combi Professor N. Harris McClamroch Senior Research Scientist Steven J. Ostro, Jet Propulsion Laboratory c Eugene Gregory Fahnestock 2009 DEDICATION To the Creator of the Universe, including the many small worlds I have had the joy and pleasure of studying in conducting the work herein, and many more worlds yet to become known to mankind. ii ACKNOWLEDGEMENTS I would like to acknowledge all those who have made it possible for me to pro- duce this dissertation, directly and indirectly. Foremost, I would like to thank my advisor, Dan Scheeres, for his encouragement, guidance, and constructive oversight in pursuing my graduate studies. I also wish to thank him for making possible so many opportunities that have shaped my professional development, and for his advice both in matters of academic research and otherwise. I would also like to thank all of those who instructed me and mentored me both at the Ohio State University and at the University of Michigan, thereby enabling and encouraging me to embark on the path of conducting this research. In addition I would like to thank the members of my committee for taking the time and effort from their busy schedules and professional pursuits to give input for this dissertation, and in most cases collaborating with me earlier in research and paper-writing. In particular I would like to thank Steve Ostro for providing valuable data for the work described herein, supercomputer access, advice, and the example of someone playing a key role in shaping the field of asteroid studies as it is today. I also thank others in various fields with whom I’ve had the privilege of collaborat- ing, including Alan W. Harris (the elder), Taeyoung Lee, Jean-Luc Margot, Melvin Leok, Petr Pravec, and many more. I would also like to thank R. Scott Erwin, Seth Lacy, and others at AFRL for helping to persuade me to pursue my graduate studies in the first place, and Scott in particular for his unflagging support since then. iii I would also like to gratefully acknowledge the generous financial support provided at various stages during my graduate studies by the University of Michigan Aerospace Engineering Department, by the Air Force Office of Scientific Research through the National Defense Science and Engineering Graduate Fellowship Program, and by the National Science Foundation through its Graduate Research Fellowship Program. I would also like to thank those at the Air Force Research Laboratory, the Lockheed Martin Corporation, the Jet Propulsion Laboratory at California Institute of Tech- nology, NASA Ames, and the University of California System who provided me with interim employment, support, and/or great professional experiences at various times in my career thus far. Finally, but most importantly, I would like to thank my parents for their strong and unwavering support in all of my pursuits and endeavors over all the years, and without which this dissertation would never have come about. iv TABLE OF CONTENTS DEDICATION .................................. ii ACKNOWLEDGEMENTS .......................... iii LIST OF FIGURES ............................... viii LIST OF TABLES ................................ xii LIST OF APPENDICES ............................ xiv ABSTRACT ................................... xv CHAPTER I. Introduction .............................. 1 II. Development and Implementation of F2BP Simulation Method- ology ................................... 12 2.1 Polyhedral Formulation for Mutual Potential . 15 2.2 Gradients of Polyhedral Formulation for Mutual Potential . 17 2.2.1 Computing force terms for EOM describing absolute motion in inertial frame . 17 2.2.2 Computing force terms for EOM describing relative motion in a body-fixed frame . 20 2.2.3 Computing torque terms for EOM describing abso- lute motion in inertial frame . 21 2.2.4 Computing torque terms for EOM describing relative motion in a body-fixed frame . 27 2.3 Incorporation of Gradients into F2BP Equations of Motion . 27 2.4 Simulation Package Implementation with Parallelization . 35 2.5 Simulation Package Validation, and Performance Gains . 40 2.5.1 Test cases with a pair of octahedral bodies . 41 2.5.2 Test case using a pair of artificial asteroid mesh mod- els of intermediate size . 46 v 2.5.3 Test case using large-sized binary asteroid compo- nent models . 53 III. Application of F2BP Simulation Methodology to Binary NEA (66391) 1999 KW4 .......................... 60 3.1 Nominal Model of KW4 System . 63 3.2 Variations Relative to Nominal Model of KW4 to Explore Sys- tem Excitation . 67 3.3 Possible Relaxed and Excited Dynamical Configurations for KW4 and Similar Systems . 68 3.4 Demonstration of Perihelion Passage Excitation . 73 IV. Analytical Formulae Describing F2BP Motion of KW4-Like Systems and Estimation of Their Characteristics . 84 4.1 Representation for Mutual Potential to Second Degree and Order 85 4.2 Effect of Primary Oblateness on Mutual Orbit Elements . 87 4.3 Effect of Primary Oblateness on Primary Spin Axis Orientation 97 4.4 Effect of Secondary Triaxiality on Librational Dynamics of the Secondary . 108 4.5 Utility of Analytical Formulae for Mass Property Measurement 114 V. Simulation and Analysis of Particle Motion within Binary Asteroids ................................ 116 5.1 Methodology for Precise Dynamic Simulation of Test Particles within F2BP . 117 5.2 Analysis of RF3BP Particle Trajectory Results . 123 5.3 Investigation of Ejecta from Binary Components . 125 5.3.1 Setup for simulating batches of ejecta particles . 126 5.3.2 Ejecta particle dispositions and binary component angular momentum changes . 130 5.4 Investigation of Primary Equator Regolith Lofting and Hy- pothesized Binary Evolution Mechanism . 138 5.4.1 Precise dynamic simulation results . 141 5.4.2 Novel probabilistic mapping approach . 147 5.4.3 Results and implications . 161 5.5 Investigation of Spacecraft and Debris Trajectory Stability within Binaries . 175 5.5.1 System setup and parameter space to be explored . 177 5.5.2 Global stability characterization results . 181 5.5.3 Technique for improvement of local stability charac- terization . 190 5.5.4 Local stability characterization results . 194 vi 5.5.5 Findings applicable to design of future space missions to binary asteroids . 196 VI. Conclusions and Future Research Directions . 199 6.1 Summary of Research Contributions and Results . 199 6.2 Topics for Future Study . 204 APPENDICES .................................. 210 BIBLIOGRAPHY ................................ 218 vii LIST OF FIGURES Figure 2.1 Normalized wall clock time and relative-to-single-processor speedup ratio vs. number of processors used . 40 2.2 (Validation scenario 1) Difference between RKF7(8) and LGVI output 43 2.3 (Validation scenario 3) Disruption of the binary octahedra system . 46 2.4 Three dimensional plot of trajectory, for intermediate-sized artificial asteroid model test case . 48 2.5 Body angular velocity vectors in inertial frame, for intermediate-sized artificial asteroid model test case . 49 2.6 Co-orbital semi-major axis and eccentricity, for intermediate-sized artificial asteroid model test case . 50 2.7 Variation from initial value of body kinetic energies, total kinetic energy, potential energy, and total system energy, for intermediate- sized artificial asteroid model test case . 51 2.8 Expanded view of variation from initial value of total system energy and total angular momentum vector components, for intermediate- sized artificial asteroid model test case . 52 2.9 Attitude rotation matrix errors, for intermediate-sized artificial as- teroid model test case . 53 2.10 Semi-major axis behavior, over 2 week duration . 57 2.11 Eccentricity behavior, over 2 week duration . 57 2.12 Normalized angular momentum vector projections in the inertial X-Y plane, over one year duration . 58 viii 2.13 Comparison of inclination response for approximate and high-fidelity body models . 58 3.1 Effective gravitational slope for both Alpha and Beta according to the nominal model setup . 66 3.2 Comparison, between simulated cases, of quasi-projections of the or- bit, Alpha, and Beta angular momenta direction vectors . 71 3.3 Comparison of trajectories of standard osculating orbit elements be- tween the most relaxed and most excited configurations for KW4 . 74 3.4 Comparison between most relaxed and most excited configurations identified in text, of the components of angular velocity of Beta, in its own frame, and of the magnitudes of angular acceleration acting upon Alpha (α1) and upon Beta (α2)................. 75 3.5 Trajectory of center of mass of Alpha in the frame fixed to Beta . 75 3.6 Comparison between most relaxed and most excited configurations of Beta libration angle behavior . 76 3.7 Illustration of relative accuracy of polyhedron plus point mass and two-point-mass formulations for mutual potential between a third body and the Alpha component of an octohedral “test” binary system 78 3.8 Initial system configuration for simulation of perihelion passage by KW4 . 81 3.9 Excitation (or lack thereof) of different period dynamic modes of system across simulated perihelion passage . 82 4.1 Illustration of angles orienting frames involved
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