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Significance of Specific Force Models in Two Applications: Solar Sails to Sun-Earth L4/L5 and GRAIL Data Analysis Suggesting Lava Tubes and Buried Craters on the Moon

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Significance of Specific Force Models in Two Applications: Solar Sails to Sun-Earth L4/L5 and GRAIL Data Analysis Suggesting Lava Tubes and Buried Craters on the Moon Purdue University Purdue e-Pubs Open Access Dissertations Theses and Dissertations January 2016 Significance of Specific orF ce Models in Two Applications: Solar Sails to Sun-Earth L4/L5 and GRAIL aD ta Analysis Suggesting Lava Tubes and Buried Craters on the Moon Rohan Sood Purdue University Follow this and additional works at: https://docs.lib.purdue.edu/open_access_dissertations Recommended Citation Sood, Rohan, "Significance of Specific orF ce Models in Two Applications: Solar Sails to Sun-Earth L4/L5 and GRAIL Data Analysis Suggesting Lava Tubes and Buried Craters on the Moon" (2016). Open Access Dissertations. 1374. https://docs.lib.purdue.edu/open_access_dissertations/1374 This document has been made available through Purdue e-Pubs, a service of the Purdue University Libraries. Please contact [email protected] for additional information. Graduate School Form 30 Updated 3414814237 PURDUE UNIVERSITY GRADUATE SCHOOL Thesis/Dissertation Acceptance This is to certify that the thesis/dissertation prepared By Rohan Sood Entitled Significance of Specific Force Models in Two Applications: Solar Sails to Sun-Earth L4/L5 and GRAIL Data Analysis Suggesting Lava Tubes and Buried Craters on the Moon For the degree of DOCTOR OF PHILOSOPHY Is approved by the final examining committee: Kathleen C. Howell Chair Henry J. Melosh James M. Longuski Dengfeng Sun To the best of my knowledge and as understood by the student in the Thesis/Dissertation Agreement, Publication Delay, and Certification Disclaimer (Graduate School Form 32), this thesis/dissertation adheres to the provisions of Purdue University’s “Policy of Integrity in Research” and the use of copyright material. Approved by Major Professor(s): Kathleen C. Howell Approved by: Weinong Wayne Chen 11/15/2016 Head of the Departmental Graduate Program Date SIGNIFICANCE OF SPECIFIC FORCE MODELS IN TWO APPLICATIONS: SOLAR SAILS TO SUN-EARTH L4/L5 AND GRAIL DATA ANALYSIS SUGGESTING LAVA TUBES AND BURIED CRATERS ON THE MOON A Dissertation Submitted to the Faculty of Purdue University by Rohan Sood In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy December 2016 Purdue University West Lafayette, Indiana ii In loving memory of papa. iii ACKNOWLEDGMENTS I would like to extend my gratitude and love to my family who supported me as I left home to in pursuit of my dreams. Although I am so far away, I can feel your presence as you were always there to support me in all my endeavors. Taking one step at a time, I move closer to my life goals, but I will always remember my roots. To my family, I will always love you and support you unconditionally. I would like to extend my gratitude and appreciation to Professor Kathleen C. Howell for providing me with opportunities to learn, evolve and succeed. Professor Howell has been a continuous source of support and guidance as I progressed through my academic career. Learning and working with her is a wonderful experience, and for that I consider myself very fortunate to have her not only as my advisor, but as my mentor. I feel equally privileged to have been given the opportunity to work with Professor Henry J. Melosh on NASA’s GRAIL mission and his ever-motivating discussions that go beyond the research work. I am thankful for his support and his knowledge that has helped me expand my intellectual horizons. I would also like to acknowledge Professor James M. Longuski and Professor Dengfeng Sun for serving as committee members and reviewing my research work. They have been a wonderful asset providing insightful discussions and views on a wide variety of topics. As I paved my way through higher education, I will always remem- ber the support and guidance of Professor John L. Crassidis and Professor Puneet Singla, who have both been great motivators to me. My research group at Purdue University is extremely supportive and helpful. Every individual member, from past to present, has helped me to critically analyze a problem in one way or another. Their love and support, both within and outside the work environment, have always made me feel like a part of another family, and for that I thank each and every one. iv Finally, I would like to thank the School of Aeronautics and Astronautics at Pur- due University for supporting me with teaching and research assistantships. I am grateful to NASA’s Simulation and Graphics Branch at Johnson Space Center in Houston, Texas for providing financial support towards my education and research work at Purdue University under NASA Grant# NNX12AC08G. Additionally, I am thankful for GRAIL mission research funded by the NASA Discovery Program un- der contract to the Massachusetts Institute of Technology and the Jet Propulsion Laboratory, California Institute of Technology. v TABLE OF CONTENTS Page List of Tables ................................... viii List of Figures .................................. ix ABSTRACT ................................... xvi 1 INTRODUCTION .............................. 1 1.1 Problem Definition ........................... 1 1.2 Previous Contributions ......................... 4 1.2.1 Trajectory and Mission Design to Sun-Earth L4,L5 ..... 4 1.2.2 Solar Sails ............................ 5 1.2.3 GRAIL Data Analysis ..................... 7 1.2.4 Current Work .......................... 8 2 DYNAMICAL SYSTEM MODELS ..................... 13 2.1 Classical Two-body Problem ...................... 13 2.2 The Circular Restricted Three-body Problem ............. 14 2.3 Restricted Three-body Problem with Solar Sail ........... 19 2.4 Higher Fidelity -body Model with Solar Sail ............ 24 N 3 RESTRICTED THREE-BODY PROBLEM ................ 27 3.1 Historical Background: CR3BP .................... 27 3.2 Integral of Motion ............................ 28 3.3 Equilibrium Solutions .......................... 29 3.4 Linearized Motion About the Equilibrium Solutions ......... 32 4 NUMERICAL METHODS .......................... 41 4.1 The State Transition Matrix ...................... 41 4.2 Differential Corrections Algorithm ................... 43 4.2.1 Fixed-Time Single Shooting .................. 46 4.2.2 Variable-Time Single Shooting ................. 50 4.3 Multiple Shooting Algorithm ...................... 52 4.3.1 Fixed-Time Multiple Shooting ................. 54 4.3.2 Variable-Time Multiple Shooting ............... 55 4.4 Periodic Orbits in the CR3BP ..................... 57 4.4.1 Construction of Periodic Orbits ................ 57 4.5 Periodic Orbits and Invariant Manifolds ............... 62 vi Page 5 SPACECRAFT TRAJECTORY DESIGN IN CIRCULAR RESTRICTED THREE-BODY PROBLEM (CR3BP) ................... 67 5.1 Selection Criteria – Design Space: ................... 67 5.2 Trajectory Design Options: ....................... 69 5.3 Baseline Trajectory: ........................... 77 6 SOLAR SAIL TRAJECTORY DESIGN TO THE VICINITY OF L4 AND L5 .......................... 81 6.1 Sail Based Differential Correction: ................... 81 6.2 Lightness Parameter Selection: ..................... 83 6.3 Solar Sail Transfer Families to L4 and L5: .............. 84 6.3.1 Transfers to the Vicinity of L5 ................. 87 6.3.1.1 Arrival Criterion ................... 87 6.3.1.2 Effects of Sail Parameter on SRP Acceleration ... 87 6.3.1.3 Displacement of Traditional L5 ........... 89 6.3.1.4 Jacobi Analysis .................... 91 6.3.1.5 Non-optimal Parking Orbit Departures ....... 92 6.4 Solar Sail L5 Trajectory Analysis for β = 0.022: ........... 92 6.4.1 Sail Transfer and Baseline Trajectory ............. 93 6.4.2 Jacobi Analysis for β = 0.022 Transfer to L5 ......... 95 6.4.3 Sail Orientation Angles ..................... 96 6.5 Locally Optimal Departure ∆V .................... 98 7 SOLAR SAIL IN HIGH FIDELITY EPHEMERIS MODEL ............................ 103 7.1 Additional Perturbing Bodies ..................... 103 7.2 Solar Sail Trajectory in Ephemeris .................. 105 7.2.1 Earth-Sun Ephemeris ...................... 105 7.2.2 Solar Sail in Earth-Sun Ephemeris .............. 107 7.2.3 Solar Sail in Earth-Sun-Moon-Venus-Jupiter Ephemeris Model 109 7.3 Sail Ephemeris Model Comparison .................. 111 8 GRAIL GRAVITY DATA ANALYSIS: LAVA TUBES AND BURIED CRATERS ON THE MOON ................ 113 8.1 Overview ................................. 113 8.2 Detection Techniques .......................... 113 8.2.1 Free-air and Bouguer Gravity ................. 114 8.2.2 Gradiometry and Cross-Correlation .............. 116 8.3 Lava Tubes ............................... 118 8.3.1 Scientific Interests ....................... 118 8.3.2 General Survey ......................... 120 8.3.3 Lava Tube Candidates ..................... 122 8.3.3.1 Application to Marius Hills Skylight Region .... 122 vii Page 8.3.3.2 Application to Additional Skylights/Melt Pits ... 127 8.3.3.3 Additional Lava Tube Candidates .......... 130 8.3.4 Forward Modeling ....................... 134 8.4 Buried Craters ............................. 134 8.4.1 Detection of Buried Craters .................. 135 8.4.2 Speculated Buried Crater 1 (Ashoka) ............. 137 8.4.2.1 Gradiometry, Free-air and Bouguer Gravity Anomalies 138 8.4.2.2 Buried Peak-ring Basin: Ashoka ........... 140 8.4.3 Speculated Buried Crater 2 (Earhart) ............. 141 8.4.3.1 Gradiometry, Free-air and Bouguer Gravity Anomalies 141 8.4.3.2 Earhart Crater’s Regional Topography ....... 143 8.4.3.3 Buried Peak-ring Basin: Earhart .......... 144 8.4.4 Validation of the Detected Buried Craters .......... 145 9 CONCLUDING REMARKS ......................... 147 9.1 Leveraging
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