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Design of Frozen Orbits for Lunar Navigation and Communications Missions

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Design of Frozen Orbits for Lunar Navigation and Communications Missions DESIGN OF FROZEN ORBITS FOR LUNAR NAVIGATION AND COMMUNICATIONS MISSIONS By Joel Jefferson Konkle Parker A Thesis Submitted to the Faculty of Mississippi State University in Partial Fulfillment of the Requirements for the Degree of Master of Science in Aerospace Engineering in the Department of Aerospace Engineering Mississippi State, Mississippi August 2008 Copyright by Joel Jefferson Konkle Parker 2008 DESIGN OF FROZEN ORBITS FOR LUNAR NAVIGATION AND COMMUNICATIONS MISSIONS By Joel Jefferson Konkle Parker Approved: ___________________________________________________ ___________________________________________________ Carrie D. Olsen Gregory D. Olsen Assistant Professor Assistant Professor of Aerospace Engineering of Aerospace Engineering (Director of Thesis) (Committee Member) ___________________________________________________ ___________________________________________________ Ming Xin Pasquale Cinnella Assistant Professor Professor of Aerospace Engineering of Aerospace Engineering Graduate Coordinator of the (Committee Member) Department of Aerospace Engineering ___________________________________________________ W. Glenn Steele Interim Dean of the James Worth Bagley College of Engineering Name: Joel Jefferson Konkle Parker Date of Degree: August 9, 2008 Institution: Mississippi State University Major Field: Aerospace Engineering Major Professor: Dr. Carrie D. Olsen Title of Study: DESIGN OF FROZEN ORBITS FOR LUNAR NAVIGATION AND COMMUNICATIONS MISSIONS Pages in Study: 133 Candidate for Degree of Master of Science Eccentric lunar frozen orbits are analyzed in this study in relation to lunar navigation and communications missions, particularly the proposed Magnolia-1 mission. A review of background material and existing literature is presented, and potential limitations are discussed. Perturbation analyses are performed in both a preliminary and a numerical fashion, and a general set of perturbations is identified. Analysis of potential orbits is performed through calculation of a maximum deviation metric and through visualization as a function of initial orbital elements. Trends are identified within a closed search space by varying elements individually and in combination. Potential orbit designs for the Magnolia-1 mission are selected and a method of orbit refinement is used to improve behavior. Conclusions are made involving general trends related to eccentric lunar frozen orbits and the specific designs proposed for the Magnolia-1 mission, and a method for the design of similar orbits is suggested. DEDICATION I would like to dedicate this thesis to my wife, Amy, for her endless patience, support, and love. ii ACKNOWLEDGEMENTS The author expresses his heartfelt gratitude to the many people whose assistance made this research possible. Sincere thanks are due to Dr. Carrie D. Olsen, my major professor, for her tireless effort in helping me through the process and providing innumerable kind words of advice and support. Thanks are also due to the other members of my committee, Dr. Gregory D. Olsen and Dr. Ming Xin, for their help in reviewing this thesis. Furthermore, gratitude must be extended to Dr. Todd Ely of the Jet Propulsion Laboratory, Pasadena, California, for his effort to answer my questions regarding his work, and to Christopher Becker, for assisting me in various technical aspects of this research. Finally, many thanks are extended to the Department of Aerospace Engineering and the Bagley College of Engineering of Mississippi State University for their generous support and encouragement throughout my graduate studies. iii TABLE OF CONTENTS DEDICATION ............................................................................................................................................................... ii ACKNOWLEDGEMENTS ....................................................................................................................................... iii LIST OF TABLES ........................................................................................................................................................ vi LIST OF FIGURES.................................................................................................................................................... vii CHAPTER I. INTRODUCTION ......................................................................................................................................... 1 II. BACKGROUND ............................................................................................................................................ 4 Earth/Moon System ................................................................................................................................ 4 Magnolia-1 Mission ................................................................................................................................. 8 Frozen Orbits ........................................................................................................................................... 10 Analysis Methodology .......................................................................................................................... 13 III. PERTURBATION ANALYSIS ................................................................................................................ 21 Visual Analysis......................................................................................................................................... 21 Numerical Analysis ................................................................................................................................ 33 IV. NUMERICAL SEARCH ........................................................................................................................... 41 Methodology ............................................................................................................................................ 41 Design Orbit.............................................................................................................................................. 44 Single-Element Trend Analysis ......................................................................................................... 53 Multi-Element Trend Analysis .......................................................................................................... 70 V. ORBIT SELECTION ................................................................................................................................. 88 Initial Orbit Selection............................................................................................................................ 88 Refined Orbit Selection ..................................................................................................................... 108 iv VI. CONCLUSIONS ...................................................................................................................................... 127 REFERENCES ........................................................................................................................................................ 132 v LIST OF TABLES 1. Orbital parameters of the Moon about Earth [2] ........................................................................ 4 2. First 10 zonal terms of Earth gravity field (JGM3, normalized) [4] .................................... 7 3. First 10 zonal terms of Moon gravity field (LP165P, normalized) [4] ................................ 8 4. Magnolia-1 mission requirements [5] ............................................................................................. 9 5. Baseline design orbit for visual analysis ...................................................................................... 23 6. Visual analysis orbits ............................................................................................................................ 23 7. Visual analysis plot scale ..................................................................................................................... 25 8. Maximum deviation from combined gravity field and third-body model ...................... 36 9. Maximum deviation from combined gravity model and third-body model .................. 37 10. Maximum deviation from full third-body model (Earth J2, Sun, Jupiter) ....................... 39 11. Maximum deviation from 50x50 LP165P gravity model ....................................................... 40 12. Numerical search constraints ........................................................................................................... 42 13. Magnolia-1 design orbit [5] ............................................................................................................... 45 14. Design orbit maximum deviation .................................................................................................... 52 15. Preliminary design orbits ................................................................................................................... 96 16. Refined design orbits ......................................................................................................................... 119 17. Percent coverage (five years) ......................................................................................................... 122 18. Maximum revisit time (five years) ............................................................................................... 123 19. Mean access time (five years) .......................................................................................................
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