OPTIMAL PHASING AND PERFORMANCE MAPPING FOR TRANSLUNAR SATELLITE MISSIONS ACROSS THE EARTH-MOON NODAL CYCLE A Thesis Presented to The Academic Faculty By Richard A. J. Hunter In Partial Fulfillment of the Requirements for the Degree Master of Science in the Daniel Guggenheim School of Aerospace Engineering Georgia Institute of Technology May 2020 Copyright c Richard A. J. Hunter 2020 OPTIMAL PHASING AND PERFORMANCE MAPPING FOR TRANSLUNAR SATELLITE MISSIONS ACROSS THE EARTH-MOON NODAL CYCLE Approved by: Dr. Brian C. Gunter Daniel Guggenheim School of Aerospace Engineering Georgia Institute of Technology Dr. Edgar G. Lightsey Daniel Guggenheim School of Aerospace Engineering Georgia Institute of Technology Dr. Koki Ho Daniel Guggenheim School of Aerospace Engineering Georgia Institute of Technology Date Approved: January 08, 2020 “Exploration is in our nature. We began as wanderers, and we are wanderers still. We have lingered long enough on the shores of the cosmic ocean. We are ready at last to set sail...” Carl Sagan To my mother and father, whose strong work ethic, intelligence, and boundless support has placed within reach a profession that brings challenge and wonder. ACKNOWLEDGEMENTS I was exceedingly fortunate to receive my graduate education at the Georgia Institute of Technology. My time at the Guggenheim School of Aerospace Engi- neering has been transformative, though I did not make the journey alone. First and foremost, I would like to thank my mother Jane, and father Tim. Their love and support has always been steadfast, despite a son intent on leaving a re- spectable job to cross half a world for the foolhardy pursuits of rocket science. My sister Rachel, and brother James have inspired me endlessly through their stunning achievements in academia, athletics, and professional life. Their dedica- tion and vision heavily influenced the leap of faith into graduate studies. Dr. Brian Gunter has played a pivotal role in my masters degree. He provided the foundation in astrodynamics and orbit determination that would become the focus of my career. More importantly, he has proved an invaluable and enthusiastic mentor throughout this research, helping me navigate a complex problem through significant challenges. I very much look forward to our joint ventures in the future. I would also like to acknowledge Dr. Glenn Lightsey, whose intelligence and good humor were ever present and appreciated in the lab. Together with Dr. Gunter and Dr. Koki Ho, he has made the SSDL an engaging, collaborative environment that will continue to excel as a top space research and academic center. I am very grateful to the Georgia Tech collegiate triathlon team, particularly Peter Griffiths, Vincent Terrier, Kalina Paunovska, Chris Douglas, Elizabeth Spiers, Thomas Easley, Marc Papakyriakou, and David Wolfson for the camaraderie and exercise that kept me sane over the past two years. Finally, a special thank you to Dr. Avinash Rao for the conversational spark that began this research. For your support through the considerable trials we faced, I will forever be immensely grateful. v TABLE OF CONTENTS Acknowledgments . v List of Tables . xi List of Figures . xii Chapter 1: Motivation and Background . 1 1.1 Motivation . 1 1.1.1 Lunar Exploration: A New Focus . 1 1.1.2 Pathfinders: Small Satellite Lunar Applications . 4 1.1.3 The Barrier of Translunar Injection . 6 1.2 Background . 16 1.2.1 The Lunar Orbit . 16 1.2.2 Apollo Architecture . 21 1.2.3 Exploration Mission 1 Architecture . 23 1.2.4 Beresheet/Chandrayaan 2 Architecture . 25 1.2.5 Gravity Recovery and Interior Laboratory Architecture . 26 1.2.6 Optimal Lunar Pathfinder Architecture . 27 1.2.7 Lunar Arrival Conditions . 29 1.2.8 Knowledge Gap . 30 vi 1.3 Objectives . 31 1.3.1 Research Question 1: Payload Mass Dependency . 32 1.3.2 Research Question 2: Arrival Orbital Element Dependency . 32 1.3.3 Research Question 3: Departure Epoch Dependency . 33 1.3.4 Research Question 4: Launch Vehicle Compatibility . 33 Chapter 2: Technical Approach . 35 2.1 Parameter Space . 35 2.1.1 Fixed Parameters . 35 2.1.2 Variable Parameters . 37 2.1.3 Parameter Space Summary . 38 2.2 The General Mission Analysis Tool: GMAT . 38 2.3 Time Scales . 39 2.3.1 International Atomic Time: TAI . 39 2.3.2 Terrestrial Time: TT . 40 2.3.3 Universal Time: UT1 . 40 2.3.4 Coordinated Universal Time: UTC . 41 2.4 Time Formats . 41 2.4.1 Julian Date: JD . 41 2.4.2 Modified Julian Date Format: MJD . 41 2.4.3 Gregorian Date: GD . 42 2.5 Coordinate Frames . 43 2.5.1 Earth Centered Inertial Frame: ECI . 43 vii 2.5.2 Earth-Moon Rotating Frame: EMR . 43 2.5.3 Lunar Centered Inertial Frame: LCI . 44 2.5.4 Lunar Centered Lunar Fixed Frame: LCLF . 45 2.5.5 Velocity Normal Bi-Normal Frame: VNB . 46 2.6 Orbital Dynamics: The Equations of Motion . 46 2.7 Central-Body and Third-Body Gravity . 48 2.7.1 Non-Spherical Gravity . 53 2.7.2 Atmospheric Drag . 58 2.7.3 Solar Radiation Pressure . 60 2.7.4 Relativistic Correction . 62 2.7.5 Spacecraft Thrust . 63 2.8 Numerical Propagators . 66 2.9 Solver . 70 2.10 Spacecraft Model . 74 2.11 Summary of the Mathematical Architecture . 87 2.12 Trajectory Design Algorithm . 88 2.12.1 Phase 1: Coarse TLI to Target Moon . 89 2.12.2 Phase 2: Fine Impulse TLI and LOI . 89 2.12.3 Phase 3: Coarse Finite TLI Burn . 89 2.12.4 Phase 4: Fine Finite TLI Burn . 90 2.12.5 Phase 5: Fine Finite LOI and IAB Burns . 90 2.12.6 Phase 6: RAAN Coast . 91 2.12.7 Phase 7: Fine Tune Parking Orbit for Landing . 91 viii 2.12.8 Phase 8: Initiate Descent . 93 2.12.9 Phase 9: Final Approach . 93 2.12.10 Phase 10: Braking, Parabolic Free-fall, and Landing . 94 Chapter 3: Results . 95 3.1 Data Filtration and Indexing . 95 3.1.1 PACE Output . 95 3.1.2 Filtering . 96 3.1.3 Indexing . 99 3.1.4 Analysis of Filtered Results . 101 3.2 Flyby . 101 3.3 Orbit Insertion . 113 3.4 Landing . 126 3.5 Phased Translunar Injection . 137 3.6 Low Thrust Propulsion . 141 Chapter 4: Conclusions . 145 4.1 Conclusion 1: Payload Mass Dependency . 146 4.2 Conclusion 2: Arrival Orbital Element Dependency . 148 4.3 Conclusion 3: Departure Epoch Dependency . 151 4.4 Conclusion 4: Launch Vehicle Compatibility . 153 4.5 Final Remarks . 157 Appendix A: Flyby: Nodal Cycle Performance Distribution for Optimal Departures - Mission Mass and Flight Time . 160 ix Appendix B: Flyby: Nodal Cycle Performance Distribution for Optimal Departures - ∆v and Burn Time . 166 Appendix C: Orbit Insertion: Nodal Cycle Performance Distribution for Optimal Departures - Mission Mass and Flight Time . 172 Appendix D: Orbit Insertion: Nodal Cycle Performance Distribution for Optimal Departures - ∆v and Burn Time . 178 Appendix E: Landing: Nodal Cycle Performance Distribution for Opti- mal Departures - Mission Mass and Flight Time . 184 Appendix F: Landing: Nodal Cycle Performance Distribution for Opti- mal Departures - ∆v and Burn Time . 190 Appendix G: Trajectory Design Algorithm . 196 References . 219 x LIST OF TABLES 1.1 EM1 secondary payload small satellite missions . 5 1.2 TRL 9 small satellite propulsion technologies . 7 1.3 Earth-Moon segment characteristics for the Apollo 10, 11, 12 [7][8][9] 22 1.4 Earth-Moon segment characteristics for EM1 [10] . 24 2.1 Parameter space summary . 38 2.2 Force model comparison . 69 2.3 Baseline mission assumptions . 75 2.4 Kennedy Space Center compatible launch vehicles . 76 2.5 Ti-6AI-4V Titanium mechanical properties . 80 2.6 Spacecraft subsystem power demand . 84 3.1 Direct vs phased translunar injection, full thrust . 139 3.2 Direct vs phased translunar injection, half thrust . 140 3.3 High thrust vs low thrust transfer . 143 xi LIST OF FIGURES 1.1 Simplified lunar Hohmann transfer . 10 1.2 Lunar range . 17 1.3 Lunar argument of perigee, equatorial, J2000 mean equinox . 18 1.4 Lunar RAAN, ecliptic, J2000 mean equinox . 19 1.5 Lunar inclination, ecliptic, J2000 mean equinox . 19 1.6 Lunar declination, equatorial, J2000 mean equinox . 20 1.7 Lunar inclination, equatorial, J2000 mean equinox . 20 1.8 Apollo trajectory, circular parking orbit, free return . 22 1.9 EM1 trajectory, eccentric parking orbit, near-Hohmann . 23 1.10 Beresheet/Chandrayaan 2 trajectory, multiple apogee raising burns, phasing orbits . 25 1.11 GRAIL trajectory, weak stability boundary transfer [12] . 27 1.12 Ground trace targeting with lunar orbit Keplerian elements . 30 2.1 ECI frame . 43 2.2 EMR frame . 44 2.3 LCI frame . 45 2.4 LCLF frame . 46 xii 2.5 Relative acceleration of perturbing effects in Earth Orbit, Satellite Orbits, Figure 3.1 [14] . 48 2.6 N-Body inertial reference frame . 50 2.7 GMAT integration test cases, Verification and Validation of the Gen- eral Mission Analysis Tool (GMAT), table 8 [13] . 67 2.8 Comparison of GMAT integrator performance, Verification and Val- idation of the General Mission Analysis Tool (GMAT), table 9 [13] . 67 2.9 Newton-Raphson method differential correction . 70 2.10 TLI stage subsystems architecture . 78 2.11 Algorithm phases 1 and 2 . ..