Purdue University Purdue e-Pubs Open Access Dissertations Theses and Dissertations 12-2016 Gravity-assist trajectories to Venus, Mars, and the ice giants: Mission design with human and robotic applications Kyle M. Hughes Purdue University Follow this and additional works at: https://docs.lib.purdue.edu/open_access_dissertations Part of the Aerospace Engineering Commons, and the Physics Commons Recommended Citation Hughes, Kyle M., "Gravity-assist trajectories to Venus, Mars, and the ice giants: Mission design with human and robotic applications" (2016). Open Access Dissertations. 940. https://docs.lib.purdue.edu/open_access_dissertations/940 This document has been made available through Purdue e-Pubs, a service of the Purdue University Libraries. Please contact [email protected] for additional information. GRAVITY-ASSIST TRAJECTORIES TO VENUS, MARS, AND THE ICE GIANTS: MISSION DESIGN WITH HUMAN AND ROBOTIC APPLICATIONS A Dissertation Submitted to the Faculty of Purdue University by Kyle M. Hughes In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy December 2016 Purdue University West Lafayette, Indiana Graduate School Form 30 Updated PURDUE UNIVERSITY GRADUATE SCHOOL Thesis/Dissertation Acceptance This is to certify that the thesis/dissertation prepared By Kyle M. Hughes Entitled Gravity-Assist Trajectories to Venus, Mars, and the Ice Giants: Mission Design with Human and Robotic Applications For the degree of Doctor of Philosophy Is approved by the final examining committee: James M. Longuski Chair Kathleen C. Howell Martin J. Corless William A. Crossley 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): James M. Longuski Approved by: Weinong Wayne Chen 12/7/2016 Head of the Departmental Graduate Program Date ii ACKNOWLEDGMENTS I would like to thank my advisor Jim Longuski for his invaluable insight through- out this entire work, and more generally, for teaching me how to be a researcher and astrodynamicist. Working in his research group has been an invaluable experience and a great positive influence my life and future career. I am, to say the least, grateful for having the opportunity to work with Professor Longuski, and I will aim to follow his example throughout my career. I would also like to thank my committee members Professors William Crossley, Martin Corless, and Kathleen Howell for their support and feedback. Professor Howell's very memorable course on advanced orbital dynam- ics was the most fascinating and fun experience I've had in a classroom. I would also like to thank my colleagues Sarag Saikia, Jim Moore, Blake Rogers, and Alec Mudek for all of their help and insight, often through long discussions at Armstrong Hall and on the phone, which significantly improved in many ways the quality of this thesis. I would like to thank my collaborators Parul Agrawal, Gary Allen, Helen Hwang, and Raj Venkatapathy at Ames Research Center for pushing my research into the atmospheres of the Gas and Ice Giants; Mike Loucks, John Carrico, and Dennis Tito for their support and interest in my contribution to Inspiration Mars; and Buzz Aldrin for sharing so many hours of his time with me and our research group, and allowing me to contribute to his vision for putting a permanent human presence on Mars. I would also like to thank Alinda Mashiku, Trevor Williams, and Jacob Englander at Goddard Space Flight Center for letting me pester them with endless questions, and helping me to find the next step in my career path. I would like to thank my mom and dad, Paulette and Mike, who many times helped me financially during this work, and have always given their support and en- couragement, without which this work may never have taken place. I would especially like to acknowledge my mom, who we lost in 2013. Her sense of humor, delightful iii cynicism, and unfailing ability to help me put things in perspective, helped keep me sane through most of my life and especially during graduate school. I continually work to follow her example in all aspects of my life, and be mindful of the advice I may only speculate she would give. I would also like to thank my sister Laura for our long phone conversations that helped me get through difficult times of loss and stress. Most importantly, I would like to thank my wife Mariah for her support, encour- agement, and infinite patience with me, which I depend on daily. I will be forever grateful to her for her sacrifice in leaving her home and effectively postponing her career so that I may pursue this degree. iv TABLE OF CONTENTS Page LIST OF TABLES :::::::::::::::::::::::::::::::: vi LIST OF FIGURES ::::::::::::::::::::::::::::::: viii ABSTRACT ::::::::::::::::::::::::::::::::::: xiii 1 THE PATCHED-CONIC METHOD OF COMPUTING GRAVITY-ASSIST TRAJECTORIES ::::::::::::::::::::::::::::::: 1 1.1 Lambert's Problem ::::::::::::::::::::::::::: 3 1.2 The Tisserand Graph :::::::::::::::::::::::::: 4 1.2.1 Selecting Candidate Paths: Pathfinding :::::::::::: 5 2 INTERPLANETARY HYPERBOLIC ENCOUNTERS: APPROACH AND DEPARTURE TRAJECTORIES NEAR A TARGET BODY ::::::: 9 2.1 Planetocentric Equatorial Frames ::::::::::::::::::: 9 2.2 Hyperbolic Approach Trajectories ::::::::::::::::::: 12 2.2.1 Locus of Possible Solutions ::::::::::::::::::: 13 2.2.2 Probe Entry Parameters for an Oblate Body ::::::::: 21 2.2.3 Consequences of Interplanetary Trajectory Design on Launch 32 2.2.4 Spacecraft Deflection Maneuver for Probe Release During Flyby 33 2.2.5 Launch Vehicle Performance :::::::::::::::::: 38 3 CATALOG OF TRAJECTORIES TO URANUS FROM 2024 TO 2038 IN- CLUDING AN OPPORTUNITY FOR A SATURN PROBE ::::::: 45 3.1 Background ::::::::::::::::::::::::::::::: 45 3.2 Methods ::::::::::::::::::::::::::::::::: 47 3.2.1 Computing the Trajectory Design Space ::::::::::: 47 3.2.2 Defining the Capture Science Orbit and Estimating the Deliv- ered Mass :::::::::::::::::::::::::::: 51 3.2.3 Investigating Select Cases ::::::::::::::::::: 52 3.3 Cataloging Trajectories to Uranus ::::::::::::::::::: 55 3.4 Catalogs for Trajectories that Capture Inside the Rings of Uranus : 66 3.5 Candidate Trajectory for a Saturn-Uranus Mission :::::::::: 67 3.6 Aerocapture ::::::::::::::::::::::::::::::: 73 3.7 Conclusion :::::::::::::::::::::::::::::::: 75 4 50-YEAR CATALOG OF GRAVITY-ASSIST TRAJECTORIES TO NEP- TUNE ::::::::::::::::::::::::::::::::::::: 81 4.1 Introduction ::::::::::::::::::::::::::::::: 81 v Page 4.2 Methods ::::::::::::::::::::::::::::::::: 83 4.3 Uranus-Neptune Alignment :::::::::::::::::::::: 85 4.4 Catalog of Trajectories to Neptune :::::::::::::::::: 85 4.5 Neptune Probe and Orbiter Mission using the 2031 M0JN Trajectory 96 4.6 Candidate Trajectories for Aerocapture :::::::::::::::: 100 4.7 Conclusion :::::::::::::::::::::::::::::::: 102 5 FAST FREE RETURNS TO MARS AND VENUS WITH APPLICATION TO INSPIRATION MARS :::::::::::::::::::::::::: 105 5.1 Introduction ::::::::::::::::::::::::::::::: 106 5.2 Methods ::::::::::::::::::::::::::::::::: 107 5.2.1 Satellite Tour Design Program (STOUR) ::::::::::: 107 5.2.2 Pareto-Optimal Set ::::::::::::::::::::::: 110 5.2.3 Earth Entry Parameters and Constraints ::::::::::: 111 5.2.4 Gauss Pseudospectral Optimization Software (GPOPS) ::: 116 5.3 Results :::::::::::::::::::::::::::::::::: 116 5.3.1 Rarity of the Nominal Inspiration Mars Free-Return Trajectory 117 5.3.2 Investigation of Fast Mars Free-Returns with Venus Gravity Assist :::::::::::::::::::::::::::::: 127 5.3.3 Earth Entry Analysis :::::::::::::::::::::: 144 5.3.4 The 2023 EVME High Entry-Speed Free-Returns :::::: 151 5.3.5 The Case for Venus ::::::::::::::::::::::: 155 5.3.6 Feasibility of Launch :::::::::::::::::::::: 159 5.4 Conclusion :::::::::::::::::::::::::::::::: 160 6 VERIFICATION OF TRAJECTORIES TO ESTABLISH EARTH-MARS CYCLERS ::::::::::::::::::::::::::::::::::: 163 6.1 Introduction ::::::::::::::::::::::::::::::: 163 6.2 V1 Leveraging ::::::::::::::::::::::::::::: 164 6.2.1 Selected Cyclers and Their Characteristics :::::::::: 165 6.3 Patched Conic Propagator Analysis :::::::::::::::::: 167 6.4 Low-Thrust Analysis :::::::::::::::::::::::::: 168 6.5 Results :::::::::::::::::::::::::::::::::: 169 6.5.1 STOUR Verification of V1-Leveraging Establishment Trajec- tories ::::::::::::::::::::::::::::::: 169 6.5.2 Validation of Low-Thrust Establishment Trajectories :::: 171 6.6 Conclusion :::::::::::::::::::::::::::::::: 179 7 CONCLUDING REMARKS ::::::::::::::::::::::::: 181 7.1 Contribution of Work :::::::::::::::::::::::::: 181 7.2 Potential Advancement of Work :::::::::::::::::::: 182 REFERENCES :::::::::::::::::::::::::::::::::: 185 VITA ::::::::::::::::::::::::::::::::::::::: 195 vi LIST OF TABLES Table Page 3.1 Trajectory Search Constraints ::::::::::::::::::::::: 49 3.2 Uranus Trajectory Catalog: SLS Block 1B :::::::::::::::: 58 3.3 Uranus Trajectory Catalog: Delta IV Heavy ::::::::::::::: 59 3.4 Uranus Trajectory Catalog: Atlas V 551 ::::::::::::::::: 60 3.5 Uranus Trajectory Catalog: SLS Block 1B|5 Mg or Less of Propellant 63 3.6 Saturn-Uranus Trajectory Catalog: SLS Block 1B :::::::::::: 65 3.7 Saturn-Uranus Trajectory Catalog: Delta IV Heavy ::::::::::: 65 3.8 Uranus Trajectory Catalog: Atlas V 551|Capture Inside Rings :::: 66 3.9 Uranus Trajectory Catalog: Delta IV Heavy|Capture Inside Rings :: 67 3.10 Uranus Trajectory