THE TRAJECTORY OPTIMIZATION & SPACE LOGISTICS OF ASTEROID MINING MISSIONS Scott Dorrington A thesis in fulfilment of the requirements for the degree of Doctor of Philosophy School of Mechanical and Manufacturing Engineering Faculty of Engineering University of New South Wales, Sydney June 2019 i ii iii ORIGINALITY STATEMENT ‘I hereby declare that this submission is my own work and to the best of my knowledge it contains no materials previously published or written by another person, or substantial proportions of material which have been accepted for the award of any other degree or diploma at UNSW or any other educational institution, except where due acknowledgement is made in the thesis. Any contribution made to the research by others, with whom I have worked at UNSW or elsewhere, is explicitly acknowledged in the thesis. I also declare that the intellectual content of this thesis is the product of my own work, except to the extent that assistance from others in the project's design and conception or in style, presentation and linguistic expression is acknowledged.’ COPYRIGHT STATEMENT ‘I hereby grant the University of New South Wales or its agents a non-exclusive licence to archive and to make available (including to members of the public) my thesis or dissertation in whole or part in the University libraries in all forms of media, now or here after known. I acknowledge that I retain all intellectual property rights which subsist in my thesis or dissertation, such as copyright and patent rights, subject to applicable law. I also retain the right to use all or part of my thesis or dissertation in future works (such as articles or books).’ ‘For any substantial portions of copyright material used in this thesis, written permission for use has been obtained, or the copyright material is removed from the final public version of the thesis.’ AUTHENTICITY STATEMENT ‘I certify that the Library deposit digital copy is a direct equivalent of the final officially approved version of my thesis.’ iv The Trajectory Optimization & Space Logistics of Asteroid Mining Missions Scott Dorrington – June 2019 ABSTRACT Near-Earth asteroids are expected to be rich in mineral resources which, if extracted, could have tremendous benefits in lowering the costs of conducting space exploration missions, and could potentially generate significant monetary returns. Despite this potential, there remain many unanswered questions surrounding asteroid mining: What is the best strategy? Which are the best targets? How much material can be retrieved? How much profit can be generated? This thesis aims to answer these questions, determining the optimal trajectory design, mission architecture, and asteroid targets to maximize the total net present value (NPV) of an asteroid mining operation. A parametric economic model is formulated to assess the feasibility of numerous mission alternatives over a range of system, mission, and cost parameters. This analysis shows that the optimal strategy uses multiple return-trip missions, with propellant processed from asteroid resources. New methods are then developed for the combinatorial trajectory optimization of multiple return-trip missions, identifying optimal flight itineraries that maximize NPV, rather than minimizing delta-V. These trajectories account for the distribution of asteroid-derived resources to a propellant depot and customer spacecraft between consecutive trips. A location-routing problem is developed to identify the optimal orbital location of the propellant depot, and the routing of spacecraft throughout the supply chain network to maximize total sellable mass delivered to customers. These methods are then applied to assess the economic values of over 100 candidate asteroids, with realistic trajectories over multiple return-trip missions. These candidates were filtered from the entire list of 19,880 near-Earth asteroids known at the time of writing, as having either known/assumed C-complex taxonomic classes, low delta-Vs, or orbital elements close to Earth. The results produced a list of 35 asteroids with positive NPVs. These missions could be achieved with capital costs of around $400M, generating large profits ranging from $198.27M to $1547.7M over 20 years, with positive returns after the first or second trips. These results confirm the economic viability of asteroid mining missions, however it is noted that additional data and understanding of asteroid composition is needed to reduce the large uncertainty in the presence of resources before asteroid mining should commence. v ACKNOWLEDGEMENTS I would like to thank my supervisors, Dr John Olsen and Dr Nathan Kinkaid, for their support and guidance throughout this degree, and their valuable insight into the PhD process. To Dr Olsen in particular, for taking over main supervisory duties following Dr Kinkaid’s departure from the university. Thanks are also given to Dr Naomi Tsafnat for her teaching of the orbital mechanics course that first inspired me to peruse this field of research, and for allowing me to tutor the course over the past few years. I would also like to thank Prof. Andrew Dempster and other staff at the Australian Centre for Space Engineering Research for their interest and support in my research; and the other PhD students at the Centre and other faculties perusing other fields of Off- Earth mining and space-related research. Special thanks are given to friends and colleagues in my own faculty. To Ali Ahmed for his friendship and encouragement over the years, and to William Crowe for countless discussions over our mutual research interests in all things asteroids. Thanks are also given to other space friends I have met around the world, and to my friends back home for providing much needed distractions from the worlds of academia and space. Finally, I would like to give the most thanks to my family for their endless support and encouragement throughout this PhD, my undergrad degree, and my entire life. vi CONTENTS 1 INTRODUCTION ........................................................................................................ 1 1.1 MOTIVATION FOR ASTEROID MINING ....................................................................... 1 Feasibility .................................................................................................................. 1 1.2 AIMS OF THESIS ........................................................................................................ 2 1.3 OVERVIEW OF CHAPTERS ......................................................................................... 3 1.4 METHODOLOGY ........................................................................................................ 4 Trajectory Design Methods ....................................................................................... 4 Economic Models ...................................................................................................... 5 Graph Theory Methods ............................................................................................. 5 1.5 PUBLICATIONS PRODUCED FROM THIS WORK .......................................................... 6 Journal Paper: .......................................................................................................... 6 Refereed Conference Paper: ..................................................................................... 6 Conference Papers (abstract refereed): ................................................................... 6 2 ASTEROID PROPERTIES & RESOURCES .......................................................... 8 2.1 SOURCES OF ASTEROID OBSERVATIONAL DATA ...................................................... 8 2.1.1 Photometric Observations ................................................................................ 9 2.1.2 Spectroscopic Observations ........................................................................... 11 2.1.3 Spacecraft Missions ....................................................................................... 14 2.2 ORBITAL PROPERTIES ............................................................................................. 17 2.2.1 Classical Orbital Elements ............................................................................ 17 2.2.2 Designation and Numbering Convention ....................................................... 19 2.2.3 Other Orbital Properties ................................................................................ 19 2.2.4 Asteroid Groups ............................................................................................. 22 2.3 DELTA-V ESTIMATES ............................................................................................. 28 2.3.1 Hohmann Transfers ........................................................................................ 28 2.3.2 Shoemaker-Helin Equations .......................................................................... 31 2.4 PHYSICAL PROPERTIES ........................................................................................... 33 2.4.1 Viewing Geometry .......................................................................................... 33 2.4.2 Phase Curve ................................................................................................... 34 2.4.3 Light Curve .................................................................................................... 35 2.4.4 Mean Diameter .............................................................................................. 36 2.4.5