Communication Strategies for Colonization Mission to Mars A Thesis Submitted to the Faculty of Universidad Carlos III de Madrid In Partial Fulfillment of the Requirements for the Bachelor’s Degree in Aerospace Engineering By Pablo A. Machuca Varela June 2015 Dedicated to my dear mother, Teresa, for her education and inspiration; for making me the person I am today. And to my grandparents, Teresa and Hernan,´ for their care and love; for being the strongest motivation to pursue my goals. Acknowledgments I would like to thank my advisor, Professor Manuel Sanjurjo-Rivo, for his help and guidance along the past three years, and for his advice on this thesis. Professor Sanjurjo-Rivo first accepted me as his student and helped me discover my passion for the Orbital Mechanics research area. I am very thankful for the opportunity Professor Sanjurjo-Rivo gave me to do research for the first time, which greatly helped me improve my knowledge and skills as an engineer. His valuable advice also encouraged me to take Professor Howell’s Orbital Mechanics course and Professor Longuski’s Senior Design course while at Purdue University, as an exchange student, which undoubtedly enhanced my desire, and created the opportunity, to become a graduate student at Purdue University. I would like to thank Sarag Saikia, the Mission Design Advisor of Project Aldrin-Purdue, for his exemplary passion and enthusiasm for the field. Sarag is responsible for making me realize the interest and relevance of a Mars communication network. He encouraged me to work on this thesis, and advised me along the way. I highly appreciate his advice and guidance to achieve my academic goals as well, and for making me dream of a brighter future. I would like to give special thanks to Emily Zimovan, the Mission Design Team Leader of Project Aldrin- Purdue, for her collaboration and contribution to this project. Emily helped me analyze the S1L1 cycler trajectory in the circular-coplanar model, had the original idea of using the cycler vehicles as communication relays, and found the orbit opportunities for the cyclers in STOUR. She performed an exceptional work as a team leader and I greatly enjoyed the innumerous hours we worked together. I am very grateful to have met Emily, and to have had her as a classmate and as a teammate; and most importantly, I am very grateful to have Emily as a friend. I must thank Universidad Carlos III de Madrid and Purdue University for the opportunity to study abroad in the US, which consequently opened up the door to a whole new spectrum of personal, academic and professional experiences and possibilities. I would like to express my deepest gratitude to Madison Neuenschwander, for her support, motivation and love over the past year. She encouraged me to follow my dreams, she made me recognize my deepest passions and motivations, challenged my perspective and beliefs, and helped me change and grow as a person. I feel extremely fortunate to have Madison in my life. I would like to thank my family in Chile: cousins (Cristian, Rolo, Dani and Paula), aunts (Marcela and Cristina), uncles (Andoni and Rolando–may he rest in peace) and grandparents (Teresa and Hernan),´ for being the reason I pursue my goals; for their care and love that remained strong despite the distance. Last, I would like to thank my mother, Teresa, for her brave effort and sacrifice to provide a life full of ready- to-be-opened doors to her children: my brother (Sebastian)´ and myself. She has become my biggest inspiration, and she taught me the values and principles that make me the person I am today. I would like to dedicate this thesis, in particular, to her, together with all I have ever achieved; as everything I have ever done, and everything I will ever do, is thanks to the opportunities she helped me realize I now have. iii Abstract Earth-Mars cycler trajectories could be used as a periodic and cost-efficient human transportation sys- tem from Earth to Mars in a future mission to colonize Mars. Continuous and reliable communication between Mars and the Earth will be required in such a mission. In a circular-coplanar model, the exis- tance of a particularly interesting cycler trajectory (ballistic outbound Earth-Mars S1L1 cycler trajectory) is proven, which has relatively short Earth-Mars transfer times, low relative velocities with respect to the planets at the encounters, and an intermediate Earth encounter within every two-synodic-period cycle. Two outbound Earth-Mars S1L1 cycler vehicles launched one synodic period apart could be used to max- imize the number of trips from Earth to Mars. A new and economic method to maintain communication over periods of direct Earth-Mars link blockage (i.e. Earth-Mars solar conjunction) is introduced for a mission such that two outbound Earth-Mars S1L1 cycler vehicles are used for human transportation to Mars, using the cycler vehicles also as communication relays to avoid the need of a heliocentric com- munications satellite constellation to communicate from and to Mars. The analysis is performed in a circular-coplanar model and in a more realistic model (i.e. ephemeris model for the states of Earth and Mars, and STOUR results for the orbit parameters of the cycler trajectories). Continuous communication with only one cycler vehicle in orbit is proven not to be possible. In a mission with permanent human settlements on Mars and Phobos (inside Stickney Crater), two two-satellite Mars-centered communica- tion constellations are designed (in a circular-coplanar model) to continuously communicate the colonies on Phobos and Mars, and the Earth (directly or through the cycler vehicles), which could avoid the need of a three- or four-satellite constellation around Mars. A communication constellation consisted of two satellites in a stationary orbit around Mars is determined to be a more cost-efficient solution than two satellites in Phobos’ orbit. The link performance of each of the communication links is analyzed for the communication architecture composed of two areostationary satellites, the colonies on Mars and Phobos, two cycler vehicles and the ground stations on Earth. Power requirements, antenna sizes and frequency are estimated for a demanding HDTV transmission from Mars and Phobos to Earth. iv Table of Contents Pablo A. Machuca Varela Table of Contents Page Acknowledgements iii Abstract iv Table of Contents v List of Figures vii List of Tables ix 1 Introduction 1 2 Circular-Coplanar Model of the S1L1 Cycler Trajectory3 2.1 Main Assumptions . .3 2.2 Given Information . .3 2.3 Analysis . .4 2.3.1 Lambert’s Problem . .4 2.3.2 The Ballistic S1L1 Cycler Trajectory . .6 3 Cyclers as Communication Relays 11 3.1 Main Assumptions . 11 3.2 Visibility Analysis . 12 3.2.1 Circular-Coplanar Model . 12 3.2.2 Ephemeris Model . 15 3.3 Communication Link Distance . 17 4 Communications Satellite Constellation around Mars 21 4.1 Introduction . 21 4.2 Main Assumptions . 22 Communication Strategies for Colonization Mission to Mars v Table of Contents Pablo A. Machuca Varela 4.3 Proposed Solutions . 22 4.3.1 Two Communication Satellites in Phobos’ Orbit . 22 4.3.2 Two Communication Satellites in an Areostationary Orbit . 23 4.4 Visibility Analysis . 25 4.4.1 Two Communication Satellites in Phobos’ Orbit . 26 4.4.2 Two Communication Satellites in an Areostationary Orbit . 30 4.5 Minimum Number of Antennas Required . 32 4.5.1 Two Communication Satellites in Phobos’ Orbit . 33 4.5.2 Two Communication Satellites in an Areostationary Orbit . 34 4.6 Limitations . 34 4.6.1 Two Communication Satellites in Phobos’ Orbit . 34 4.6.2 Two Communication Satellites in an Areostationary Orbit . 36 4.7 Comparison of the Proposed Solutions . 40 5 Link Budget Analysis 42 5.1 Main Assumptions . 42 5.2 Communication Links . 43 5.3 Maximum Propagation Path Length . 44 5.4 Link Equation . 44 5.5 Model Validation . 49 5.6 Link Design and Sizing . 52 5.6.1 Frequency . 52 5.6.2 Antenna Diameter . 52 5.6.3 Power Requirement . 53 5.7 Link Performance . 53 6 Conclusions 55 7 References 56 Communication Strategies for Colonization Mission to Mars vi List of Figures Pablo A. Machuca Varela List of Figures Page 2.1 Generic Space Triangle . .5 2.2 V1 at Earth Encounter as a function of τ .................................6 2.3 Apohelion of the Outer Leg as a function of τ ..............................7 2.4 Velocity Diagram of a Generic Hyperbolic Flyby of Earth . .8 2.5 Ballistic Earth-Mars S1L1 Cycler Trajectory . .9 3.1 Communication Link before Solar Conjunction . 11 3.2 Communication Link Availability, Circular-Coplanar Model . 13 3.3 Continuous Earth-Mars Communication Link, Circular-Coplanar Model . 14 3.4 Communication Link Availability, Ephemeris Model . 15 3.5 Continuous Earth-Mars Communication Link, Ephemeris Model . 16 3.6 Possible Communication Link Distances . 17 3.7 Continuous Earth-Mars Communication Link Distance . 18 3.8 Communication Link Distance . 19 4.1 Communication Satellites around Mars for Continuous Communication . 21 4.2 Geometry of Communications Satellite Constellation in Phobos’ Orbit . 22 4.3 Communication Links of Communications Satellite Constellation, Phobos’ Orbit . 23 4.4 Geometry of Communications Satellite Constellation, Areostationary Orbit . 24 4.5 Communication Links of Communications Satellite Constellation, Areostationary Orbit . 25 4.6 Minimum Elevation Angle and ∆φ Configuration . 26 4.7 Availability of Communication Links from Satellites, Phobos’ Orbit . 27 4.8 Availability of Communication Links from Mars, Phobos’ Orbit . 28 4.9 Availability of Communication Links from Phobos, Phobos’ Orbit . 29 4.10 Availability of Communication Links from Satellites, Areostationary Orbit . 30 4.11 Availability of Communication Links from Mars, Areostationary Orbit .