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CubeSat Constellation Implementation and Management Using Differential Drag by MASANGRMNS8TUTE OF TECHNOLOGY Zachary Thomas Lee IJUL 112017 B.S. Mechanical Engineering United States Military Academy, 2015 LIBRARIES ARCHIVES Submitted to the Department of Aeronautics and Astronautics in partial fulfillment of the requirements for the degree of Master of Science in Aeronautics and Astronautics at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY June 2017 Massachusetts Institute of Technology 2017. All rights reserved. Signature redacted A uthor ............................ Department ronaucstronautics , eoatic and Atoatc May 25, 2017 Certified by................Signature redacted V Kerri Cahoy Associate Professor of Aeronautics and Astronautics Thesis Supervisor Accepted by.................Signature redacted Youssef M. Marzouk Associate Professor of Aeronautics and Astronautics Chair, Graduate Program Committee Disclaimer: The views expressed in this thesis are those of the author and do not reflect the official policy or position of the United States Army, the United States Department of Defense, or the United States Government. 2 CubeSat Constellation Implementation and Management Using Differential Drag by Zachary Thomas Lee Submitted to the Department of Aeronautics and Astronautics on May 25, 2017, in partial fulfillment of the requirements for the degree of Master of Science in Aeronautics and Astronautics Abstract Space missions often require the use of several satellites working in coordination with each other. Industry examples include Planet, which is working to develop a constellation of over 100 Cube Satellites (CubeSats) to obtain global imagery data daily, and Astro Digital, which seeks to implement a constellation of multispectral imaging satellites to image the entire Earth every three to four days [1, 2]. CubeSat constellations are also being considered for applications such as secure laser commu- nication relays and for weather sensing with short revisit times [3, 4]. Such missions require several CubeSats with regular spacing within an orbital plane to achieve their objectives. However, an appropriately arranged constellation can be particularly difficult to implement for CubeSats. Cold gas propulsion systems with the ability to provide tens of meters per second of delta-V (for a 3U CubeSat) exist and can be used for constellation management on timescales of weeks [5, 6, 7, 8, 9]. Monopropellant systems also currently exist for CubeSats, but, like cold gas systems, they can require significant power, mass, volume, and thermal management resources, and they also carry more risk [9, 10]. Launch services providers often limit acceptance of pressurized vessels, which can limit launch opportunities for CubeSats with cold gas or monopropellant propulsion systems. Although electric propulsion systems can provide up to 100 m/s delta-V for a 3U CubeSat, they also have mass, volume, cost, and power impacts, and they typically require timescales on the order of weeks to months to cause significant changes [6, 11, 9]. In low Earth orbit, there is sufficient drag to perturb satellite orbits. Though it varies widely based on conditions, at 500 kilometer (km) altitude, the acceleration due to drag on a 3U CubeSat can be around 15 ' per unit area [12]. Over time, this is enough acceleration to change a satellite's orbit. By controlling the attitude of a satellite, the profile area can be changed. By manipulating the profile area, the drag force can be changed, and satellites can be moved relative to each other within an orbital plane. Using differential drag at 550 km altitude, a 3U CubeSat can.move its true anomaly 180 degrees relative to another in the same orbital plane in about 3 100 days. Previous work with differential drag for constellation management has focused on linearized control schemes for formation flight. However, the linearized equations used for close-proximity flight are not valid for maximum-separation missions [13, 14, 15]. While some work does exist on maximum-separation missions, conditions are simplified or details on the estimation and control scheme are omitted or inadequate [8, 16, 17, 18, 19]. This work uses an unscented Kalman filter to estimate mean orbital elements and a novel control scheme to first offset and then match relative mean semi- major axes. The separation of mean semi-major axes creates different mean motions such that allow for the relative mean anomalies to be controlled. Simulation results demonstrate that differential drag can be used to control and maintain satellites within 0.5 degrees of the desired mean anomaly relative to other satellites. For two satellites in the same orbital plane at 500 km altitude seeking to maximize separation, 0.5 degrees corresponds to an angle that can be traversed in under 10 seconds. For Earth observation mission, this has a negligible effect on revisit times and can be considered an acceptable result. Thesis Supervisor: Kerri Cahoy Title: Associate Professor of Aeronautics and Astronautics 4 Acknowledgments While not without its difficulties, earning my degree at MIT has been an incredible journey, and I am so thankful to have had the opportunity to study and conduct research at MIT and Lincoln Laboratory. Having the support of my friends, family, and peers has meant more to me than words can express. Specifically, I would like to thank Professor Kerri Cahoy, my thesis advisor, for her guidance throughout my time at MIT. From the day I started to now, I have grown so much, and I could not have achieved this without Kerri. I would also like to thank Michael DiLiberto, Bill Blackwell, Dan Cousins, and Weston Marlow for mentoring me and taking the time to welcome me into a new project and teach me throughout my time working at Lincoln Laboratory. The entire MiRaTA team has taught me about satellite engineering, and they have made my experience a rewarding one. I am grateful to have worked with such an amazing team. My parents and brothers have always been supportive in my endeavors. Studying at MIT has been a dream of mine since I was a teenager, and I would not be here without the support of my family. Lastly, my friends have consistently encouraged me to pursue my goals, and this has helped keep me motivated throughout graduate school. Simply put, I could not have graduated MIT without the support of those close to me. 5 Contents Abstract ....... .............. 3 Acknowledgments ............... 5 Contents.. ................... 7 List of Figures. ................ 9 List of Tables ................. 10 Key Nomenclature .............. 11 1 Introduction 13 1.1 Introduction ............... 13 1.1.1 CubeSats ............ 13 1.1.2 Constellations .......... 18 1.2 Contributions .......... .... 20 1.3 Organization .............. 21 2 Background 22 2.1 Chapter Overview ............ 22 2.2 Orbits and Astrodynamics ....... 22 2.2.1 O rbits .............. 23 2.2.2 Orbital Perturbations ...... 24 2.2.3 Gauss's Variational Equations . 34 2.2.4 Mean Orbital Elements ..... 36 2.2.5 Clohessy-Wiltshire Equations . 38 2.3 Propulsion ....... ......... 39 2.4 Global Positioning System ....... 41 2.5 Two-Line Elements .......... 42 2.6 Orbit Estimation ............ 42 2.6.1 Unscented Kalman Filter .... 46 2.7 Attitude Determination and Control 49 2.7.1 Sensors ... ........... 50 2.7.2 Actuators ............ 50 2.7.3 CubeSat Performance ...... 51 2.8 Orbit Control through Differential Drag 52 3 Modeling and Simulation Approach 57 3.1 Chapter Overview ............ 57 3.2 Simulation Overview .... ...... 57 6 3.2.1 Orbit Propagation . ....................... 58 3.2.2 Simulation Parameters .... .................. 60 3.3 E stim ation . ............... ............... .. 61 3.4 C ontrol .............. .................... 64 3.5 Case Studies ................................ 69 3.5.1 Case Study 1: NPSCuL 8-CubeSat Deployer .......... 71 3.5.2 Case Study 2: TROPICS Low Inclination Orbit ........ 73 3.5.3 Case Study 3: Polar, Elliptical Orbit ..... ......... 74 3.5.4 Case Study 4: Planet Flock 1-C Comparison . ......... 75 3.5.5 Sensitivity Study on Implementation Time .. ......... 76 3.5.6 Station Keeping After Implementation ............. 77 3.6 Additional Considerations ...... ............ ...... 77 3.6.1 Reaction Wheel Saturation . ........... ........ 78 3.6.2 Orbit Lifetime ........ ........... ........ 78 3.6.3 Power Generation ... ............ .......... 79 3.7 Chapter Summary ... ......................... 79 4 Analysis and Results 80 4.1 Chapter Overview .............. ............... 80 4.2 UKF Performance for a Single CubeSat in Case 3: Polar, Elliptical Orbit 80 4.3 Results for Case Study 1: NPSCuL 8-CubeSat Deployer ........ 85 4.4 Results for Case Study 2: TROPICS Low Inclination Orbit ...... 90 4.5 Results for Case Study 3: Polar, Elliptical Orbit . ........... 92 4.6 Results for Case Study 4: Planet Flock 1-C Comparison .. ..... 95 4.7 Sensitivity Study on Implementation Time ..... .......... 98 4.8 Station Keeping After Implementation .. ............... 99 4.9 Chapter Summary ............. ............... 102 5 Conclusion and Future Work 104 5.1 Sum m ary ............. ............... ..... 104 5.2 Research Contributions ................ .......... 105 5.3 Future W ork ................................ 105 References 107 7 List of Figures 1-1 Number of CubeSat launches by year from 2005 to 2015 [30] 15 1-2 CubeSat mission status [42] .. .. .. .. .. .. .. .. 17 1-3 TROPICS constellation concept [3]. .. .. .. .. .. .. 19 1-4 Satellite size comparison . .. .. .

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