INCREASING ORBITAL ENERGY VIA TETHER RETRIEVAL AND DEPLOYMENT IN A SYNCHRONOUS CONFIGURATION by AIDA FERRO ARDANUY B.S, Polytechnic University of Catalonia, Castelldefels, 2012 M.S, Polytechnic University of Catalonia, Terrassa, 2015 A thesis submitted to the Graduate Faculty of the University of Colorado Colorado Springs in partial fulfillment of the requirements for the degree of Master of Science Department of Mechanical and Aerospace Engineering 2017 This thesis for the Master of Science degree by Aida Ferro Ardanuy has been approved for the Department of Mechanical and Aerospace Engineering by Steven Tragesser, Chair Peter Gorder Radu Cascaval Date: 8/1/2017 ii Ferro Ardanuy, Aida (M.S., Mechanical Engineering) Increasing Orbital Energy via Tether Retrieval and Deployment in a Synchronous Configuration Thesis directed by Professor Steven Tragesser ABSTRACT The aim of this thesis is to propose a new control law for deployment and retrieval of a tethered satellite system in order to increase the orbital energy without using propellant. The system is considered to be a non-rotating momentum exchange tether that does not release any of the end masses. Also, it is assumed that the system does not conserve total angular momentum and the cycle of retrieving and deploying is done under the equilibrium assumption maintaining a synchronous configuration around the Earth. Therefore, the net tangent force due the different orbital altitude of the masses produces a net angular impulse used to increase the orbital energy. iii ACKNOWLEDGEMENTS First of all, I want to say thank you to my family that from Barcelona had encourage and support me with anything I needed. Also, my friends, whom I could count on them at any time making this 5.240 mile to vanish. Thank you to the new friends done here at Colorado Springs that made me feel like home, sharing adventures at the mountain, travelling and the countless hours at the library. Thank you to all the faculty and stuff of the department of Mechanical and Aerospace Engineering, especially the invaluable help of my advisor, Steven Tragesser, for the hours, dedication and orientation invested during these months. Finally, thank you a lot to the Balsells Fellowship that gave me the opportunity to learn and keep growing in a different world. Without you this thesis would not have been possible. Per començar, vull donar les gràcies a la meva família, que desde Barcelona, m’han estat donant ànims i suport en tot el que he necessitat. També als meus amics de sempre, per fer que aquests 8.434 km no semblin tanta distància i poder comptar amb ells a cada moment. Gracies també, als nous amics d’aqui Colorado Springs que m’han fet sentir com a casa compartint aventures per la montanya, viatjant i les hores d’estudi a la biblioteca. Agrair a tot el servei docent del department de “Mechanical and Aerospace Enginering”, sobretot la inestimable ajuda del tutor d’aquest projecte, Steven Tragesser, per les hores, dedicació i l’orientació rebuda al llarg d’aquets mesos. Per acabar, agrair a la beca Balsells l’oportunitat que m’han donat per aprendre i continuar creixent en un món nou. Sense vosaltres no hagués estat possible. iv TABLE OF CONTENTS CHAPTER I. INTRODUCTION ......................................................................................................... 1 1.1 State of art ........................................................................................................ 1 1.2 Outline of the thesis .......................................................................................... 5 II. THEORETICAL DEVELOPMENT ............................................................................... 7 2.1 Model .................................................................................................................... 7 2.2 Equations of motion .............................................................................................. 8 2.2.1 Translational movement ................................................................................. 9 2.2.2 Rotational movement .....................................................................................10 2.2.3 General equations .........................................................................................11 2.3 Control law for equilibrium orientation ..................................................................12 2.4 Mission concept ...................................................................................................16 2.4.1 Cycle for orbit pumping ..................................................................................16 2.4.2 Analytic development of change in orbit energy .............................................18 III. Results .....................................................................................................................20 3.1 Validation .............................................................................................................20 3.1.1 Linearly increasing case ................................................................................20 3.1.2 Quasi-equilibrium case ..................................................................................23 3.2 Optimal retrieval and deployment angles .............................................................24 v 3.3 Optimal mass and length factors ..........................................................................28 3.4 Mission results .....................................................................................................30 IV. CONCLUSIONS .......................................................................................................33 REFERENCES ..............................................................................................................34 APPENDICES ...............................................................................................................36 A. Tether length and rate of change development ...................................................36 vi LIST OF FIGURES FIGURE 1. Gravity force depending on tether orientation ............................................................. 5 2. Model representation .................................................................................................. 8 3. Net tangent force .......................................................................................................17 4. Libration angle vs Time. Rate of change km/s. Mantri ..............................21 5. Libration angle vs Time. Rate of change l = − km/s ...........................................21 6. Libration angle vs Time. Rate of change l = − km/s. Mantri ...............................22 7. Libration angle vs Time. Rate of change l = − km/s ...........................................22 8. Comparison between new control law andl =classic − control law ...................................24 9. Libration angle vs. Time, retrieval ..............................................................................25 10. Tether length vs. Time, retrieval ..............................................................................26 11. Semi-major axis vs. Time, retrieval ..........................................................................26 12. Tangent force vs. Tether length ...............................................................................27 13. Effect of the mass and length factor on the orbit pumping .......................................29 14. Tether length variation vs. Time ...............................................................................31 15. Libration angle variation vs. Time ............................................................................31 16. Semi-major axis variation vs. Time ..........................................................................32 vii CHAPTER I INTRODUCTION 1.1 State of art The tether satellite system (TSS) consists of a long thin cable that couples two masses such as satellites, spacecraft, space stations, astronauts or even asteroids. Its main purpose is to provide space transportation without using propellant. Nevertheless, it is also used in other types of missions such as experiments of the upper atmosphere, cargo transfer or as a physical connection between the astronaut and the spacecraft. The inception of the tethered satellite system derived from the space tether, introduced by the scientist Tsiolkovsky back in 1895. He visualized a long tether anchored to the Earth’s surface going up to space for traveling purposes. Then, it seemed like an idea worthy of a Jules Verne novel, so it was not until 65 years later, when the scientist Artsutanov developed the concept on a Sunday Pravda supplement [1]. He defined it as a synchronous tether with a geostationary mother ship and two cables deploying towards and away from Earth respectively, thus the centrifugal force acting on the upper part of the structure will compensate for the gravitational force acting on the lower part. During the following years the theory of the space elevator was never given much credence, but in the 1960s, using the idea of an anchored satellite, the scientist Colombo proposed a system of two satellites connected by a tether to be used for low-orbital-altitude research [2]. Also, on a report published by NASA, Rupp contributed to the study of the dynamics of a system being deployed along its local vertical assuming the tether maintains 1 equilibrium [3]. From then on, the TSS got the attention of the space researchers and publications about this