Dynamics and Control Functional Division Report Jon Chrone Kevin Daugherty Jeremy Davis Kevin Earle Josh Ellis Mark Grigg Bhalvinder Gulati Becky Maiorano Ellen McDorman Josh Michener November 18, 2004 Contents List of Figures v List of Tables vi List of Abbreviations vii List of Symbols ix 1 Introduction 1 1.1 Astrodynamics . 1 1.1.1 Orbit Types . 1 1.1.2 Orbit Trade Studies . 2 1.1.3 The ∆v Budget . 2 1.1.4 Orbit Determination & Maintenance . 2 1.2 Attitude Determination and Control System . 3 1.2.1 Requirements . 3 1.2.2 Modes . 4 1.2.3 Disturbance Torques . 4 1.2.4 Control Approaches . 5 1.2.5 Algorithms . 6 1.3 Propulsion . 7 1.3.1 Propulsion System Alternatives . 7 1.3.2 Mission Phase Requirements . 9 1.3.3 Performance Considerations . 9 1.4 Interactions Between Dynamics and Control Subdivisions . 9 1.4.1 Astrodynamics and ADCS . 9 1.4.2 Astrodynamics and Propulsion . 10 1.4.3 ADCS and Propulsion . 10 1.5 Interaction with Other Functional Divisions . 10 1.5.1 Structures and Launch Vehicles . 10 1.5.2 Power, Thermal, and Environments . 11 1.5.3 Communications, Command and Data Handling . 12 1.6 Conclusion . 12 ii 2 Modelling and Analysis 13 2.1 Astrodynamics . 13 2.1.1 Equations of Motion . 13 2.1.2 Orbit Geometry . 15 2.1.3 Mission Analysis . 20 2.1.4 Orbit Maneuvers . 25 2.1.5 Launch Windows . 32 2.1.6 Orbit Perturbations . 32 2.1.7 Orbit Maintenance and Stationkeeping . 35 2.1.8 Guidance and Navigation Subsystem . 36 2.2 Attitude Determination and Control Systems . 36 2.2.1 Requirements . 36 2.2.2 Control Modes . 37 2.2.3 Sensors . 39 2.2.4 Disturbance Torques . 45 2.2.5 Control Approaches . 48 2.2.6 Algorithms . 52 2.3 Propulsion . 63 2.3.1 Specific Impulse and the Rocket Equation . 64 2.3.2 Chemical Rockets . 65 2.3.3 Cold Gas Propulsion . 71 2.3.4 Electric Propulsion . 72 2.3.5 Thermal Propulsion . 74 2.3.6 Propellant-less Propulsion . 76 2.3.7 Conclusion . 78 2.4 Analysis Tools . 78 2.4.1 Satellite Tool Kit . 79 2.4.2 WinOrbit . 79 2.4.3 Spacecraft Control Toolbox . 79 2.5 Interactions with Other Functional Divisions . 79 2.5.1 Astrodynamics and S&LV . 80 2.5.2 Astrodynamics and PT&E . 80 2.5.3 Astrodynamics and CC&DH . 80 2.5.4 ADCS and S&LV . 81 2.5.5 ADCS and PT&E . 81 2.5.6 ADCS and CC&DH . 81 2.5.7 Propulsion and S&LV . 81 2.5.8 Propulsion and PT&E . 82 2.5.9 Propulsion and CC&DH . 82 2.6 Interactions Among D&C Subdivisions . 82 2.6.1 Astrodynamics and ADCS . 83 2.6.2 Astrodynamics and Propulsion . 83 iii 2.6.3 ADCS and Propulsion . 83 2.7 Conclusion . 84 3 Examples 85 3.1 Orbit Examples . 85 3.1.1 Hohmann Transfer from Earth to Mars . 85 3.1.2 Type I Direct Earth-Mars Transfer . 90 3.2 ADCS Examples . 92 3.2.1 Torques . 93 3.2.2 Algorithms . 94 3.2.3 Control Approaches . 95 3.3 Propulsion Examples . 97 3.3.1 Selection of an Upper-Stage Rocket and Sizing of Propellant Tanks for a Mission to Mars . 97 3.3.2 Low Earth Orbit to Geosynchronous Orbit Transfer . 100 3.3.3 Earth to Venus Transfer . 101 3.4 Conclusion . 102 4 Summary and Conclusions 103 4.1 Astrodynamics . 103 4.1.1 Conclusions . 104 4.1.2 Recommendations . 105 4.2 ADCS . 106 4.2.1 Conclusions . 107 4.2.2 Recommendations . 108 4.3 Propulsion . 109 4.3.1 Conclusions . 110 4.3.2 Recommendations . 111 4.4 Conclusion . 112 A Astronomical Data 115 B Useful Tables 116 iv List of Figures 2.1 Geometry of an elliptical orbit . 16 2.2 Geometry of a parabolic orbit . 18 2.3 Geometry of a hyperbolic orbit . 19 2.4 The (3-1-3) Euler angle description of the orbit plane . 21 2.5 Illustration of a Hohmann transfer orbit . 26 2.6 Illustration of an orbit plane change maneuver . 27 2.7 Departure orbit to reach outer planet . 28 2.8 Departure orbit to reach inner planet . 28 2.9 Arrival orbit to the inner planet Venus . 29 2.10 Arrival orbit to the outer planet Mars . 30 2.11 Solar Sail Pitch Angle. 31 2.12 Schematic of an Ideal Rocket. 66 2.13 Schematic of a Typical Hydrazine Rocket. 69 2.14 Schematic of a Typical Solid Rocket . 70 2.15 Solid Rocket Grain Designs with Their Thrust Time Histories. 71 2.16 Schematic of a Typical Hybrid Rocket. 71 2.17 Nuclear Electric Propulsion Vehicle Concept . 73 2.18 Nuclear Thermal Propulsion Vehicle Concept . 75 2.19 Solar Orbit Transfer Vehicle. 76 2.20 Physical Solar Sail. 77 2.21 Magnetic Solar Sail. 77 3.1 Hohmann transfer from Earth to Mars . 86 3.2 Nonminimum energy transfer orbit from Earth to Mars . 90 3.3.