Space Flight Dynamics

Craig A. Kluever is C. W. LaPierre Professor of Mechanical and Aerospace Engineering, University of Missouri-Columbia, USA. He has industry experience as an aerospace engineer on the Space Shuttle program and has performed extensive research at the University of Missouri in collaboration with NASA involving trajectory optimization, space mission design, entry flight mechanics, and guidance and control of aerospace vehicles.

• Preface xi1 Historical Overview 11.1 Introduction 11.2 Early Modern Period 11.3 Early Twentieth Century 31.4 Space Age 42 Two-Body Orbital Mechanics 72.1 Introduction 72.2 Two-Body Problem 72.3 Constants of Motion 112.3.1 Conservation of Angular Momentum 112.3.2 Conservation of Energy 132.4 Conic Sections 152.4.1 Trajectory Equation 152.4.2 Eccentricity Vector 202.4.3 Energy and Semimajor Axis 212.5 Elliptical Orbit 232.5.1 Ellipse Geometry 242.5.2 Flight-Path Angle and Velocity Components 242.5.3 Period of an Elliptical Orbit 312.5.4 Circular Orbit 322.5.5 Geocentric Orbits 332.6 Parabolic Trajectory 382.7 Hyperbolic Trajectory 422.8 Summary 46Further Reading 46Problems 473 Orbit Determination 553.1 Introduction 553.2 Coordinate Systems 553.3 Classical Orbital Elements 573.4 Transforming Cartesian Coordinates to Orbital Elements 603.5 Transforming Orbital Elements to Cartesian Coordinates 663.5.1 Coordinate Transformations 683.6 Ground Tracks 753.7 Orbit Determination from One Ground-Based Observation 793.7.1 Topocentric-Horizon Coordinate System 793.7.2 Inertial Position Vector 813.7.3 Inertial Velocity Vector 823.7.4 Ellipsoidal Earth Model 853.8 Orbit Determination from Three Position Vectors 883.9 Survey of Orbit-Determination Methods 953.9.1 Orbit Determination Using Angles-Only Measurements 953.9.2 Orbit Determination Using Three Position Vectors 973.9.3 Orbit Determination from Two Position Vectors and Time 973.9.4 Statistical Orbit Determination 983.10 Summary 99References 100Problems 1004 Time of Flight 1074.1 Introduction 1074.2 Kepler’s Equation 1074.2.1 Time of Flight Using Geometric Methods 1074.2.2 Time of Flight Using Analytical Methods 1084.2.3 Relating Eccentric and True Anomalies 1124.3 Parabolic and Hyperbolic Time of Flight 1174.3.1 Parabolic Trajectory Flight Time 1174.3.2 Hyperbolic Trajectory Flight Time 1194.4 Kepler’s Problem 1234.5 Orbit Propagation Using Lagrangian Coefficients 1274.6 Lambert’s Problem 1354.7 Summary 145References 145Problems 1465 Non-Keplerian Motion 1515.1 Introduction 1515.2 Special Perturbation Methods 1525.2.1 Non-Spherical Central Body 1535.3 General Perturbation Methods 1595.3.1 Lagrange’s Variation of Parameters 1605.3.2 Secular Perturbations due to Oblateness ( J2) 1645.4 Gauss’ Variation of Parameters 1745.5 Perturbation Accelerations for Earth Satellites 1805.5.1 Non-Spherical Earth 1805.5.2 Third-Body Gravity 1825.5.3 Atmospheric Drag 1855.5.4 Solar Radiation Pressure 1895.6 Circular Restricted Three-Body Problem 1925.6.1 Jacobi’s Integral 1945.6.2 Lagrangian Points 1955.7 Summary 203References 203Problems 2046 Rocket Performance 2136.1 Introduction 2136.2 Rocket Propulsion Fundamentals 2136.3 The Rocket Equation 2146.4 Launch Trajectories 2196.5 Staging 2266.6 Launch Vehicle Performance 2316.7 Impulsive Maneuvers 2336.8 Summary 234References 235Problems 2357 Impulsive Orbital Maneuvers 2417.1 Introduction 2417.2 Orbit Shaping 2427.3 Hohmann Transfer 2457.3.1 Coplanar Transfer with Tangential Impulses 2487.4 General Coplanar Transfer 2527.5 Inclination-Change Maneuver 2567.6 Three-Dimensional Orbit Transfer 2597.7 Summary 264References 264Problems 2648 Relative Motion and Orbital Rendezvous 2758.1 Introduction 2758.2 Linear Clohessy–Wiltshire Equations 2758.3 Homogeneous Solution of the Clohessy–Wiltshire Equations 2808.4 Orbital Rendezvous Using the Clohessy–Wiltshire Equations 2888.5 Summary 298References 298Problems 2989 Low-Thrust Transfers 3039.1 Introduction 3039.2 Electric Propulsion Fundamentals 3049.3 Coplanar Circle-to-Circle Transfer 3069.3.1 Comparing Impulsive and Low-Thrust Transfers 3139.4 Coplanar Transfer with Earth-Shadow Effects 3159.5 Inclination-Change Maneuver 3189.6 Transfer Between Inclined Circular Orbits 3209.7 Combined Chemical-Electric Propulsion Transfer 3229.8 Low-Thrust Transfer Issues 3289.9 Summary 329References 329Problems 33010 Interplanetary Trajectories 33510.1 Introduction 33510.2 Patched-Conic Method 33810.2.1 Sphere of Influence 33910.2.2 Coplanar Heliocentric Transfers between Circular Orbits 34110.3 Phase Angle at Departure 35110.4 Planetary Arrival 35510.5 Heliocentric Transfers Using an Accurate Ephemeris 35910.5.1 Pork-Chop Plots 36710.5.2 Julian Date 36810.6 Gravity Assists 37010.7 Summary 378References 379Problems 37911 Atmospheric Entry 38511.1 Introduction 38511.2 Entry Flight Mechanics 38611.3 Ballistic Entry 39011.4 Gliding Entry 39611.5 Skip Entry 40411.6 Entry Heating 41211.7 Space Shuttle Entry 41811.8 Summary 422References 423Problems 42312 Attitude Dynamics 42912.1 Introduction 42912.2 Rigid Body Dynamics 43012.2.1 Angular Momentum of a Rigid Body 43212.2.2 Principal Axes 43812.2.3 Rotational Kinetic Energy 43912.2.4 Euler’s Moment Equations 44112.3 Torque-Free Motion 44212.3.1 Euler Angle Rates 44712.4 Stability and Flexible Bodies 45712.4.1 Spin Stability about the Principal Axes 45712.4.2 Stability of Flexible Bodies 45912.5 Spin Stabilization 46412.5.1 Dual-Spin Stabilization 46612.6 Disturbance Torques 46712.6.1 Gravity-Gradient torque 46712.6.2 Aerodynamic Torque 46812.6.3 Solar Radiation Pressure Torque 46912.6.4 Magnetic Torque 47012.7 Gravity-Gradient Stabilization 47012.8 Summary 476References 477Problems 47713 Attitude Control 48513.1 Introduction 48513.2 Feedback Control Systems 48513.2.1 Transfer Functions 48613.2.2 Closed-Loop Control Systems 48913.2.3 Second-Order System Response 49013.3 Mechanisms for Attitude Control 49713.3.1 Reaction Jets 49713.3.2 Momentum-Exchange Devices 49713.3.3 Magnetic Torquers 50113.4 Attitude Maneuvers Using Reaction Wheels 50113.5 Attitude Maneuvers Using Reaction Jets 51313.5.1 Phase-Plane Analysis of Satellite Attitude Dynamics 51313.5.2 Reaction Jet Control Law 51813.6 Nutation Control Using Reaction Jets 52713.7 Summary 534References 535Further Reading 535Problems 535Appendix A: Physical Constants 541Appendix B: Review of Vectors 543B.1 Introduction 543B.2 Vectors 543B.3 Vector Operations 544B.3.1 Vector Addition 544B.3.2 Cross Product 545B.3.3 Dot Product 546B.3.4 Scalar Triple Product 547B.3.5 Vector Triple Product 547Appendix C: Review of Particle Kinematics 549C.1 Introduction 549C.2 Cartesian Coordinates 549C.3 Polar Coordinates 551C.4 Normal-Tangential Coordinates 552Index