Interplanetary Astrodynamics

Description

Focusing on the orbital mechanics tools and techniques necessary to design, predict, and guide a trajectory of a spacecraft traveling between two or more bodies in a Solar System, this book covers the dynamical theory necessary for describing the motion of bodies in space, examines the N-body problem, and shows applications using this theory for designing interplanetary missions. While most orbital mechanics books focus primarily on Earth-orbiting spacecraft, with a brief discussion of interplanetary missions, this book reverses the focus and emphasizes the interplanetary aspects of space missions. Written for instructors, graduate students, and advanced undergraduate students in Aerospace and Mechanical Engineering, this book provides advanced details of interplanetary trajectory design, navigation, and targeting. Cover Half Title Title Page Copyright Page Dedication Table of Contents Authors Acknowledgements Chapter 1 Introduction 1.1 Purpose of Book 1.2 Structure of Book 1.3 History of Interplanetary Astrodynamics 1.3.1 History of the Study of Orbital Mechanics 1.3.2 Ancient A stronomers and Mathematicians 1.3.3 Middle Ages Astronomers and Mathematicians 1.3.4 18th-, 19th-, and 20th-Century Astronomers and Mathematicians 1.3.5 Pre-space Age and Space Age Engineers, Scientists, and Mathematicians 1.4 Interplanetary S pace Missions 1.4.1 Earth Moon Missions 1.4.2 Planetary Missions 1.4.2.1 Planetary Orbiters 1.4.2.2 Planetary Landers 1.4.2.3 Planetary Flybys and Orbiters 1.4.3 Future Missions Chapter 2 Kinematics, Dynamics, and Astrodynamics 2.1 Newton’s Laws 2.2 Kepler’s Laws 2.3 Two-Body Problem 2.4 Conic Sections 2.4.1 Elliptical Orbits 2.4.2 Circular Orbits 2.4.3 Parabolic Orbits 2.4.4 Hyperbolic Orbits 2.5 Orbital Elements 2.5.1 Describing Orbits in Two Dimensions 2.5.2 Describing Orbits in Three-Dimensions 2.5.3 Cartesian Orbital Elements 2.5.4 Cylindrical a nd Spherical Orbital Elements 2.5.5 Classical Orbital Elements 2.5.6 Other Types of Orbital Elements to Mitigate Singularities 2.6 Kepler’s Problem 2.6.1 Kepler’s Equation for Elliptical Orbits 2.6.1.1 Solution to Kepler’s Problem for Elliptical Orbits 2.6.2 Kepler’s Equation for Parabolic Orbits 2.6.2.1 Solution to Kepler’s Problem for Parabolic Orbits 2.6.3 Kepler’s Equation for Hyperbolic Orbits 2.6.3.1 Solution to Kepler’s Problem for Hyperbolic Orbits 2.6.4 Kepler’s Problem Using Universal Variables 2.6.4.1 Solution to Kepler’s Problem Using Universal Variables 2.6.5 Lagrange Coefficients 2.7 Perturbations 2.7.1 Lagrange’s Planetary Equations 2.7.2 Gravitational 2.7.3 Non-gravitational 2.8 Numerical Integration 2.8.1 Cowell’s Method 2.8.2 Encke’s Method 2.8.3 Euler-Cauchy Methods and Predictor-Corrector Methods 2.8.4 Runge-Kutta Problems Chapter 3 N-Body Problem 3.1 Formulation of the N-Body Problem 3.2 Restricted Three-Body Problem 3.2.1 Circular Restricted Three-Body Problem 3.2.2 Lagrange Points 3.2.3 Stability of Libration Points 3.2.4 Jacobi Integral 3.2.5 Tisserand’s Criterion 3.2.6 The State-Transition Matrix 3.3 Elliptical Restricted Three-Body Problem 3.4 Circular Restricted Four-Body Problem 3.5 Elliptical Restricted Four-Body Problem 3.6 Orbits in the Restricted Three-Body Problem 3.6.1 Lyapunov Orbits 3.6.2 Distant Retrograde Orbits 3.6.3 Lissajous Orbits 3.6.4 Halo Orbits 3.7 Dynamical Systems Theory 3.7.1 Differential Correction 3.7.2 Poincaré Sections 3.7.3 Invariant Manifolds 3.7.4 Orbit Classification 3.7.5 Transit Orbit Search 3.7.6 Weak Stability Boundary 3.8 Applications of Libration Point Orbits 3.8.1 Libration Point Missions Problems Chapter 4 Coordinate Frames, Time, and Planetary Ephemerides 4.1 Introduction to Coordinate Systems 4.2 Inertial Coordinate Systems 4.2.1 Planet-Centered Inertial 4.2.2 Heliocentric 4.2.3 Catalogs of Fundamental Stars (FK) 4.2.4 International Celestial Reference Frame 4.2.5 Barycentric and Geocentric Celestial Reference Systems 4.2.6 B-Plane 4.3 Rotating Coordinate Systems 4.3.1 Ground Tracks 4.3.2 Topocentric Coordinate Frames 4.4 Time 4.4.1 Solar and Sidereal Time 4.4.2 International Atomic Time (TAI) 4.4.3 Ephemeris Time (ET) 4.4.4 Barycentric Dynamical Time (TDB) and Barycentric Coordinate Time (TCB) 4.4.5 Terrestrial Time (TT) and Terrestrial Dynamical Time (TDT) 4.4.6 Universal Time and Its Variations 4.4.7 Julian date (JD) and Modified Julian Date (MJD) 4.4.8 Leap Seconds 4.4.9 One-Way Light Time (OWLT) 4.4.10 Spacecraft Event Time (SCET) 4.4.11 Mission Elapsed Time (MET) 4.5 Lunar Ephemerides Relative to the Earth 4.6 Solar Ephemerides Relative to the Earth 4.7 Planetary Motion Relative to the Sun 4.7.1 Low-Fidelity Motion 4.7.2 High-Fidelity Motion 4.8 JPL Horizons 4.8.1 Alternative Access Methods 4.8.2 Tracking the New Horizons Spacecraft – A JPL Horizons Example 4.8.3 Comparing Low-Fidelity Motion with High-Fidelity Motion Problems Chapter 5 Trajectory Design 5.1 Introduction to Trajectory Design 5.1.1 Useful Orbits 5.2 Orbital Transfers 5.2.1 Optimal, Two-Burn Coplanar Transfers 5.2.2 Optimal Three-Burn Coplanar Orbit Transfers 5.2.3 Three-Dimensional Transfers 5.3 Lambert’s Problem 5.3.1 Classical Solution to Lambert’s Problem 5.3.2 Universal Variable Solution to Lambert’s Problem 5.3.3 Multi-rev Lambert’s Problem 5.3.4 Examples of Lambert’s Problem 5.4 Relative Motion 5.4.1 The Hill-Clohessy-Wiltshire Equations 5.4.2 Rendezvous between Spacecraft 5.4.3 Rendezvous around a Distant Body 5.5 Basics of Orbit Design 5.5.1 Patched Conics 5.5.2 Sphere of Influence 5.5.3 Phases 5.5.3.1 Phase 1: Planetary Departure 5.5.3.2 Phase 2: Heliocentric Cruise 5.5.3.3 Phase 3: Planetary Arrival 5.6 Example 1: Interplanetary Hohmann Transfer between Earth and Mars 5.7 Example 2: Realistic Interplanetary Transfer between Earth and Mars 5.8 Porkchop Plots 5.9 Broken-Plane Transfers 5.10 Launch Geometry 5.10.1 Launch Window 5.10.2 Launch Periods and Synodic Period 5.11 Propulsive Maneuvers 5.11.1 Impulsive Maneuvers 5.11.2 Trajectory Correction Maneuvers 5.11.3 Orbit Trim Maneuver 5.12 Gravity Assists 5.12.1 Geometry 5.12.1.1 Two-Dimensional Gravity Assists 5.12.1.2 Three-Dimensional Gravity Assists 5.13 Free-Return Trajectories 5.14 Atmospheric Interactions 5.14.1 Aerocapture 5.14.2 Aerobraking 5.14.3 Entry, Descent, and Landing (EDL) 5.14.3.1 Precision Landing 5.15 Roundtrip Trajectory Design 5.15.1 Robotic Sample-Return Missions 5.15.2 Human Roundtrip Missions 5.15.3 Cycler Orbits 5.16 Low-Thrust Trajectories 5.16.1 Electric Propulsion 5.16.2 Solar Sails 5.16.3 Low-Thrust Missions 5.16.3.1 Radial Thrust 5.16.3.2 Tangential Thrust Problems Chapter 6 Navigation and Targeting 6.1 Tracking Sources and Methods 6.1.1 Deep Space Network 6.1.2 Radiometric Measurements 6.1.2.1 Doppler 6.1.2.2 Range 6.1.3 Delta-Differential One-Way Range (Delta-DOR) 6.2 Optical Navigation 6.3 Deterministic Orbit Determination 6.4 Statistical Orbit Determination 6.5 Maneuver Planning and Execution 6.5.1 Mid-Course Corrections Determination 6.5.2 Statistical Methods Applied to Targeting 6.6 Monte Carlo Simulations for Mission Planning Problems Appendix A: Astronomical Constants Appendix B: Spherical Trigonometry Appendix C: Planetary Ephemerides Appendix D: Initial Conditions for Periodic Orbits in the Circular Restricted Three-Body Problem for the Earth-Moon System Appendix E: Initial Conditions for Periodic Orbits in the Circular Restricted Three-Body Problem for the Mars-Phobos System References Index