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One of the major challenges of modern space mission design is the orbital mechanics -- determining how to get a spacecraft to its destination using a limited amount of propellant. Recent missions such as Voyager and Galileo required gravity assist maneuvers at several planets to accomplishtheir objectives. Today's students of aerospace engineering face the challenge of calculating these types of complex spacecraft trajectories. This classroom-tested textbook takes its title from an elective course which has been taught to senior undergraduates and first-year graduate students forthe past 22 years. The subject of orbital mechanics is developed starting from the first principles, using Newton's laws of motion and the law of gravitation to prove Kepler's empirical laws of planetary motion. Unlike many texts the authors also use first principles to derive other importantresults including Kepler's equation, Lambert's time-of-flight equation, the rocket equation, the Hill-Clohessy-Wiltshire equations of relative motion, Gauss' equations for the variation of the elements, and the Gauss and Laplace methods of orbit determination. The subject of orbit transfer receivesspecial attention. Optimal orbit transfers such as the Hohmann transfer, minimum-fuel transfers using more than two impulses, and non-coplanar orbital transfer are discussed. Patched-conic interplanetary trajectories including gravity-assist maneuvers are the subject of an entire chapter and areparticularly relevant to modern space missions.
John E. Prussing is Professor Emeritus of Aerospace Engineering at the University of Illinois at Urbana-Champaign.
Bruce A. Conway is Professor of Aerospace Engineering at the University of Illinois at Urbana-Champaign.
Table of Contents
Each Chapter ends with References and Problems.
Chapter 1: The n-Body Problem
1.2 Equations of Motion for the n-Body Problem
1.3 Justification of the Two-Body Model
1.4 The Two-Body Problem
1.5 The Elliptic Orbit
1.6 Parabolic, Hyperbolic, and Rectilinear Orbits
1.7 Energy of the Orbit
Chapter 2: Position in Orbit as a Function of Time
2.2 Position and Time in an Elliptic Orbit
2.3 Solution for the Eccentric Anomaly
2.4 The f and g Functions and Series
2.5 Position versus Time in Hyperbolic and Parabolic Orbits: Universal Variables
Chapter 3: The Orbit in Space
3.2 The Orbital Elements
3.3 Determining the Orbital Elements from r and v
3.4 Velocity Hodographs
Chapter 4: The Three-Body Problem
4.2 Stationary Solutions of the Three-Body Problem
4.3 The Circular Restricted Problem
4.4 Surfaces of Zero Velocity
4.5 Stability of the Equilibrium Points
4.6 Periodic Orbits in the Restricted Case
4.7 Invariant Manifolds
4.8 Special Solutions
Chapter 5: Lambert's Problem
5.2 Transfer Orbits Between Specified Points
5.3 Lambert's Theorem
5.4 Properties of the Solutions to Lambert's Equation
5.5 The Terminal Velocity Vectors
5.6 Applications of Lambert's Equation
5.7 Multiple-Revolution Lambert Solutions
Chapter 6: Rocket Dynamics
6.2 The Rocket Equation
6.3 Solution of the Rocket Equation in Field-Free Space
6.4 Solution of the Rocket Equation with External Forces
6.5 Rocket Payloads and Staging
6.6 Optimal Staging
Chapter 7: Impulsive Orbit Transfer
7.2 The Impulsive Thrust Approximation
7.3 Two-Impulse Transfer Between Circular Orbits
7.4 The Hohmann Transfer
7.5 Coplanar Extensions of the Hohmann Transfer
7.6 Noncoplanar Extensions of the Hohmann Transfer
7.7 Conditions for Interception and Rendezvous
Chapter 8: Continuous-Thrust Transfer
8.2 Equation of Motion
8.3 Propellant Consumption
8.4 Quasi-Circular Orbit Transfer
8.5 The Effects of Nonconstant Mass
8.6 Optimal Quasi-Circular Orbit Transfer
8.7 Constant-Radial-Thrust Acceleration
8.8 Shifted Circular Orbits
Chapter 9: Interplanetary Mission Analysis
9.2 Sphere of Influence
9.3 Patched Conic Method
9.4 Velocity Change from Circular to Hyperbolic Orbit
9.5 Planetary Flyby (Gravity-Assist) Trajectories
9.6 Gravity-Assist Applications
Chapter 10: Linear Orbit Theory
10.2 Linearization of the Equations of Motion
10.3 The Hill-Clohessy-Wiltshire (CW) Equations
10.4 The Solution of the CW Equations
10.5 Linear Impulsive Rendezvous
10.6 State Transition Matrix for a General Conic Orbit
Chapter 11: Perturbation
11.2 The Perturbation Equations
11.3 Effect of Atmospheric Drag
11.4 Effect of Earth Oblateness
11.5 Effects of Solar-Lunar Attraction
11.6 Effect on the Orbit of the Moon
Chapter 12: Canonical Systems and the Lagrange Equations
12.2 Hamilton's Equations
12.3 Canonical Transformations
12.4 Necessary and Sufficient Conditions for a Canonical Transformation
12.5 Generating Functions
12.6 Jacobi's Theorem
12.7 Canonical Equations for the Two-Body Problem
12.8 The Delaunay Variables
12.9 Average Effects of Earth Oblateness Using Delaunay Variables
12.10 Lagrange Equations
Chapter 13: Perturbations Due to Nonspherical Terms in the Earth's Potential
13.2 Effect of the Zonal Harmonic Terms
13.3 Short-Period Variations
13.4 Long-Period Variations
13.5 Variations at O(J2/2)
13.6 The Potential in Terms of Conventional Elements
13.7 Variations Due to the Tesseral Harmonics
13.8 Resonance of a Near-Geostationary Orbit
Chapter 14: Orbit Determination
14.2 Angles-Only Orbit Determination
14.3 Laplacian Initial Orbit Determination
14.4 Gaussian Initial Orbit Determination
14.5 Orbit Determination from Two Position Vectors
14.6 Differential Correction
Appendix 1: Astronomical Constants
Appendix 2: Physical Characteristics of the Planets
Appendix 3: Elements of the Planetary Orbits