Orbital Mechanics

by Prussing, John E.; Conway, Bruce A.

• ISBN13: 9780195078343
• ISBN10: 0195078349
• Format: Hardcover
• Copyright: 1993-09-23
• Publisher: Oxford University Press

Summary

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.

Author Biography

John A. Prussing and Bruce A. Conway are Professors of Aeronautical and Astronautical Engineering at the University of Illinois at Urbana-Champaign.

Table of Contents

The n - Body Problem	3	(23)
Introduction	3	(3)
Equations of Motion for the n - Body Problem	6	(3)
Justification of the Two-Body Model	9	(3)
The Two-Body Problem	12	(3)
The Elliptic Orbit	15	(2)
Parabolic, Hyperbolic, and Rectilinear Orbits	17	(2)
Energy of the Orbit	19	(7)
References	22	(1)
Problems	22	(4)
Position in Orbit as a Function of Time	26	(20)
Introduction	26	(1)
Position and Time in an Elliptic Orbit	26	(4)
Solution for the Eccentric Anomaly	30	(2)
The f and g Functions and Series	32	(4)
Position versus Time in Hyperbolic and Parabolic Orbits: Universal Variables	36	(10)
References	42	(1)
Problems	42	(4)
The Orbit in Space	46	(16)
Introduction	46	(1)
The Orbital Elements	46	(3)
Determining the Orbital Elements from r and v	49	(5)
Velocity Hodographs	54	(8)
References	59	(1)
Problems	59	(3)
Lambert's Problems	62	(19)
Introduction	62	(1)
Transfer Orbits Between Specified Points	62	(5)
Lambert's Theorem	67	(3)
Properties of the Solutions to Lambert's Equation	70	(5)
The Terminal Velocity Vectors	75	(3)
Applications of Lambert's Equation	78	(3)
References	79	(1)
Problems	79	(2)
Rocket Dynamics	81	(18)
Introduction	81	(1)
The Rocket Equation	81	(2)
Solution of the Rocket Equation in Field-Free Space	83	(4)
Solution of the Rocket Equation with External Forces	87	(1)
Rocket Payloads and Staging	88	(4)
Optimal Staging	92	(7)
References	97	(1)
Problems	97	(2)
Impulsive Orbit Transfer	99	(21)
Introduction	99	(1)
The Impulsive Thrust Approximation	99	(3)
Two-Impulse Transfer between Circular Orbits	102	(2)
The Hohmann Transfer	104	(4)
Coplanar Extensions of the Hohmann Transfer	108	(4)
Noncoplanar Extensions of the Hohmann Transfer	112	(2)
Conditions for Intercept and Rendezvous	114	(6)
References	117	(1)
Problems	118	(2)
Interplanetary Mission Analysis	120	(19)
Introduction	120	(1)
Sphere of Influence	121	(3)
Patched Conic Method	124	(4)
Velocity Change from Circular to Hyperbolic Orbit	128	(1)
Planetary Flyby (Gravity-Assist) Trajectories	129	(5)
Flyby Following a Hohmann Transfer	134	(5)
References	137	(1)
Problems	137	(2)
Linear Orbit Theory	139	(16)
Introduction	139	(1)
Linearization of the Equations of Motion	139	(3)
The Hill-Clohessy-Wiltshire (CW) Equations	142	(2)
The Solution of the CW Equations	144	(6)
Linear Impulsive Rendezvous	150	(5)
References	153	(1)
Problems	153	(2)
Perturbation	155	(15)
Introduction	155	(1)
The Perturbation Equations	155	(9)
Effect of Atmospheric Drag	164	(1)
Effect of Earth Oblateness	164	(6)
References	168	(1)
Problems	168	(2)
Orbit Determination	170	(18)
Introduction	170	(2)
Angles-Only Orbit Determination	172	(1)
Laplacian Initial Orbit Determination	173	(3)
Gaussian Initial Orbit Determination	176	(4)
Orbit Determination from Two Position Vectors	180	(1)
Differential Correction	181	(7)
References	185	(1)
Problems	186	(2)
Appendix 1 Astronomical Constants	188	(1)
Appendix 2 Physical Characteristics of the Planets	189	(1)
Appendix 3 Elements of the Planetary Orbits	190	(1)
Index	191