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Modern Astrodynamics : Fundamentals and Perturbation Methods - Victor R. Bond

Modern Astrodynamics

Fundamentals and Perturbation Methods

Hardcover Published: 24th March 1996
ISBN: 9780691044590
Number Of Pages: 264

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Newton's laws of motion and his universal law of gravitation described mathematically the motion of two bodies undergoing mutual gravitational attraction. However, it is impossible to solve analytically the equation of motion for three gravitationally interacting bodies. This book discusses some techniques used to obtain numerical solutions of the equations of motion for planets and satellites, which are of fundamental importance to solar-system dynamicists and to those involved in planning the orbits of artificial satellites.

The first part introduces the classical two-body problem and solves it by rigorously developing the six integrals of the motion, starting from Newton's three laws of motion and his law of gravitation and then using vector algebra to develop the integrals. The various forms of the solution flow naturally from the integrals. In the second part, several modern perturbation techniques are developed and applied to cases of practical importance. For example, the perturbed two-body problem for an oblate planet or for a nonsymmetric rotating planet is considered, as is the effect of drag on a satellite. The two-body problem is regularized, and the nonlinear differential equation is thereby transformed to a linear one by further embedding several of the integrals. Finally, a brief sketch of numerical methods is given, as the perturbation equations must be solved by numerical rather than by analytical methods.

"The book brings primarily a very good theoretical insight into modern problems of astrodynamics. Moreover, it brings even a survey of numerical methods to be used to solve practical orbital problems."--Space Science Reviews

Preface
Backgroundp. 3
The Two-Body Problemp. 12
Kepler's Lawsp. 31
Methods of Computationp. 40
The f and g Functionsp. 58
Two-Point Boundary Value Problemsp. 81
Applicationsp. 91
Perturbation Theoryp. 117
Special Perturbation Methodsp. 147
Runge-Kutta Methodsp. 184
Types of Perturbationsp. 198
Appendixesp. 215
Coordinate Transformationsp. 217
Hyperbolic Motionp. 225
Conic Sectionsp. 230
Transfer-Angle Resolutionp. 233
Stumpff Functionsp. 236
Orbit Geometryp. 239
Referencesp. 243
Indexp. 247
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780691044590
ISBN-10: 0691044597
Audience: Tertiary; University or College
Format: Hardcover
Language: English
Number Of Pages: 264
Published: 24th March 1996
Country of Publication: US
Dimensions (cm): 24.36 x 16.31  x 2.31
Weight (kg): 0.55