Kurth Introduction to the Mechanics of the Solar System

1. Auflage 2013
ISBN: 978-1-4831-4728-4
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 188 Seiten, Web PDF

Introduction to the Mechanics of the Solar System introduces the reader to the mechanics of the solar system and covers topics ranging from the periods of the planets to their flattening and its effects on the orbits of satellites. Kepler's three laws of planetary motion are also discussed, along with the law of gravity; the two-body problem; and perturbations in the motions of the moon and the planets. This book is comprised of four chapters and begins with an analysis of the kinematics of a single planet, focusing on the work of Johannes Kepler, particularly his determination of the orbits of the Earth and Mars and his formulation of his three laws of planetary motion. The following chapters explore systems of ordinary differential equations; determination of orbits using Laplace's method and Gauss' method; the equations of motion and their integrals; the perturbation equations of celestial mechanics; and Lagrange's solution of the three-body problem. The notations of the Earth and the moon are also considered. This monograph is intended for astronomers and astronomy students.

Autoren/Hrsg.

Kurth, Rudolf

Inhaltsverzeichnis

1;Front Cover;1
2;Introduction to the Mechanics of the Solar System;4
3;Copyright Page;5
4;Table of Contents;8
5;Preface;6
6;CHAPTER I. THE KINEMATICS OF A SINGLE PLANET;12
6.1;1. The periods of the planets;12
6.2;2. Kepler's determination of the orbits of the Earth and Mars : his first law;19
6.3;3. Kepler's second and third laws;24
6.4;4. The elements of a planetary orbit;26
6.5;5. The computation of the motion of a planet;29
6.6;6. Orbital determinations and their improvement;41
6.7;7. Summary and discussion;50
6.8;Exercises;51
6.9;NOTES;52
7;CHAPTER II. THE DYNAMICS OF A SINGLE PLANET;55
7.1;1. The law of gravity and the law of motion;55
7.2;2. Systems of ordinary differential equations;63
7.3;3. The two body problem;67
7.4;4. The determination of orbits;77
7.5;5. Summary;82
7.6;Exercises;84
7.7;NOTES;85
8;CHAPTER III. THE DYNAMICS OF THE PLANETARY SYSTEM;87
8.1;1. The equations of motion and their integrals;87
8.2;2. Perturbations in the coordinates;97
8.3;3. Perturbations in the elements;108
8.4;4. The perturbation equations of celestial mechanics;121
8.5;5. Perturbations in the motions of the planets;131
8.6;6. Perturbations in the motion of the Moon;133
8.7;7. The perturbation of the perihelion of Mercury;143
8.8;8. Lagrange's solutions of the three body problem;147
8.9;9. The problème restreint;148
8.10;10. Summary;153
8.11;Exercises;155
8.12;NOTES;157
9;CHAPTER IV. THE PLANETS AND THE MOON AS RIGID BODIES;159
9.1;1. Perturbations of the orbits of satellites caused by flattening of the planets;159
9.2;2. The rotation of the Earth;165
9.3;3. The rotation of the Moon;181
9.4;4. Summary and conclusion;184
9.5;Exercises;184
9.6;NOTES;185
10;INDEX;186