Rudolf Kurth 
Introduction to the Mechanics of the Solar System [PDF ebook] 

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.