Classical newtonian gravity

This book gives an introduction to classical Newtonian gravitation and potential theories, as pieces of Physics essential for understanding classical mechanics and particularly relevant for Astrophysics. Among the four fundamental forces of Physics, gravity has the unique aspect of being an unscreened force which permeates the whole universe. Moreover, although Einstein’s general relativity provides a more extended framework for gravity, for most of the practical purposes, both in the field of pure scientific investigation and in the applicative one, Newtonian gravity provides much simpler and sufficiently approximated results, whenever applied in the regime of weak field. To reach the aim, the book is structured as follows. In the first chapter, some essential elements of vectorial calculus are recalled, especially to provide the formalism used in the following chapters. In the second chapter, classical Newtonian gravity theory for one and a generic number N of point masses is presented and discussed. The theory for point masses is naturally extended to the continuous case in the same chapter. In the third chapter, the paradigmatic case of spherical symmetry in the mass density distribution (central force) is dealt with the introduction of the useful tool of qualitative treatment of motion. In chapter four, the general case of nonsymmetric mass density distribution is discussed. In this chapter, classical potential theory is presented, with elements of harmonic theory, which is essential to understand the series development of the potential discussed in the second part of the chapter. The short, final, chapter five deals with the specific case of the motion of a satellite around the Earth. Examples and exercises are presented throughout the book to clarify aspects of the theory.