The N-Body Problem

The solution of the N-body problem is one of the oldest problems in science and it is most relevant even in today's physics for its applications to cosmology and astronomy. Leading mathematicians attacked this problem over more than three centuries without arriving at a definite answer. A central role is played by periodic or stable orbits with a particular emphasis on understanding gravity and how it operates among astronomical bodies, and their stability at all in the long run. Here the author organizes his presentation through a systematic study of the different possible configurations for each specific N (number of bodies, assuming them with uniform mass density and discarding other influences), and its use is illustrated by the calculation of the different possible types of bodies' motion combinations as a base for comparing them with experimental results obtained in known systems. Many cases are distinguished and studied separately and detailed calculations are given. This development has also the treatment of the relativistic view of the N-Body Problem under a novel approach of Relativity. As a result, within the classical study Newton's assumption for the expression of the Universal Force among bodies for N > 2 was detected as erroneous; but not only were that, within the very beginnings of the relativistic analysis, Einstein's mass definition (and of course, his energy definition ) were found also erroneous. Corrections of these concepts were developed and used. Another new topic in this book is the used Three-Dimensional Relativistic framework allowing a simple and systematic treatment for the three-body problem and more, namely for values of N> 3, without needing in any configuration case to assume, as usually done, small or vanishing mass values. This work will be of interest to research mathematicians, physicists, computer scientists, engineers, etc. The author has made efforts to produce an essentially self-contained text, which makes it accessible not only to advanced students, but those in undergraduate level.