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.
About the Author: The author, Jorge A. Franco, was born on April 23, 1943, in Zaraza, Guárico, Venezuela. He obtained a degree in Electrical Engineering from the Universidad Central de Venezuela in 1975. Later, in 1984, he earned a Master's degree in Engineering at Carleton University in Ottawa in 1984, Canada. He worked at the Venezuelan Telephone Company (CANTV) since 1972 until his retirement in 2003. During a vacation trip in September 1995, one of his daughters motivated him to visit the facilities of CERN in Geneva. There, he was very deeply impressed with the research carried out in CERN, as well as with its infrastructure. This experience, together with his interest in relativistic physics since a young age, prompted him to start developing the Vectorial Relativity approach and the solution of the N-Body problem in 1996. During his "new career", he served as an editor of the Electronic Journal of Theoretical Physics (EJTP) from 2005 to 2006. Later, in September 2006 he was co-founder of the Journal of Vectorial Relativity which was available until June 2011. The journal was closed in September 2011, owing to problems with the internet servers. More recently, he participated in the International Conference on General Relativity, ICGR-2015, celebrated in November 2015, in the Sant Gadge Baba Amravati University, Amravati, India. Today, he continues trying to go further in his research.