Introduction — The Theory of Orbits from Epicycles to “Chaos”

Abstract

The subject of this book is the study of the orbits followed by a body (mass point) subjected to the gravitational attraction of a given number of other bodies (mass points). We shall start from the minimum number (the two-body problem) and proceed to the case where it is convenient to represent the action exerted by a great number of bodies by means of a mean poten­tial. Although the concept of the orbit as a continuous line drawn in three-dimensional space by the subsequent positions of a moving mass point may appear elementary and hence be considered a primitive notion which should only require intuition, nevertheless it has, over the centuries, undergone some kind of evolution. In view of future developments, we shall choose as a start­ing point for the evolution of the concept of the orbit the formulation given by the Greeks in the third century B.C.