Existence of Analytical Continuation and its Parametric Representation for μ≠0 Corresponding to the Circular Orbits for μ=0 in the Restricted Problem of Three Bodies in Three Dimensional Coordinate System.

Abstract

In this paper my aim is to show the existence of analytical continuation in the restricted problem of three bodies in three dimensional coordinate system. Similar problem was taken up by Hill [3] to show the existence of analytical continuation in lunar motion, but it was too much restricted. Birkhoff[2] also studied the problem in more general form, but this treatment was restricted only upto the plane. It was not easy to say whether the existence can be extended to space. I have done the problem for the space. During my study I have very often used the works done by Birkhoff & amp;Hill.