Literal Analytical Solution of Three DimensionalPhotogravitational Circular Restricted Three Body Problem

Abstract

This paper is devoted to construct the literal analytical solutions in power series form for photogravitationalcircular restricted three body problem in three dimensional space, and taking into account that both primaries are light energysource. (RT3D2R) The importance of these analytical solutions is that, they are invariant under many operations such, addition, multiplication, exponentiation, integration, differentiation, etc. Actuallypower series provides usan excellent flexibility in obtaining simple analytical expressions which related to the motion of the third body.  Besides power series enables us of obtaining full numerical solutions of restricted three body problemat any given set of initial values. As a typical example, literal analytical expressions for the coefficients of the power series were developed in terms of the initial values for N=3.