On Periodic Orbits in the Restricted Problem of Three Bodies in a Three Dimensional Coordinate System

This paper is an extension of paper [1] which also studies the existence of periodic orbits in the restricted problem of three bodies in a three dimensional coordinate system. Instead of taking p₂₀ = g₃₀ = P₃₀ = 0 for the generating solution as in [1], we have chosen the following conditions:

(i) P₂₀ ≠ 0, q₃₀ = P₃₀ = 0

and (ii) P₂₀ ≠ 0, q₃₀ ≠ 0, P₃₀ = 0(n)

The existence of periodic orbits is studied in both cases, using the same variables and the same method as in [1]. Our study will be restricted only to the first approximation.