Photo – gravitational Effect on the Sitnikov Five – body Problem forming Square Configuration

Abstract

This paper deals with an extension of Sitnikov problem. Presently by considering the four radiating primaries at the vertices of a square and moving on the common circular orbit and the fifth body (infinitesimal mass) moving along the vertical line through the centre of the circular orbit, we form a new problem. We have developed the series solution of the Sitnikov five – body problem by the method of Lindstedt – Poincare. Also, we have examined the stability of the libration points with the help of the nature of roots of the characteristic equation. Thus, it is found that photo – gravitation has no effect on the Lindstedt – Poincare series solution but the libration points still stable.