Series solutions of the Sitnikov restricted N+1-body problem: elliptic case

Abstract

Following Giacaglia (1967), in Sect. 2 we have developed equation of motion of the Sitnikov restricted N + 1-body problem in elliptic case. We assumed that the primaries are at the vertices of a regular N-gon so the distances of the primaries from center of mass are time depending. In Sect. 3 we have linearized the equation of motion to obtain the Hill's type equation and then find the approximate solution. In Sects. 4 and 5 the series solutions of the Sitnikov restricted N + 1-body problem have been developed by the method of Lindstedt-Poincaré and iteration of Green's function respectively. In Sect. 6 the two series solutions have been compared graphically by putting N = 2, 3 and 4 for different eccentricity.