Periodic solutions in the photogravitational restricted four-body problem

Abstract

The restricted four-body problem consists of an infinitesimal particle which is moving under the Newtonian gravitational attraction of three finite bodies m1, m2, m3. The three bodies (primaries) are moving in circular orbits about their common centre of mass fixed at the origin of the coordinate system, according to the solution of Lagrange where they are always at the vertices of an equilateral triangle. The fourth body does not affect the motion of the primaries. We consider that the primary body m1 is dominant and is a source of radiation while the other two small primaries have equal masses m2 = m3. We investigate the network of the families of simple symmetric periodic solutions of the problem and we study the effect of radiation on the distribution of the periodic orbits, their stability, as well as the evolution of the families when the radiation parameter varies. Poincaré surface of section of the problem as the dominant primary radiates are illustrated. Series of horizontal- and vertical-critical periodic orbits by varying the mass parameter m3 and typical critical asymmetric solutions of the problem are also given.