Existence of libration points in the generalized photogravitational restricted problem of three bodies

Abstract

The motion of an infinitesimal mass under the gravitational field of two radiating bodies of finite mass is investigated analytically, with a focus on the possible existence of libration points, in the framework of the generalized restricted three-body problem. The analysis of Simmons et al. (1985) is extended to the case of an oblate-spheroid (rather than spherical) infinitesimal mass. A general radiation-pressure expression is introduced; the equations of motion are derived; and conditions for the existence of collinear, coplanar, and triangular libration points are obtained. It is shown that in the general case there are seven libration points: three collinear, two coplanar, and two triangular. Nine points are possible for small degrees of infinitesimal-mass oblateness