Equilibrium Points and Related Periodic Motions in the Restricted Three-Body Problem with Angular Velocity and Radiation Effects

Abstract

The paper deals with a modification of the restricted three-body problem in which the angular velocity variation is considered in the case where the primaries are sources of radiation. In particular, the existence and stability of its equilibrium points in the plane of motion of the primaries are studied. We find that this problem admits the well-known five planar equilibria of the classical problem with the difference that the corresponding collinear points may be stable depending on the parameters of the problem. For all planar equilibria, sufficient parametric conditions for their stability have been established which are used for the numerical determination of the stability regions in various parametric planes. Also, for certain values of the parameters of the problem for which the equilibrium points are stable, the short and long period families have been computed. To do so, semianalytical expressions have been found for the determination of appropriate initial conditions. Special attention has been given to the continuation of the long period family, in the case of the classical restricted three-body problem, where we show numerically that periodic orbits of the short period family, which are bifurcation points with the long period family, are connected through the characteristic curve of the long period family.