Critical mass value and secular solutions of the generalised photogravitational Robe's restricted three-body problem

Abstract

The secular solutions of Robe's restricted three-body problem is dealt in this paper when the first primary is an oblate spheroid-rigid shell, filled with homogeneous, incompressible fluid, with its equatorial plane coincident with the plane of motion and the second primary is a source of radiation. The collinear equilibria have conditional retrograde elliptical orbits around them in the linear sense, while the triangular points have long or short periodic retrograde elliptical orbits for the mass parameter, 0 ?????crit, the critical mass parameter, which decreases with the increase in oblateness and radiation force. However, retrograde elliptical periodic orbits exist for the case ??=3D ?crit through special choice of initial conditions, the eccentricity of which increases with oblatenes and decreases with radiation force for oblateness, which is not zero.