Periodic orbits under combined effects of oblateness and radiation in the restricted problem of three bodies

Abstract

In this paper, we study the existence of libration points and their linear stability when the three participating bodies are axisymmetric and the primaries are radiating, we found that the collinear points remain unstable, it is further seen that the triangular points are stable for 0<μ<μ _c , and unstable for $\mu_{c}\leq\mu\leq\tfrac{1}{2}$ where $\mu_{c}\in(0,\tfrac{1}{2})$, it is also observed that for these points the range of stability will decrease. In addition to this we have studied periodic orbits around these points in the range 0<μ<μ _c , we found that these orbits are elliptical; the frequencies of long and short orbits of the periodic motion are affected by the terms which involve parameters that characterize the oblateness and radiation repulsive forces. The implication is that the period of long periodic orbits adjusts with the change in its frequency while the period of short periodic orbit will decrease.