On the triangular libration points in photogravitational restricted three-body problem with variable mass

TLDR: In this paper, the authors investigated the triangular libration points in the photogravitational restricted three-body problem of variable mass, in which both the attracting bodies are radiating as well and the infinitesimal body vary its mass with time according to Jeans' law.

Abstract: This paper investigates the triangular libration points in the photogravitational restricted three-body problem of variable mass, in which both the attracting bodies are radiating as well and the infinitesimal body vary its mass with time according to Jeans' law. Firstly, applying the space-time transformation of Meshcherskii in the special case when q=1/2, k=0, n=1, the differential equations of motion of the problem are given. Secondly, in analogy to corresponding problem with constant mass, the positions of analogous triangular libration points are obtained, and the fact that these triangular libration points cease to be classical ones when alpha not equal 0, but turn to classical L (4) and L (5) naturally when alpha=0 is pointed out. Lastly, introducing the space-time inverse transformation of Meshcherskii, the linear stability of triangular libration points is tested when alpha > 0. It is seen that the motion around the triangular libration points become unstable in general when the problem with constant mass evolves into the problem with decreasing mass.