The general three-body problem studies the mutual interaction of three masses by determining their motion under the gravitational force using the Newton’s laws of motion and Newton’s law of gravitation. It is established that the closed form solution does not exist for the general three body problem. Further research introduced study of Circular Restricted Three-body problem. In this case one of the bodies is considered to have infinitesimal mass whose motion in circular orbits is influenced by the gravitational force of two massive primaries and the infinitesimal mass does not affect the motion of primaries. Lagrange proposed particular solution for this problem by considering a rotating frame such that the center of mass of the two primaries is taken as origin, the line joining the primary masses is x-axis, y-axis is taken perpendicular to x-axis in the plane of motion of primaries and z-axis is perpendicular to both x-axis and y-axis. The particular solution took the form of both collinear and non-collinear solutions. Associated with these solutions are the five points known as equilibrium points. Equilibrium points are the points where the forces acting on the body with infinitesimal mass in a rotating system are balanced hence there is no motion relative to the rotating system. Small particles like meteors, cosmic dust are considered as body with infinitesimal mass then their motion is influenced by the light pressure due to radiation emitted by the two primaries, hence along with the gravitational force another force due to light pressure was considered which paved way to the study of photogravitational three-body problem. In photogravitational circular restricted three body problem, the Infinitesimal mass experiences apart from the gravitational attractive force Fg, a repulsive force due to light pressure Fp, from both the primaries. In this paper, we present some valuable and interesting findings which have relevant real world applications. We prove the existence of out of plane equilibrium points for the Photo-Gravitational Circular Restricted three-body Problem and establish that they lie on a circle in a plane perpendicular to the plane of motion of primaries. It is also proved that for the equal values of radiation parameters which are less than 1, the triangles formed on either side of x-axis, by the line joining 1-μ and L4 or L5 having length r1, line joining μ and L4 or L5 having length r2 and the line joining the two primaries which are at unit distance is an isosceles triangle instead of being an equilateral triangle which was established by Lagrange in case of the non-photo-gravitational circular restricted three–body problem by formulating and solving the mathematical model of the photogravitational circular restricted three body problem.
Existence and regions of location of out of plane equilibrium points for photo-gravitational circular restricted three-body problem
Meera Joshi, S. N. Hasan; Existence and regions of location of out of plane equilibrium points for photo-gravitational circular restricted three-body problem. AIP Conf. Proc. 21 June 2023; 2649 (1): 030034. https://doi.org/10.1063/5.0119273
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