Effects of Radiation Pressure on the Elliptic Restricted Four-Body Problem

Sahar H Younis,Ghada F Mohamdien,M N Ismail,A H Ibrahiem,Waqar A Khan

doi:10.1155/2021/5842193

Abstract

In this paper, under the effects of the largest primary radiation pressure, the elliptic restricted four-body problem is formulated in Hamiltonian form. Moreover, the canonical equations are obtained which are considered as the equations of motion. The Lagrangian points within the frame of the elliptic restricted four-body problem are obtained. The true anomalies are considered as independent variables. An analytical and numerical approach had been used. A code of Mathematica version 12 is constructed to truncate these considerations and is applied on the Earth-Moon-Sun system. In addition, the stability and periodicity of the motion about the equilibrium points are studied by using the Poincare maps. The motion about the collinear point L2 is presented as an example for the obtained results, and some families of periodic orbits are presented.

Highlights

Several systems in space dynamics such as two-body, threebody, and four-body are considered
Since the primaries are moving in elliptical orbits, to study the motion about any of the libration points and its stability, it is more convenient to introduce the independent variable f2 instead of the independent variable t, so that let
The new coordinates which depend on the true anomaly as independent variable are used

Summary

Introduction

Several systems in space dynamics such as two-body, threebody, and four-body are considered. Grebenikov et al [10] studied the problem of the four constrained bodies, by building the Hamiltonian technique, and obtained equilibrium solutions and found six possible equilibrium configurations. Chakraborty and Narayan [14] investigated the equilibrium points, linear stability, zero velocity curves, and fractal trough of the four-body constrained elliptic problem. We study the problem of the four bodies under the influence of the combined forces of gravity of the elementary bodies that revolve in an elliptical orbit around their center of mass and the pressure of radiation of the largest primary. The canonical equations are applied to the Earth-Moon-Sun system model to calculate the corresponding solutions for both the trigonometric and linear equilibrium points. The Poincare maps are presented to show these stabilities

Description of the Problem

The Hamiltonian of the Problem

H X ð13Þ

Results and Discussion

Conclusion