Solar Radiation Pressure Effects on Stability of Periodic Orbits in Restricted Four-Body Problem

Abstract

In this work, the Hamiltonian of the four-body problem is considered under the effects of solar radiation pressure. The equations of motion of the infinitesimal body are obtained in the Hamiltonian canonical form. The libration points and the corresponding Jacobi constants are obtained with different values of the solar radiation pressure coefficient. The motion and its stability about each point are studied. A family of periodic orbits under the effects of the gravitational forces of the primaries and the solar radiation pressure are obtained depending on the pure numerical method. This purpose is applied to the Sun-Earth-Moon-Space craft system, and the results obtained are in a good agreement with the previous work such as (Kumari and Papadouris, 2013).

Stability Analysis in the Restricted Four Body Problem With Oblatness and Radiation Pressure.

“…Through this work, the four-body problem under the effects of the radiation and oblatness is studied. We observe that the locations of the libration points are shifted compared with those obtained by [20] who found the libration points of the four-body problem under gravitational and radiation only. The stability by applying the Lyapunov center theorem gives a good agreement with the Poincare map.…”

“…To apply our study the Sun-Earth-Moon system is considered, where the masses of the Earth, the Moon and the Sun in the canonical system are given as . We take where is the mass ratio of the two primaries, and the unit distance between the two primaries is equal unity [19] and [20]. A code is constructed using Mathematica to obtain the libration point to prove that the potential of the system is Lyapunov function and is positive definite, finally to find the periodic orbits about this libration points and the Poincare maps.…”

“…Let (13) We can write the Hamiltonian system as: (14) Where J is the asymptotic matrix, (15) To study the motion near the libration point let Then from Eqs. (14), (15) and (20) (21) This is reduced to: (22) Then the auxiliary equation for the linearized system is given by: (23) Eq. (23) has four roots which imply the behavior of the motion about the libration point.…”

“…In [18] the authors studied equilibrium points and zero velocity surfaces in the restricted four-body problem with solar wind drag. The authors [19] and [20] put a model for the sun's radiation effect on restricted four bodies. [21] the author used Lyapunov's center theorem to study the existence of periodic orbits families about the equilibrium points of a dynamical system with degrees of freedom described by a real analytical Hamiltonian .…”