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).
Highlights
Since the restricted four-body problem has an important role in astro-dynamics and space dynamics, many attempts dealing with this problem have been done using numerical and analytical methods
In this work the Hamiltonian of the restricted four-body problem is constructed under the effect of solar radiation pressure, the location of the libration points are obtained at different values of the solar radiation pressure coefficient, the stability of motion about the collinear libration points is studied and Poincare surface sections is used to illustrates these stabilities
Jacobi constant at different values of the solar radiation pressure β, it is notice that there is a shift in positions of each of libration points related to the values of the solar radiation pressure coefficient β
Summary
Since the restricted four-body problem has an important role in astro-dynamics and space dynamics, many attempts dealing with this problem have been done using numerical and analytical methods. The network of the families of simple symmetric periodic solutions of the restricted four-body problem was investigated and the effect of radiation on the periodic orbits was studied, their stability, as well as the evolution of the families when the radiation parameter varies, and Poincare sections of the problem are illustrated [9]. The Effect of Solar Radiation Pressure on the Libration Points of the Restricted Four-Body Problem was studied and the periodic orbits were presented [12]. The existence of collinear and non-collinear equilibrium points and their linear stability in the framework of photo gravitational circular restricted four-body problem with Stokes drag acting as a dissipative force and the first primary as a radiating body and the second primary as an oblate spheroid was studied numerically [15]. In this work the Hamiltonian of the restricted four-body problem is constructed under the effect of solar radiation pressure, the location of the libration points are obtained at different values of the solar radiation pressure coefficient, the stability of motion about the collinear libration points is studied and Poincare surface sections is used to illustrates these stabilities
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