In this work, the circumstances of eclipse for a circular satellites' orbit are studied. The time of passage of the ingress and egress points is calculated. Finally, the eclipse intervals of satellites' orbit are calculated. An application was done taken into account the effects of solar radiation pressure and Earth's oblateness on the orbital elements of circular orbit satellite.
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).
In this work, a dynamical system of four bodies is constructed. The forces which govern the motion are mutual gravitational attractions of the primaries, and radiation pressure force emitted from the more massive body. The equations of motion for the four bodies have taken into account the radiation pressure. We have deduced that these equations can be solved by Laplace transformations; the eigenvalues are obtained to study the motion about the libration points which are taken from the classical method, then the stability around the libration points is studied. The results obtained are presented. We remark that this model has special importance in astrodynamics to send spacecraft to stable regions to move in gravitational fields for some planetary system.
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