An Analytical Solution for the Perturbed Restricted Three-Body Problem Using Variation of Parameters Method

M.N. Ismail, A.H. Ibrahim, Sahar H. Younis, Ghada F. Mohamdien


In this work, the equations of motion of the restricted three-body problem under the effects of the oblateness of less massive primary and the radiation pressure of the bigger massive primary are expressed. The analytical solution is obtained by the variation of parameters method. The locations of the libration points are obtained. The periodic orbits around each of these points are investigated for the Sun-Earth system, the zero-velocity curves, the phase spaces, and the Poincare surface sections are presented for one of the collinear libration points and one of the non-linear libration points. The obtained results are compared with previous works such as Kunitsyn[13] and Schuerman[14], and good agreements with these results are found.

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