Variation Mass Effects on the Stability of Libration Points of Restricted Three Body Problem (Laplace Transformation)
Sahar H. Younis
Department of Mathematics, Faculty of Science (Girls), Al-Azhar Univesity, Egypt.
Fatma M. Elmalky
Department of Mathematics, Faculty of Science (Girls), Al-Azhar Univesity, Egypt.
M. N. Ismail *
Department of Astonomy and Meteorology, Faculty of Science, Al-Azhar University, Egypt.
*Author to whom correspondence should be addressed.
Abstract
In this work a dynamical system of three bodies with decreasing mass with respect to time is deduced. The Jean’s law is applied onto equations of motion. The equations of motion in this case are differed from that with constant mass only by small perturbing force considered as the variation of mass. This system is solved by using Laplace and Inverse Laplace Transformation. An application is done on the Earth–Moon-|Spacecraft system. The results obtained are compared with the previous work obtained by Explicit Rung-Kutta method and it was in a good agreement.
Keywords: Laplace and Inverse Laplace transformation, dynamical systems, restricted three body problem (RTBP), perturbation methods.