Generalized Elliptic Restricted Four-Body Problem with Variable Mass

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Generalized Elliptic Restricted Four-Body Problem with Variable Mass Abdullah A. Ansari1* and Sada Nand Prasad2** 1

International Center for Advanced Interdisciplinary Research (ICAIR), Sangam Vihar, New Delhi, India 2 Department of Mathematics Acharya Narendra Dev College, University of Delhi, Delhi, India Received March 18, 2020; revised March 18, 2020; accepted March 24, 2020

Abstract—The elliptic case of restricted four-body problem with variable mass of infinitesimal body is studied here. The three primary bodies which are placed at the vertices of an equilateral triangle and moving in the elliptical orbits around their common center of mass. Out of these primaries we have considered that one massive body is having radiating effect and other two bodies are oblate in shapes. The fourth body which have infinitesimal mass, are varying its mass according to Jeans law. We derive the equations of motion of the infinitesimal body under the generalized sense in the elliptic restricted four-body problem by using the Meshcherskii-space time transformations. Further we numerically study about the equilibrium points, Poincare´ surfaces of section, regions of possible motion and basins of the attracting domain by considering the variation of parameters used. Further more we examine the stability of these equilibrium points and found them unstable. DOI: 10.1134/S1063773720040015 Keywords: elliptical orbit, variable mass, oblate, regions of motion, attracting domain.

1. INTRODUCTION In the present age to write a research article is a serious problem because of the plagiarism. We have to be straight forward towards our aim and goal for the research. Here our field is celestial mechanics and dynamical astronomy which lies in the field of applied mathematics and is branch of mechanics. This study is related to the celestial bodies and behaviour of their motions. During last decades, researchers focused on the study of motion of a small body (in general satellite) under the influence of two, three or four massive bodies but small body is not influencing them. Accordingly they have considered their configurations while these bodies are moving either in circular or elliptical orbits with many other perturbations. Some of them are as follows: By supposing the bigger primary as oblate spheroid, Sharma and SubbaRao (1976) studied the stationary solutions and their characteristic exponents in the circular restricted 3-body problem. Kalvouridis (1997) investigated the equilibrium points and permissible regions of motion of the minor bodies under the effect of radiated oblate primaries. Douskos (2010) revealed the basins of attraction in the generalized Hill’s problem. Baltagiannis et al. (2011) studied the stability of the equilibrium points of the infinitesimal body * **

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which is moving under the influence of the three primaries. These primaries are situated at the vertices of an equilateral triangle, moving in circular orbits around their common center of mass to which they cons