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Analysis of Copenhagen problem with a repulsive quasi‐homogeneous Manev‐type potential within the frame of variable mass
Author(s) -
Suraj Md Sanam,
Mittal Amit,
Kaur Charanpreet,
Aggarwal Rajiv
Publication year - 2020
Publication title -
astronomische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.394
H-Index - 63
eISSN - 1521-3994
pISSN - 0004-6337
DOI - 10.1002/asna.202013640
Subject(s) - variable (mathematics) , infinitesimal , physics , convergence (economics) , inverse , plane (geometry) , classical mechanics , inverse problem , type (biology) , mathematical analysis , mathematics , geometry , geology , paleontology , economics , economic growth
The present problem is devoted to the special case of restricted problem of three bodies, always referred as the Copenhagen problem when we consider the primaries of equal masses. In this manuscript, we have considered the third body of infinitesimal mass as variable and moreover, instead of taking only Newtonian potential and forces, a quasi‐homogeneous potential produced by the main primaries has also been taken into account. This implies that, in order to approximate the phenomena such as the radiation pressure or the primaries' nonsphericity, we insert an inverse cube corrective term to the gravitational law of inverse square. In this model, the impact of the parameters, arise as a result of variable mass on the number and locations of the in‐plane and out‐of‐plane equilibrium points, is discussed. Moreover, their stability is also analyzed and the impact of these parameters on the regions, where motion of the third particle is possible, is unveiled. The basins of convergence associated with these equilibrium points are also illustrated by the Newton–Raphson iterative scheme of two or more variables.