On the existence of libration points in the spatial collinear restricted four-body problem within frame of repulsive Manev potential and variable mass

2018 ◽  
Vol 117 ◽  
pp. 94-104 ◽  
Author(s):  
Md Sanam Suraj ◽  
Amit Mittal ◽  
Charanpreet Kaur ◽  
Rajiv Aggarwal
Keyword(s):  
Body Problem ◽  
Variable Mass ◽  
Libration Points ◽  
Four Body Problem

Stability of libration points in the restricted four-body problem with variable mass

2016 ◽  
Vol 361 (10) ◽  
Author(s):  
Amit Mittal ◽  
Rajiv Aggarwal ◽  
Md. Sanam Suraj ◽  
Virender Singh Bisht
Keyword(s):  
Body Problem ◽  
Variable Mass ◽  
Libration Points ◽  
Four Body Problem

Exploring the Location and Linear Stability of the Equilibrium Points in the Equilateral Restricted Four-Body Problem

2020 ◽  
Vol 30 (10) ◽  
pp. 2050155
Author(s):  
Euaggelos E. Zotos
Keyword(s):  
Linear Stability ◽  
Body Problem ◽  
Equilibrium Points ◽  
Libration Points ◽  
The Other ◽  
Classification Method ◽  
Four Body Problem ◽  
The Masses ◽  
Stable Points ◽  
Planar Version

The planar version of the equilateral restricted four-body problem, with three unequal masses, is numerically investigated. By adopting the grid classification method we locate the coordinates, on the plane [Formula: see text], of the points of equilibrium, for all possible values of the masses of the primaries. The linear stability of the libration points is also determined, as a function of the masses. Our analysis indicates that linearly stable points of equilibrium exist only when one of the primaries has a considerably larger mass, with respect to the other two primary bodies, when the triangular configuration of the primaries is also dynamically stable.

Generalized Elliptic Restricted Four-Body Problem with Variable Mass

2020 ◽  
Vol 46 (4) ◽  
pp. 275-288
Author(s):  
Abdullah A. Ansari ◽  
Sada Nand Prasad
Keyword(s):  
Body Problem ◽  
Variable Mass ◽  
Four Body Problem

scholarly journals Equilibrium Points and Basins of Convergence in the Triangular Restricted Four-Body Problem with a Radiating Body

2020 ◽  
Vol 30 (02) ◽  
pp. 2030003 ◽  
Author(s):  
J. E. Osorio-Vargas ◽  
Guillermo A. González ◽  
F. L. Dubeibe
Keyword(s):  
Body Problem ◽  
Equilibrium Points ◽  
Center Of Mass ◽  
Libration Points ◽  
The Sun ◽  
Radiation Factor ◽  
Trojan Asteroid ◽  
Four Body Problem ◽  
Common Center ◽  
The Stability

In this paper, we extend the basic equilateral four-body problem by introducing the effect of radiation pressure, Poynting–Robertson drag, and solar wind drag. In our setup, three primaries lie at the vertices of an equilateral triangle and move in circular orbits around their common center of mass. Here, one of the primaries is a radiating body and the fourth body (whose mass is negligible) does not affect the motion of the primaries. We show that the existence and the number of equilibrium points of the problem depend on the mass parameters and radiation factor. Consequently, the allowed regions of motion, the regions of the basins of convergence for the equilibrium points, and the basin entropy will also depend on these parameters. The present dynamical model is analyzed for three combinations of mass for the primaries: equal masses, two equal masses, different masses. As the main results, we find that in all cases the libration points are unstable if the radiation factor is larger than 0.01 and hence able to destroy the stability of the libration points in the restricted four-body problem composed by the Sun, Jupiter, Trojan asteroid and a test (dust) particle. Also, we conclude that the number of fixed points decreases with the increase of the radiation factor.

scholarly journals The Libration Points and Hill Surfaces in the Restricted Problem of Three Variable-Mass Bodies

1993 ◽  
Vol 132 ◽  
pp. 277-288 ◽  
Author(s):  
A.A. Bekov
Keyword(s):  
Restricted Problem ◽  
Body Problem ◽  
Variable Mass ◽  
Libration Points ◽  
Stellar Systems ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Time Dependencies ◽  
Three Body

The paper deals with the study of the arising and disappearence of collinear (Eulerian) L1, L2, L3, triangular (Lagrangian) L4, L5, coplanar L6, L7, ring L0 and infinitely distant L±∞ solutions in a restricted problem of three variable-mass bodies for different time dependencies of main bodies masses and for some additional conditions imposed on the systems parameters. In this case it is assumed that the motion of variable-mass main bodies is determined by the Gylden-Mestschersky problem. The Bill surfaces in the restricted three-body problem where main bodies masses variate isotropically according to the Mestschersky law are studied. Certain possibilities of applying the results of investigations to nonstationary double stellar systems are discussed.

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