scholarly journals Beyond-Newtonian dynamics of a planar circular restricted three-body problem with Kerr-like primaries

2020 ◽  
Vol 501 (1) ◽  
pp. 713-729
Author(s):  
Shounak De ◽  
Suparna Roychowdhury ◽  
Roopkatha Banerjee
Keyword(s):  
Body Problem ◽  
Newtonian Potential ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Spin Effects ◽  
Newtonian Dynamics ◽  
Zero Values ◽  
Newtonian System ◽  
Three Body ◽  
Infinitesimal Mass

ABSTRACT The dynamics of the planar circular restricted three-body problem with Kerr-like primaries in the context of a beyond-Newtonian approximation is studied. The beyond-Newtonian potential is developed by using the Fodor–Hoenselaers–Perjés procedure. An expansion in the Kerr potential is performed and terms up to the first non-Newtonian contribution of both the mass and spin effects are included. With this potential, a model for a test particle of infinitesimal mass orbiting in the equatorial plane of the two primaries is examined. The introduction of a parameter, ϵ, allows examination of the system as it transitions from the Newtonian to the beyond-Newtonian regime. The evolution and stability of the fixed points of the system as a function of the parameter ϵ is also studied. The dynamics of the particle is studied using the Poincaré map of section and the Maximal Lyapunov Exponent as indicators of chaos. Intermediate values of ϵ seem to be the most chaotic for the two cases of primary mass ratios (=0.001, 0.5) examined. The amount of chaos in the system remains higher than the Newtonian system as well as for the planar circular restricted three-body problem with Schwarzschild-like primaries for all non-zero values of ϵ.

scholarly journals Pulsating curves of zero velocity for infinitesimal mass around oblate and triaxial rigid body of triangular equilibrium points in elliptical restricted three body problem

2017 ◽  
Vol 5 (1) ◽  
pp. 29
Author(s):  
Nutan Singh ◽  
A. Narayan
Keyword(s):  
Rigid Body ◽  
Body Problem ◽  
Equilibrium Points ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Zero Velocity ◽  
Triaxial Rigid Body ◽  
Three Body ◽  
Infinitesimal Mass

This paper explore pulsating Curves of zero velocityof the infinitesimal mass around the triangular equilibrium points with oblate and triaxial rigid body in the elliptical restricted three body problem(ER3BP).

scholarly journals Robe's Restricted Three-Body Problem with Variable Masses and Perturbing Forces

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Jagadish Singh ◽  
Oni Leke
Keyword(s):  
Body Problem ◽  
Equilibrium Points ◽  
Second Primary ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Small Perturbations ◽  
Triangular Points ◽  
Numerical Exploration ◽  
Three Body ◽  
Infinitesimal Mass

The linear stability of equilibrium points of a test particle of infinitesimal mass in the framework of Robe's circular restricted three-body problem, as in Hallan and Rana, together with effect of variation in masses of the primaries with time according to the combined Meshcherskii law, is investigated. It is seen that, due to a small perturbation in the centrifugal force and an arbitrary constant of a particular integral of the Gylden-Meshcherskii problem, every point on the line joining the centers of the primaries is an equilibrium point provided they lie within the shell. Further, a number of pairs of equilibrium points lying on the -plane and forming triangles with the centers of the shell and the second primary exist, for some values of . The points collinear with the center of the shell are found to be stable under some conditions and the range of stability depends on the small perturbations and , while the triangular points are unstable. Illustrative numerical exploration is given to indicate significant improvement of the problem in Hallan and Rana.

scholarly journals A general solution to non-collinear equilibria in terms of largest root (κ) of confocal oblate spheroid

2016 ◽  
Vol 4 (1) ◽  
pp. 1
Author(s):  
M Javed Idrisi
Keyword(s):  
General Solution ◽  
Body Problem ◽  
Oblate Spheroid ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Mean Motion ◽  
Three Body ◽  
Infinitesimal Mass

<p>This paper deals with the existence of non-collinear equilibria in restricted three-body problem when less massive primary is an oblate spheroid and the potential of oblate spheroid is in terms of largest root of confocal oblate spheroid. This is found that the non-collinear equilibria are the solution of the equations <em>r</em><sub>1</sub> = <em>n</em><sup>-2/3</sup> and κ = 1 – <em>a</em><sup>2</sup>, where <em>r</em><sub>1</sub> is the distance of the infinitesimal mass from more massive primary, <em>n</em> is mean-motion of primaries, <em>a</em> is semi axis of oblate spheroid and κ is the largest root of the equation of confocal oblate spheroid passes through the infinitesimal mass.</p>

scholarly journals On Motion around the Collinear Equilibrium Points in the Relativistic R3BP with a Smaller Triaxial Primary

2018 ◽  
Vol 13 ◽  
pp. 1-11
Author(s):  
Bello Nakone ◽  
Jagadish Singh
Keyword(s):  
Body Problem ◽  
Equilibrium Points ◽  
Restricted Three Body Problem ◽  
The Sun ◽  
Three Body Problem ◽  
Numerical Studies ◽  
Three Body ◽  
Infinitesimal Mass

This paper studies the motion of an infinitesimal mass near the collinear equilibrium points in the framework of relativistic restricted three-body problem (R3BP) when the smaller primary is a triaxial body. It is observed that the positions of the collinear points are affected by the relativistic and triaxiality factors. The collinear points are found to remain unstable. Numerical studies in this connection, with the Sun-Earth, Sun-Pluto and Earth-Moon systems have been carried out to show the relativistic and triaxiality effects.

On the modified circular restricted three-body problem with variable mass

New Astronomy ◽  
2021 ◽  
Vol 84 ◽  
pp. 101510
Author(s):  
Md Sanam Suraj ◽  
Rajiv Aggarwal ◽  
Md Chand Asique ◽  
Amit Mittal
Keyword(s):  
Body Problem ◽  
Variable Mass ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Three Body

scholarly journals GEOMETRY OF HOMOCLINIC CONNECTIONS IN A PLANAR CIRCULAR RESTRICTED THREE-BODY PROBLEM

2007 ◽  
Vol 17 (04) ◽  
pp. 1151-1169 ◽  
Author(s):  
MARIAN GIDEA ◽  
JOSEP J. MASDEMONT
Keyword(s):  
Symbolic Dynamics ◽  
Body Problem ◽  
Invariant Manifolds ◽  
Libration Point ◽  
Homoclinic Orbits ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Lyapunov Orbits ◽  
Homoclinic Connections ◽  
Three Body

The stable and unstable invariant manifolds associated with Lyapunov orbits about the libration point L1between the primaries in the planar circular restricted three-body problem with equal masses are considered. The behavior of the intersections of these invariant manifolds for values of the energy between that of L1and the other collinear libration points L2, L3is studied using symbolic dynamics. Homoclinic orbits are classified according to the number of turns about the primaries.

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