scholarly journals Influence of the Zonal Harmonics of the Primary on L4,5 in the Photogravitational ER3BP

2016 ◽  
Vol 10 ◽  
pp. 23-36
Author(s):  
Jagadish Singh ◽  
Blessing Ashagwu ◽  
Aishetu Umar
Keyword(s):  
Radiation Pressure ◽  
Body Problem ◽  
Equilibrium Points ◽  
Systems Dynamics ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Triangular Points ◽  
Zonal Harmonics ◽  
Three Body

We investigate in the framework of the elliptic restricted three-body problem (ER3BP), the influence of the zonal harmonics (J2and J4) of the primary and the radiation pressure of the secondary on the positions and stability of the triangular equilibrium points. The triangular points of the problem are affected by the parameters involved in the systems’ dynamics. The positions change with increase in the zonal harmonics, eccentricity and radiation pressure. The triangular points remain stable in the interval 0<μ<μcas shown arbitrarily.

scholarly journals Pulsating Different Curves of Zero Velocity around Triangular Equilibrium Points in Elliptical Restricted Three-Body Problem

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
A. Narayan ◽  
Amit Shrivastava
Keyword(s):  
Binary Systems ◽  
Body Problem ◽  
Equilibrium Points ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Triangular Points ◽  
Zero Velocity ◽  
Simulation Techniques ◽  
The Stability ◽  
Three Body

The oblateness and the photogravitational effects of both the primaries on the location and the stability of the triangular equilibrium points in the elliptical restricted three-body problem have been discussed. The stability of the triangular points under the photogravitational and oblateness effects of both the primaries around the binary systems Achird, Lyeten, Alpha Cen-AB, Kruger 60, and Xi-Bootis, has been studied using simulation techniques by drawing different curves of zero velocity.

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 Investigation of the effect of albedo and oblateness on the circular restricted four variable bodies problem

2017 ◽  
Vol 2 (2) ◽  
pp. 529-542 ◽  
Author(s):  
Abdullah A. Ansari
Keyword(s):  
Radiation Pressure ◽  
Body Problem ◽  
Equilibrium Points ◽  
Equations Of Motion ◽  
Variable Mass ◽  
Solar Radiation Pressure ◽  
Basins Of Attraction ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Three Body

AbstractThe present paper investigates the motion of the variable infinitesimal body in circular restricted four variable bodies problem. We have constructed the equations of motion of the infinitesimal variable mass under the effect of source of radiation pressure due to which albedo effects are produced by another two primaries and one primary is considered as an oblate body which is placed at the triangular equilibrium point of the classical restricted three-body problem and also the variation of Jacobi Integral constant has been determined. We have studied numerically the equilibrium points, Poincaré surface of sections and basins of attraction in five cases (i. Third primary is placed at one of the triangular equilibrium points of the classical restricted three-body problem, ii. Variation of masses, iii. Solar radiation pressure, iv. Albedo effect, v. Oblateness effect.) by using Mathematica software. Finally, we have examined the stability of the equilibrium points and found that all the equilibrium points are unstable.

Motion around the Triangular Equilibrium Points in the Circular Restricted Three-Body Problem under Triaxial Luminous Primaries with Poynting-Robertson Drag

2017 ◽  
Vol 12 ◽  
pp. 1-21
Author(s):  
Jagadish Singh ◽  
Ayas Mungu Simeon
Keyword(s):  
Linear Stability ◽  
Binary Stars ◽  
Body Problem ◽  
Equilibrium Points ◽  
Rigid Bodies ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Numerical Application ◽  
Triangular Points ◽  
Three Body

This paper explores the motion of an infinitesimal body around the triangular equilibrium points in the framework of circular restricted three-body problem (CR3BP) with the postulation that the primaries are triaxial rigid bodies, radiating in nature and are also under the influence of Poynting–Robertson (P-R) drag. We study the linear stability of these triangular points and for the numerical application, the binary stars Kruger 60 (AB) and Archird have been considered. These triangular points are not only perceived to move towards the line joining the primaries in the direction of the bigger primary with increasing triaxiality, they are also unstable owing to the destabilizing influence of P-R drag.

scholarly journals Effects of the albedo and disc on the zero velocity curves and linear stability of equilibrium points in the generalized restricted three-body problem

2019 ◽  
Vol 488 (2) ◽  
pp. 1894-1907
Author(s):  
Saleem Yousuf ◽  
Ram Kishor
Keyword(s):  
Linear Stability ◽  
Radiation Pressure ◽  
Body Problem ◽  
Equilibrium Points ◽  
Mass Parameter ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Zero Velocity ◽  
Zero Velocity Curves ◽  
Three Body

ABSTRACT The important aspects of a dynamical system are its stability and the factors that affect its stability. In this paper, we present an analysis of the effects of the albedo and the disc on the zero velocity curves, the existence of equilibrium points and their linear stability in a generalized restricted three-body problem (RTBP). The proposed problem consists of the motion of an infinitesimal mass under the gravitational field of a radiating-oblate primary, an oblate secondary and a disc that is rotating about the common centre of mass of the system. Significant effects of the albedo and the disc are observed on the zero velocity curves, on the positions of equilibrium points and on the stability region. A linear stability analysis of collinear equilibrium points L1, 2, 3 is performed with respect to the mass parameter μ and albedo parameter QA of the secondary, separately. It is found that L1, 2, 3 are unstable in both cases. However, the non-collinear equilibrium points L4, 5 are stable in a finite range of mass ratio μ. After analysing the individual as well as combined effects of the radiation pressure force of the primary, the albedo force of the secondary, the oblateness of both the primary and secondary and the disc, it is found that these perturbations play a significant role in the design of the trajectories in the vicinity of equilibrium points and in the analysis of their stability property. In the future, the results obtained will improve existing results and will help in the analysis of different space missions. These results are limited to the regular symmetric disc and radiation pressure, which can be extended later.

scholarly journals Effects of Perturbations on the Stability of Equilibrium Points in the CR3BP with Luminous and Heterogeneous Spheroid Primaries

2021 ◽  
Author(s):  
Jagadish Singh ◽  
Shitu Muktar Ahmad
Keyword(s):  
Body Problem ◽  
Equilibrium Points ◽  
Critical Mass ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Triangular Points ◽  
Stability Of Equilibrium ◽  
Oblate Spheroids ◽  
The Stability ◽  
Three Body

Abstract This paper studies the position and stability of equilibrium points in the circular restricted three-body problem (CR3BP) under the influence of small perturbations in the Coriolis and centrifugal forces when the primaries are radiating and heterogeneous oblate spheroids. It is seen that there exist five libration points as in the classical restricted three-body problem, three collinear Li(i=1,2,3) and two triangular Li(i= 4,5). It is also seen that the triangular points are no longer to form equilateral triangles with the primaries rather they form simple triangles with line joining the primaries. It is further observed that despite all perturbations the collinear points remain unstable while the triangular points are stable for 0 < µ < µc and unstable for µc ≤ µ ≤ ½, where µc is the critical mass ratio depending upon aforementioned parameters. It is marked that small perturbation in the Coriolis force, radiation and heterogeneous oblateness of the both primaries have destabilizing tendencies. Their numerical examination is also performed.

scholarly journals Locations of Lagrangian points and periodic orbits around triangular points in the photo gravitational elliptic restricted three-body problem with oblateness

2019 ◽  
Vol 7 (2) ◽  
pp. 25
Author(s):  
Ancy Johnson ◽  
Ram Krishan Sharma
Keyword(s):  
Periodic Orbits ◽  
Radiation Pressure ◽  
Body Problem ◽  
Critical Mass ◽  
Stable Region ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Lagrangian Points ◽  
Triangular Points ◽  
Three Body

Locations of the Lagrangian points are computed and periodic orbits are studied around the triangular points in the photogravitational elliptic restricted three-body problem (ER3BP) by considering the more massive primary as the source of radiation and smaller primary as an oblate spheroid. A new mean motion taken from Sharma et al. [13] is used to study the effect of radiation pressure and oblateness of the primaries. The critical mass parameter  that bifurcates periodic orbits from non-periodic orbits tends to reduce with radiation pressure and oblateness. The transition curves defining stable region of orbits are drawn for different values of radiation pressure and oblateness using the analytical method of Bennet [14]. Tadpole orbits with long- and short- periodic oscillations are obtained for Sun-Jupiter and Sun-Saturn systems.  

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