scholarly journals On the stability of L4,5 in the perturbed relativistic R3BP with a triaxial bigger primary

2016 ◽  
Vol 4 (2) ◽  
pp. 76
Author(s):  
Bello Nakone ◽  
Jagadish Singh
Keyword(s):  
Centrifugal Force ◽  
Small Perturbation ◽  
Coriolis Force ◽  
Stability Region ◽  
Centrifugal Forces ◽  
Small Perturbations ◽  
Triangular Points ◽  
Relativistic Factor ◽  
Coriolis And Centrifugal Forces ◽  
The Stability

In the present paper, we endeavor to study the stability of triangular points under the influence of small perturbations in the Coriolis and centrifugal forces, together with the triaxiality of the bigger primary in the framework of the relativistic R3BP. It is observed that the locations of these points are affected by the relativistic factor, triaxiality and a small perturbation in the centrifugal force, but are unaffected by that of the Coriolis force. It is also seen that for these points the range of stability region increases or decreases according as equation (14) without is greater or less than zero.

scholarly journals Existence and linear stability of triangular points in the perturbed relativistic R3BP when the bigger primary is an oblate spheroid

2016 ◽  
Vol 4 (1) ◽  
pp. 49
Author(s):  
Bello Nakone ◽  
Jagadish Singh
Keyword(s):  
Linear Stability ◽  
Centrifugal Force ◽  
Critical Mass ◽  
Oblate Spheroid ◽  
Centrifugal Forces ◽  
Mass Ratio ◽  
Small Perturbations ◽  
Coriolis Forces ◽  
Triangular Points ◽  
Coriolis And Centrifugal Forces

We study the effects of oblateness and small perturbations in the Coriolis and centrifugal forces on the locations and stability of the triangular points in the relativistic R3BP. It is observed that the positions are affected by the oblateness, relativistic, and a small perturbation in the centrifugal force, but are unaffected by that of Coriolis force. It is also seen that the relativistic terms, oblateness, small perturbations in the centrifugal and Coriolis forces influence the critical mass ratio. It is also noticed that all the former three and the latter one possess destabilizing and stabilizing behavior respectively. However, the range of stability increases or decreases according to as p >0 or p<0 where p depends upon the relativistic, oblateness and small perturbations in the Coriolis and centrifugal forces.

scholarly journals Unveiling Perturbing Effects of P-R Drag on Motion around Triangular Lagrangian Points of the Photogravitational Restricted Problem of Three Oblate Bodies

2021 ◽  
pp. 10-31
Author(s):  
Tajudeen Oluwafemi Amuda ◽  
Oni Leke ◽  
Abdulrazaq Abdulraheem
Keyword(s):  
Radiation Pressure ◽  
Equilibrium Points ◽  
Three Body Problem ◽  
Small Perturbations ◽  
Lagrangian Points ◽  
Triangular Points ◽  
Oblate Spheroids ◽  
The Stability ◽  
Zero Velocity Surfaces ◽  
Three Body

The perturbing effects of the Poynting-Robertson drag on motion of an infinitesimal mass around triangular Lagrangian points of the circular restricted three-body problem under small perturbations in the Coriolis and centrifugal forces when the three bodies are oblate spheroids and the primaries are emitters of radiation pressure, is the focus of this paper. The equations governing the dynamical system have been derived and locations of triangular Lagrangian points are determined. It is seen that the locations are influenced by the perturbing forces of centrifugal perturbation and the oblateness, radiation pressure and, P-R drag of the primaries. Using the software Mathematica, numerical analysis are carried out to demonstrate how the dynamical elements: mass ratio, oblateness, radiation pressure, P-R drag and centrifugal perturbation influence the positions of triangular equilibrium points, zero velocity surfaces and the stability. Our investigation reveals that, though the radiation pressure, oblateness and centrifugal perturbation decrease region of stability when motion is stable, however, they are not the influential forces of instability but the P-R drag. In the region when motion around the triangular points are stable an inclusion of the P-R drag of the bigger primary even by an almost negligible value of 1.04548*10-9 overrides other effect and changes stability to instability. Hence, we conclude that the P-R drag is a strong perturbing force which changes stability to instability and motion around triangular Lagrangian points remain unstable in the presence of the P-R drag.

scholarly journals Motion around triangular points in the restricted three-body problem with radiating heterogeneous primaries surrounded by a belt

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Jagadish Singh ◽  
Sunusi Haruna
Keyword(s):  
Coriolis Force ◽  
Binary Stars ◽  
Binary Systems ◽  
Equilibrium Points ◽  
Critical Mass ◽  
Three Body Problem ◽  
Small Perturbations ◽  
Triangular Points ◽  
Three Body ◽  
Dust Grain

Abstract The present paper studies the locations and linear stability of the triangular equilibrium points when both primaries are radiating and considered as heterogeneous spheroid with three layers of different densities. Additionally, we include the effects of small perturbations in the Coriolis and centrifugal forces and potential from a belt (circumbinary disc). It is observed that the positions of the triangular equilibrium points are substantially affected by all parameters (except a perturbation in Coriolis force) involved in the system.The stabilty of motion is found only when $$0 < \mu < \mu_{c}$$ 0 < μ < μ c , where $$\mu_{c}$$ μ c is the critical mass value which depends on the combined effect of radiation pressures and heterogeneity of the primaries, small perturbations and the potential from a belt.It is also seen that the Coriolis force and the belt have stabilizing effect,while the centrifugal force, radiation and heterogeineity of the primaries have destabilizing behaviour.The net effect is that the size of the region of stability decreases when the value of these parameters increases where $$\mu$$ μ is the mass ratio and $$k_{1} ,k_{2}$$ k 1 , k 2 characterize heterogeneity of both primaries. A practical application of this model could be the study of motion of a dust grain near the heterogeneous and luminous binary stars surrounded by a belt.Finally, we carried out and discuss numerical experiments aiming at computing the positions of triangular points and critical masses of three binary systems: Archid, Xi Booties and Kruger 60.

scholarly journals On the Stability ofL4,5in the Relativistic R3BP with Oblate Secondary and Radiating Primary

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Nakone Bello ◽  
Jagadish Singh
Keyword(s):  
Stability Region ◽  
Body Problem ◽  
Critical Mass ◽  
Mass Ratio ◽  
Three Body Problem ◽  
Triangular Points ◽  
Numerical Exploration ◽  
The Stability ◽  
Oblate Secondary ◽  
Three Body

We consider a version of the relativistic restricted three-body problem (R3BP) which includes the effects of oblateness of the secondary and radiation of the primary. We determine the positions and analyze the stability of the triangular points. We find that these positions are affected by relativistic, oblateness, and radiation factors. It is also seen that both oblateness of the secondary and radiation of the primary reduce the size of stability region. Further, a numerical exploration computing the positions of the triangular points and the critical mass ratio of some binaries systems consisting of the Sun and its planets is given in the tables.

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