Equilibrium Points in the Restricted Four-Body Problem with Radiation Pressure

Singh, Jagadish; Vincent, Aguda Ekele

doi:10.1007/s00601-015-1030-8

Cited by 38 publications

(15 citation statements)

References 11 publications

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“…Papadouris and Papadakis studied, under the assumption of two equal masses, the existence, location, and stability of the equilibrium points in the photogravitational version of the Lagrange configuration [20], and the periodic solutions for this system [21]. Singh and Vincent conducted a similar study but considering all primaries as radiation sources [22]. Concerning the shape of the primaries, Asique et al studied the location of the libration points and their stability in the photogravitational PR4BP when one of the primaries is an oblate/prolate spheroid [23], while in Chand et.al.…”

Section: Introductionmentioning

confidence: 99%

Orbital dynamics in the photogravitational restricted four-body problem: Lagrange configuration

2020

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We study the effect of the radiation parameter in the location, stability and orbital dynamics in the Lagrange configuration of the restricted four-body problem when one of the primaries is a radiating body. The equations of motion for the test particle are derived by assuming that the primaries revolve in the same plane with uniform angular velocity, and regardless of their mass distribution, they will always lie at the vertices of an equilateral triangle. The insertion of the radiation factor in the restricted four-body problem, let us model more realistically the dynamics of a test particle orbiting an astrophysical system with an active star. The dynamical mechanisms responsible for the smoothening on the basin structures of the configuration space is related to the decrease in the total number of fixed points with increasing values of the radiation parameter. In our model of the Sun-Jupiter-Trojan Asteroid system, it is found that despite the repulsive character of the solar radiation pressure, there exist two stable libration points roughly located at the position ofL 4 and L 5 in the Sun-Jupiter system.

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Section: Introductionmentioning

confidence: 99%

Orbital dynamics in the photogravitational restricted four-body problem: Lagrange configuration

2020

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“…The study of the existence of periodic orbits in the restricted four‐body problem fascinated many researchers in recent time: some of them are Alvarez‐Ramírez & Barrabés (), Baltagiannis & Papadakis (), Papadakis (), Burgaos‐Garcia & Delgado ()). Furthermore, the existence and stability of equilibrium points in the restricted four‐body problem are studied and presented in a series of research articles: Kumari & Kushvah (), Asique et al (), Asique et al (), Papadouris & Papadakis (), and Singh & Vincent (). The effect of small perturbations in the Coriolis and centrifugal forces on the stability of libration points in the restricted four‐body problem is studied by Singh & Vincent ().…”

Section: Introductionmentioning

confidence: 99%

Divulging the effect of small perturbations in the Coriolis and centrifugal forces in the photogravitational version of autonomous restricted four‐body problem with oblate primary

et al. 2019

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In the present problem, we have studied the effect of small perturbations in the Coriolis and centrifugal forces on the locations and stability of libration points by taking the smaller primary as radiating oblate spheroid in the restricted four‐body problem. We have supposed that all the primaries are set in an equilateral triangle configuration, moving in circular orbit around their common center of mass. We have observed that the oblateness and radiation of the third primary, and the effect of the small perturbation in centrifugal force have substantial influences on the locations of libration points but the effect of the small perturbation in the Coriolis force has no impact on their locations. However, the stability of the libration points is highly influenced by the effect of the small perturbation in the Coriolis force. Furthermore, it is obtained that the effect of the small perturbation in the centrifugal force has a substantial influence on the regions of possible motion. In addition, we have also discussed how the oblateness and radiation pressure of the third primary, and the small perturbations in the Coriolis and centrifugal forces influence geometry of the basins of convergence by using multivariate version of the Newton–Raphson iterative scheme.

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“…Shrivastava et al in [46] evaluated the equilibrium points in the Robes restricted problem of three-bodies with effect of perturbations in the coriolis and centrifugal forces. Singh et al in [50][51][52][53][54][55][56][57][58][59] studied the restricted problem of three-bodies and four-bodies in circular and elliptic cases with different perturbations. Khanna et al in [29,30] explored the existence and stability of libration points in the restricted three-body problem when the smaller primary is a triaxial rigid body and the bigger one an oblate spheroid and observed that there are five libration points in which three collinear libration points are unstable and two triangular points are stable for the particular mass parameter.…”

Section: Introductionmentioning

confidence: 99%

The effect of perturbations on the circular restricted four-body problem with variable masses

Ansari¹,

Alhussain²,

Kellil³

2017

J. Math. Computer Sci.

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This paper presents a new investigation of the circular restricted four body problem under the effect of any variation in coriolis and centrifugal forces. Here, masses of all the bodies vary with time. This has been done by considering one of the primaries as oblate body and all the primaries are placed at the vertices of a triangle. Due to the oblateness, the triangular configuration becomes an isosceles triangular configuration which was an equilateral triangle in the classical case. After evaluating the equations of motion, we have determined the equilibrium points, the surfaces of the motion, the time series and the basins of attraction of the infinitesimal body. We note that, when we increase both the coriolis and centrifugal forces, the curves, surfaces of motion, and the basins of attraction are shrinking except when we fix the centrifugal force and increase the value of coriolis force, the curves are expanding and the equilibrium points are away from the origin. The behavior of the surfaces of motion and the basins of attraction in the last case (fixing the centrifugal force and increasing the value of coriolis force) will be studied next. In all the present study, we found that all the equilibrium points are unstable.

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Equilibrium Points in the Restricted Four-Body Problem with Radiation Pressure

Cited by 38 publications

References 11 publications

Orbital dynamics in the photogravitational restricted four-body problem: Lagrange configuration

Orbital dynamics in the photogravitational restricted four-body problem: Lagrange configuration

Divulging the effect of small perturbations in the Coriolis and centrifugal forces in the photogravitational version of autonomous restricted four‐body problem with oblate primary

The effect of perturbations on the circular restricted four-body problem with variable masses

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