Analysis of stability of non-collinear equilibrium points: Application to Sun–Mars and Proxima Centauri systems

Mia, Rajib; Prasadu, Bangaru Rama; Abouelmagd, Elbaz I.

doi:10.1016/j.actaastro.2022.12.031

Cited by 9 publications

(2 citation statements)

References 30 publications

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“…More recently, the effect of oblateness on the dynamics of CRTBP has been studied in detail by several investigated the dynamics of CRTBP when both of the primaries are oblate and emit radiation, together with perturbations in the Coriolis and centrifugal force. Other authors, such as Nurul , Dermawan et al (2015) and Mia et al (2023), considered the effect of oblateness and radiation force in the Elliptic Restricted Three-Body Problem.…”

Section: Introductionmentioning

confidence: 99%

Studying the Equilibrium Points of the Modified Circular Restricted Three-body Problem: The Case of Sun–Haumea System

Nurul Huda,

Dermawan,

Saputra

et al. 2023

Res. Astron. Astrophys.

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We intend to study a modified version of the planar Circular Restricted Three-Body Problem (CRTBP) by incorporating several perturbing parameters. We consider the bigger primary as an oblate spheroid and emitting radiation while the small primary has an elongated body. We also consider the perturbation from a disk-like structure encompassing this three-body system. First, we develop a mathematical model of this modified CRTBP. We have found there exist five equilibrium points in this modified CRTBP model, where three of them are collinear and the other two are non-collinear. Second, we apply our modified CRTBP model to the Sun–Haumea system by considering several values of each perturbing parameter. Through our numerical investigation, we have discovered that the incorporation of perturbing parameters has resulted in a shift in the equilibrium point positions of the Sun–Haumea system compared to their positions in the classical CRTBP. The stability of equilibrium points is investigated. We have shown that the collinear equilibrium points are unstable and the stability of non-collinear equilibrium points depends on the mass parameter μ of the system. Unlike the classical case, non-collinear equilibrium points have both a maximum and minimum limit of μ for achieving stability. We remark that the stability range of μ in non-collinear equilibrium points depends on the perturbing parameters. In the context of the Sun–Haumea system, we have found that the non-collinear equilibrium points are stable.

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Section: Introductionmentioning

confidence: 99%

Studying the Equilibrium Points of the Modified Circular Restricted Three-body Problem: The Case of Sun–Haumea System

Nurul Huda,

Dermawan,

Saputra

et al. 2023

Res. Astron. Astrophys.

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“…However, real heaven bodies may have different shape and mass distribution and their interaction is more complicated. To make model more realistic some authors take into account an oblateness of heaven bodies and some other perturbing forces like radiation pressure and quantum effects (see, for example, [1,2,13]). Such perturbations can modify motion of the bodies or change the regions of permissible motion but the problem is the stationary one as physical parameters of the system remain constant.…”

Section: Introductionmentioning

confidence: 99%

Modelling the Evolution of the Two-Planetary Three-Body System of Variable Masses

Imanova,

Prokopenya,

Minglibayev

2023

Mathematical Modelling and Analysis

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A classical non-stationary three-body problem with two bodies of variable mass moving around the third body on quasi-periodic orbits is considered. In addition to the Newtonian gravitational attraction, the bodies are acted on by the reactive forces arising due to anisotropic variation of the masses. We show that Newtonian’s formalism may be generalized to the case of variable masses and equations of motion are derived in terms of the osculating elements of aperiodic motion on quasiconic sections. As equations of motion are not integrable the perturbative method is applied with the perturbing forces expanded into power series in terms of eccentricities and inclinations which are assumed to be small. Averaging these equations over the mean longitudes of the bodies in the absence of a mean-motion resonances, we obtain the differential equations describing the evolution of orbital parameters over long period of time. We solve the evolution equations numerically and demonstrate that the mass change modify essentially the system evolution.

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Dynamics of a small planetoid in Newtonian gravity field of Lagrangian configuration of three primaries

2023

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Analysis of stability of non-collinear equilibrium points: Application to Sun–Mars and Proxima Centauri systems

Cited by 9 publications

References 30 publications

Studying the Equilibrium Points of the Modified Circular Restricted Three-body Problem: The Case of Sun–Haumea System

Studying the Equilibrium Points of the Modified Circular Restricted Three-body Problem: The Case of Sun–Haumea System

Modelling the Evolution of the Two-Planetary Three-Body System of Variable Masses

Dynamics of a small planetoid in Newtonian gravity field of Lagrangian configuration of three primaries

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