Stability of the photogravitational restricted three-body problem with variable masses

Singh, Jagadish; Leke, Oni

doi:10.1007/s10509-009-0253-x

Cited by 75 publications

(44 citation statements)

References 10 publications

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“…Equation (14) is quadratic in λ and has the roots: (17) and Hence, the eccentricity of the long and short period orbit is found respectively by substituting the respective equations of (17) in (16) …”

Section: Now the Corresponding Characteristics Equation Of Thementioning

confidence: 99%

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Periodic Orbits around Triangular Points in the Restricted Problem of Three Oblate Bodies

Singh¹

2014

AJAA

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This paper performs a semi-analytic study of the periodic orbits around stable triangular equilibrium points when the three participating bodies are modeled as oblate spheroids, under effect of, radiation of the main masses and small change in the Coriolis and centrifugal forces. This study generalizes the one studied by AbdulRaheem and Singh, with the inclusion that the third body, due to rapid spinning, changes its shape from being a sphere, to an oblate spheroid. The orbits around these points are ellipses with long and short periodic orbits. The period, orientation, eccentricities, the semi-major and semi-minor axis of the elliptic orbits have been given. The consideration of the particle as an oblate spheroid affects all these outcomes. We clarify the discrepancies between our study and related previous studies.

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Section: Now the Corresponding Characteristics Equation Of Thementioning

confidence: 99%

“…Studies of this kind include among many, Radzievskii [8], Simmons et al [13], Singh and Leke [17]. Further generalizations are the case when the shapes of the participating bodies are not perfect spheres.…”

Section: Introductionmentioning

confidence: 99%

Periodic Orbits around Triangular Points in the Restricted Problem of Three Oblate Bodies

Singh¹

2014

AJAA

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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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“…It is observed that the collinear points are unstable and the triangular points are conditionally stable depending on the radiation factor and oblateness. Singh [11] investigated the stability of equilibrium points in the restricted three body problem in which the masses of the luminous primaries vary isotropically in accordance with the unified Meshcherskii law. They found that the collinear points are unstable and the triangular points are conditionally stable in the autonomized system.…”

Section: Introductionmentioning

confidence: 99%

Dynamics in the circular restricted three body problem with perturbations

Ansari

Alam

2017

IJAA

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This paper presents the dynamics in the restricted problem with perturbations i.e. the circular restricted three body problem by considering one of the primaries as oblate and other one having the solar radiation pressure and all the masses are variable (primaries and infinitesimal body). For finding the autonomized equations of motion, we have used the Meshcherskii transformation. We have drawn the libration points, the time series, the zero velocity curves and Poincare surface of sections for the different values of the oblateness and solar radiation pressure. Finally, we have examined the stability and found that all the libration points are unstable.

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Stability of the photogravitational restricted three-body problem with variable masses

Cited by 75 publications

References 10 publications

Periodic Orbits around Triangular Points in the Restricted Problem of Three Oblate Bodies

Periodic Orbits around Triangular Points in the Restricted Problem of Three Oblate Bodies

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

Dynamics in the circular restricted three body problem with perturbations

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