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

Singh, Jagadish; Simeon, Ayas Mungu

doi:10.18052/www.scipress.com/ifsl.12.1

Cited by 6 publications

(8 citation statements)

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“…Our results for the second partial derivatives and the characteristic equation differ from those of Singh and Taura [5], Abouelmagd et al [11], and Singh and Simeon [18] due to the elliptic nature of our potential-like function. However, the P-R drag parts of the partial derivatives coincide with those of Singh and Simeon [18], that is, for δ 2 � W 2 � 0, W ⟶ W 1 , and α ⟶ δ 1 . eir results for the second partial derivatives are…”

Section: Advances In Astronomycontrasting

confidence: 96%

“…In the case A i � B i � 0(i � 1, 2) in the present work, the obtained results of the triangular points in the circular case are in agreement with those of Singh and Simeon [18] by…”

Section: Advances In Astronomysupporting

confidence: 92%

“…Researchers like Burns et al [16], Murray [17], Singh and Simeon [18], Alhussain [19], Chakraborty and Narayan [20], Amuda et al [21], and others studied the R3BP by taking into account the P-R drag in different views. Mishra et al [22] examined the stability of triangular points under the assumption that the bigger primary is a source of radiation with the incident P-R drag while the smaller is an oblate spheroid in the frame of the ER3BP.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Impacts of Poynting–Robertson Drag and Dynamical Flattening Parameters on Motion around the Triangular Equilibrium Points of the Photogravitational ER3BP

Umar

Hussain

2021

Advances in Astronomy

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Using an analytical and numerical study, this paper investigates the equilibrium state of the triangular equilibrium points L 4 , 5 of the Sun-Earth system in the frame of the elliptic restricted problem of three bodies subject to the radial component of Poynting–Robertson (P–R) drag and radiation pressure factor of the bigger primary as well as dynamical flattening parameters of both primary bodies (i.e., Sun and Earth). The equations of motion are presented in a dimensionless-pulsating coordinate system ξ − η , and the positions of the triangular equilibrium points are found to depend on the mass ratio μ and the perturbing forces involved in the equations of motion. A numerical analysis of the positions and stability of the triangular equilibrium points of the Sun-Earth system shows that the perturbing forces have no significant effect on the positions of the triangular equilibrium points and their stability. Hence, this research work concludes that the motion of an infinitesimal mass near the triangular equilibrium points of the Sun-Earth system remains linearly stable in the presence of the perturbing forces.

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Section: Advances In Astronomycontrasting

confidence: 96%

“…In the case A i � B i � 0(i � 1, 2) in the present work, the obtained results of the triangular points in the circular case are in agreement with those of Singh and Simeon [18] by…”

Section: Advances In Astronomysupporting

confidence: 92%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Impacts of Poynting–Robertson Drag and Dynamical Flattening Parameters on Motion around the Triangular Equilibrium Points of the Photogravitational ER3BP

Umar

Hussain

2021

Advances in Astronomy

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“…The triangular points for the binaries PSR J1518 + 4904, PSR B1534 + 12, PSR B1914 + 16 and PSR B2127 + 11c are unstable due to the almost equal masses of the neutron stars. Singh and Simeon carried out a study around the triangular equilibrium points in the Circular Restricted Three-Body Problem under triaxial luminous primaries with Poynting-Robertson Drag (Singh and Simeon, 2017). Duggad and co-authors investigated the effects of triaxiality of both primaries on the position and stability of the oblate in nitesimal body in the elliptic restricted problem of three-bodies (Duggad, Dewangan and Narayan, 2021).…”

Section: Introductionmentioning

confidence: 99%

Albedo Effects in the Elliptic Restricted Three-Body Problem Under an Oblate Primary, a Triaxial Secondary and a Potential Due to Belt in the Earth-Moon System.

Singh

Tyokyaa²

2022

Preprint

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We have examined the effects of Albedo in the elliptic restricted three-body problem under an oblate primary, a triaxial secondary and a potential due to belt for the Earth-Moon system. We have found that as the perturbed parameters increases, the possible boundary regions of the primary come closer to one other, allowing particles to freely travel from one region to the next and possibly merging the permissible regions. Our study has revealed that, the formation of triangular libration points depend on the Albedo effects, semi-major axis, eccentricity of the orbits, triaxiallity and the potential due to belt. As the aforementioned parameters increase, the triangular positions ${L}_{4}$ and ${L}_{5}$ move towards the centre of origin in cases 1, 2, 3, 4 and away from the centre of the origin in cases 5, 6 and 7. Considering the range of a stable and unstable libration point for the problem under study given as $0<\mu <{\mu }_{c}$ for stable libration points and ${\mu }_{c}\le \mu \le \frac{1}{2}$ for unstable libration points, our study has established that the triangular libration points are respectively stable and unstable for cases 1, 2, 6 and cases 3, 4, 5, 7. Our study has also revealed that each set of values has at least one characteristic complex root with a positive real part. Hence, the triangular libration points for the Earth-Moon system are unstable in the sense of Lyapunov. The Earth-Moon system's Poincare Surface of Section (PSS) has demonstrated that a small change in the initial conditions, the semi-major axis, and the eccentricity of the orbits have affected the system's behavior dramatically. Further, it is seen that a chaotic dynamical behavior of the system results into either regular or irregular orbits.

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“…The collinear points are those that connect the primaries, whereas the non-collinear points are those that form equilateral triangles with them. The non-collinear libration points have been proven to be conditionally stable, whereas the collinear libration points are usually unstable 1,[3][4][5][6][7][8][9][10][11] .Because most celestial planets' orbits are elliptical rather than circular, the elliptic restricted three-body problem is the finest tool for analyzing the dynamical behavior of such systems. According to observations, most celestial planets are oblate spheroid or triaxial rigid bodies.…”

mentioning

confidence: 99%

Albedo effects in the ER3BP with an oblate primary, a triaxial secondary and a potential due to belt

Singh

Richard²

2023

Sci Rep

Self Cite

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We have examined the effects of Albedo in the Elliptic Restricted Three-Body Problem (ER3BP) with an oblate primary, a triaxial secondary, and potential due to belt for the Earth–Moon system. We have found that as the perturbed parameters increases, the possible boundary regions of the primary come closer to one other, allowing particles to travel from one region to the next freely and possibly merge the permissible regions. Our study has revealed that the formation of triangular libration points depends on the Albedo effects, semi-major axis, the Eccentricity of the orbits, triaxiality, and the potential due to the belt. As the parameters mentioned above increase, the triangular positions $${L}_{4}$$ L 4 and $${L}_{5}$$ L 5 move towards the center of origin in cases 1, 2, 3, and 4 and away from the center of the origin in cases 5, 6, and 7. Considering the range of a stable and unstable libration point for the problem under study given as $$0<\mu <{\mu }_{c}$$ 0 < μ < μ c for stable libration points and $${\mu }_{c}\leq\mu \le \frac{1}{2}$$ μ c ≤ μ ≤ 1 2 for unstable libration points, our study has established that the triangular libration points are respectively stable and unstable for cases 1, 2, and 6 and cases 3, 4, 5, and 7. Our study has also revealed that each set of values has at least one characteristic complex root with a positive real part. Hence, the triangular libration points for the Earth–Moon system are unstable in the sense of Lyapunov. The Earth–Moon system's Poincare Surface of Section (PSS) has demonstrated that a slight change in the initial conditions, the semi-major axis, and the Eccentricity of the orbits have affected the system's behavior dramatically. Further, it is seen that a chaotic dynamical behavior of the system results into either regular or irregular orbits.

show abstract

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

Cited by 6 publications

References 28 publications

Impacts of Poynting–Robertson Drag and Dynamical Flattening Parameters on Motion around the Triangular Equilibrium Points of the Photogravitational ER3BP

Impacts of Poynting–Robertson Drag and Dynamical Flattening Parameters on Motion around the Triangular Equilibrium Points of the Photogravitational ER3BP

Albedo Effects in the Elliptic Restricted Three-Body Problem Under an Oblate Primary, a Triaxial Secondary and a Potential Due to Belt in the Earth-Moon System.

Albedo effects in the ER3BP with an oblate primary, a triaxial secondary and a potential due to belt

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