Horseshoe orbits in the restricted four-body problem

Burgos-Garcia, Jaime; Bengochea, Abimael

doi:10.1007/s10509-017-3193-x

Cited by 12 publications

(4 citation statements)

References 26 publications

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“…Furthermore, several modifications of the restricted problem have been proposed in the past so as to make it more realistic to certain systems of Celestial Mechanics. Such modifications include the radiation and oblateness effects of the primaries [14][15][16][17] or the incorporation of some relativistic terms [18,19], while various works involve also a larger number for the primary bodies [20,21].…”

Section: Introductionmentioning

confidence: 99%

“…If a spatial periodic orbit has been sought, i.e., conditions (19) are fulfilled with a predetermined accuracy, a next such orbit existing in its neighbourhood can be predicted. To do so, we use the linearized system (20) and slightly change ∆ ż0 to an arbitrarily chosen small constant ε in order to get the remaining predictions in the form:…”

mentioning

confidence: 99%

“…where in system (20) we have now set δx 0 ≡ ∆x 0 , δ ẏ0 ≡ ∆ ẏ0 and δ ż0 ≡ ∆ ż0 to distinguish the prediction and correction steps. Also, the new terms appeared in (22) are…”

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confidence: 99%

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Numerical Investigation for Periodic Orbits in the Hill Three-Body Problem

Kalantonis

2020

Universe

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The current work performs a numerical study on periodic motions of the Hill three-body problem. In particular, by computing the stability of its basic planar families we determine vertical self-resonant (VSR) periodic orbits at which families of three-dimensional periodic orbits bifurcate. It is found that each VSR orbit generates two such families where the multiplicity and symmetry of their member orbits depend on certain property characteristics of the corresponding VSR orbit’s stability. We trace twenty four bifurcated families which are computed and continued up to their natural termination forming thus a manifold of three-dimensional solutions. These solutions are of special importance in the Sun-Earth-Satellite system since they may serve as reference orbits for observations or space mission design.

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Section: Introductionmentioning

confidence: 99%

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Numerical Investigation for Periodic Orbits in the Hill Three-Body Problem

Kalantonis

2020

Universe

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“…shown [13]. The photo-gravitational restricted four-body problem was studied with variable mass, zero velocity curves and Newton-Raphson basins of attraction were also discussed [14].…”

Section: Introductionmentioning

confidence: 99%

Solar Radiation Pressure Effects on Stability of Periodic Orbits in Restricted Four-Body Problem

Ismail¹,

Ibrahim²,

Zaghrout³

et al. 2019

WJM

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In this work, the Hamiltonian of the four-body problem is considered under the effects of solar radiation pressure. The equations of motion of the infinitesimal body are obtained in the Hamiltonian canonical form. The libration points and the corresponding Jacobi constants are obtained with different values of the solar radiation pressure coefficient. The motion and its stability about each point are studied. A family of periodic orbits under the effects of the gravitational forces of the primaries and the solar radiation pressure are obtained depending on the pure numerical method. This purpose is applied to the Sun-Earth-Moon-Space craft system, and the results obtained are in a good agreement with the previous work such as (Kumari and Papadouris, 2013).

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