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Dynamics of infinitesimal body in the concentric restricted five-body problem

Author

Listed:
  • Idrisi, M. Javed
  • Ullah, M. Shahbaz
  • Ershkov, S.
  • Prosviryakov, E.Y.

Abstract

This research presents a model of a specific restricted five-body problem. In this model, there are four main bodies, referred to as primary bodies. The first two primary bodies have the same mass while the third and fourth primary bodies also share an identical mass, which is lesser than the former. These primary bodies are lined up in a straight line along a designated axis. They revolve in circular paths with different distances from a common central point that represents their shared center of mass. The first set of orbits has a shorter radius compared to the second set. Simplifying the motion equations of an infinitesimally small mass reveals a single governing parameter, λ, constrained within λ ∊ (λ0, 1), λ0 = 0.417221. Within the orbital plane of these primaries, seven equilibrium points are identified: four along the x-axis, two on the y-axis, and one at the system's origin. Notably, no equilibrium points were found outside this orbital plane. The study concludes that collinear equilibrium points are linearly unstable, while the non-collinear points maintain stability for values λc < λ < 1, λc = 0.971105.

Suggested Citation

  • Idrisi, M. Javed & Ullah, M. Shahbaz & Ershkov, S. & Prosviryakov, E.Y., 2024. "Dynamics of infinitesimal body in the concentric restricted five-body problem," Chaos, Solitons & Fractals, Elsevier, vol. 179(C).
    • Handle: RePEc:eee:chsofr:v:179:y:2024:i:c:s0960077923013504
    DOI: 10.1016/j.chaos.2023.114448
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    References listed on IDEAS

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    1. Saravanamoorthi, P. & Idrisi, M. Javed & Ullah, M. Shahbaz, 2023. "Effect of radiations on in-plane equilibrium points due to central primary in the photo-gravitational restricted eight-body problem," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    2. Ullah, M. Shahbaz & Idrisi, M. Javed, 2023. "The concentric Sitnikov problem: Circular case," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
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    1. Saravanamoorthi, P. & Idrisi, M. Javed & Ullah, M. Shahbaz, 2023. "Effect of radiations on in-plane equilibrium points due to central primary in the photo-gravitational restricted eight-body problem," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).

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