TY - JOUR

T1 - Dynamics of infinitesimal body in the concentric restricted five-body problem

AU - Idrisi, Mohammad Javed

AU - Shahbaz Ullah, M.

AU - Ershkov, Sergey V.

AU - Prosviryakov, E. Yu.

PY - 2024

Y1 - 2024

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?partnerID=8YFLogxK&scp=85182512595

U2 - 10.1016/j.chaos.2023.114448

DO - 10.1016/j.chaos.2023.114448

M3 - Article

VL - 179

JO - Chaos, Solitons and Fractals

JF - Chaos, Solitons and Fractals

SN - 0960-0779

M1 - 114448

ER -