Abstract
In the current manuscript, we have explored the spatial collinear restricted four-body problem(SCR4BP) in which the three bodies, known as primaries, are situated in the collinear Euler’s configuration, where the primary \(P_0\)(\(m_0 = \beta m\)) (taken as central primary) is placed at the origin, and other two primaries \(P_1\)(\(m_1\)) and \(P_2\) \((m_2)\), which are non-spherical bodies, are placed at the same distance from the origin having masses \(m_1=m_2=m\). The massless fourth body known as test particle (or infinitesimal body) is moving under the Newtonian gravitational attraction of the primaries. This fourth body does not influence the motion of the primaries but its motion is effected by them as in the restricted three-body problem (R3BP). We have determined the long- and short-period orbits around those libration points which lie on the \(y-\)axis only in the SCR4BP for the case of two equal masses by using Fourier series method. We have studied the evolution of families of these orbits as the oblateness parameter A and mass parameter \(\beta \) evolve. The time period T of the periodic orbit is studied by using the variational graphs. By retaining the terms up to third order in the Fourier expansions, we have explored how the oblateness of the peripheral primaries as well as the mass parameter affect not only the shape, size and period but also the networks of long- and short-period orbits.
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The values of various coefficients
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Meena, O.P., Suraj, M.S., Aggarwal, R. et al. The study of periodic orbits in the spatial collinear restricted four-body problem with non-spherical primaries. Nonlinear Dyn 111, 4283–4311 (2023). https://doi.org/10.1007/s11071-022-08085-z
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DOI: https://doi.org/10.1007/s11071-022-08085-z