The paper deals with analytical and numerical investigations of the motion of a spacecraft around triangular equilibrium points of the perturbed restricted five-body problem (R5BP). The spacecraft is assumed to move in gravitational environments of four primaries under effects of small perturbations in the Coriolis and centrifugal forces. The configuration is such that the first primary is located at the origin of the coordinate system, while the second primary is collinear with the first primary and the third and fourth are located above and below on the left of the first primary. The equations of motion are stated and the locations, zero velocity, stability and the Poincaré surfaces of sections are investigated analytically and numerically when the mass of the first primary is varied coupled with effects of small perturbations in the Coriolis and centrifugal forces. It is seen that when the mass of the first primary and the centrifugal perturbation are increasing, the position of the spacecraft drifts away from the first primary. Further, it is seen that the increasing mass of the first primary and the perturbation in the centrifugal force reduces the region where motion of the spacecraft is allowed around the triangular points. Additionally, at some instances the perturbing effects can allow and restrict the spacecraft in travelling around the primaries and the triangular points. These effects grow strong enough to render the triangular points an unstable equilibrium points when the mass of the first primary exceeds nine times the mass of the Sun coupled with the Coriolis and centrifugal perturbations, otherwise they are stable. Finally, the Poincaré surfaces of section were explored, and it was seen that as the mass of the first primary is increasing, more clusters were noticed around the primaries, and this shows the presence of stable or quasi-periodic orbits which correspond to regular motion. Consequently, the orbits are stable. The problem can be applied to study motion of a spacecraft in the environments of Jupiter and three of its Moons.
Singh et al. (Thu,) studied this question.