Numerical Study of the Zero Velocity Surface and Transfer Trajectory of a Circular Restricted Five-Body Problem

Abstract

We focus on a type of circular restricted five-body problem in which four primaries with equal masses form a regular tetrahedron configuration and circulate uniformly around the center of mass of the system. The fifth particle, which can be regarded as a small celestial body or probe, obeys the law of gravity determined by the four primaries. The geometric configuration of zero-velocity surfaces of the fifth particle in the three-dimensional space is numerically simulated and addressed. Furthermore, a transfer trajectory of the fifth particle skimming over four primaries then is designed.

Stability Analysis of the Rhomboidal Restricted Six-Body Problem

“…Ismail et al [16] studied the fourbody problem by considering the effects of radiation pressure and oblateness and used the Lyapunov function to show the stability of equilibrium points. Wang and Gao [17] did a numerical study of the restricted five-body problem regarding the zero velocity surface and transfer trajectory by considering four equal masses (primaries) forming a regular tetrahedron configuration and the fifth (infinitesimal) mass moving under the gravitational influence of the four primaries. ey numerically simulated the zero velocity surface of the infinitesimal mass in the three-dimensional space and designed the transfer trajectory of the infinitesimal mass.…”