MOTION AROUND THE EQUILIBRIUM POINTS IN THE PHOTOGRAVITATIONAL R4BP UNDER THE EFFECT OF CIRCUMSTELLAR BELT
Abstract
In the present work, we study numerically the motion of an infinitesimal fourth body near the equilibrium points (EPs) of the photogravitational restricted four-body problem (Lagrangian configuration) under the effect of circumstellar belt. We consider the case where three the bodies of masses and (primaries) are sources of radiation as well as enclosed by a circumstellar belt and two of the primaries, and, have equal masses () and equal radiation factors () while the dominant primary body is of mass Firstly, these equilibria are determined and then the influence of the system parameters on their positions and stability is performed. In addition, the numerical exploration is performed using the Ross 104-Ross775a-Ross775b stellar system to compute the locations of the equilibria and the eigenvalues of the characteristic equation. For this system where the value of the mass parameter is beyond Routh’s value, we observe that they may be ten (four collinear and six non-collinear) or eight (two collinear and six non-collinear) EPs depending on the mass of the circumstellar belt. The linear stability of each equilibrium point is also studied and it is found that in the case where ten equilibria exist, the new collinear point, is always linearly stable while the other nine equilibria are always linearly unstable. In the case where eight equilibria exist, all of them are always linearly unstable. The zero velocity surfaces for the stellar system are drawn and regions of motion are analyzed for increasing values of the mass belt.
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