OUT-OF-PLANE EQUILIBRIA IN THE EQUILATERAL RESTRICTED FOUR-BODY PROBLEM WITH RADIATION PRESSURE AND ANGULAR VELOCITY VARIATION

Abstract

Three bodies of masses m1, m2 and m3 (primaries) lie always at the vertices of an equilateral triangle, while each moves in circle about the center of mass of the system fixed at the origin of the coordinate system. A fourth infinitesimal body is moving under the Newtonian gravitational attraction of the primaries and does not affect the motion of the three bodies. In this version, the angular velocity of the three primary bodies is taken into account in the case where all the primaries are radiation sources and the two small primary bodies m2 and m3 are identical, that is, they have the same mass (m2=m3= 𝜇 ), and have the same radiation factor (q2=q3 ) while the dominant primary body m1 is of mass 1-2 𝜇 . Based on this consideration, we numerically investigate the out-of-plane equilibrium positions of the small body and their parametric dependence. Finally, the stability of these points is studied and they are found to be unstable due to positive real part in complex roots