Collinear Libration Points in the Photogravitational CR3BP with Zonal Harmonics and Potential from a Belt

Abstract

We have studied a reformed type of the classic restricted three-body problem where the bigger primary is radiating and the smaller primary is oblate; and they are encompassed by a homogeneous circular cluster of material points centered at the mass center of the system (belt). In this dynamical model, we have derived the equations that govern the motion of the infinitesimal mass under the effects of oblateness up to the zonal harmonics J 4 of the smaller primary, radiation of the bigger primary and the gravitational potential generated by the belt. Numerically, we have found that, in addition to the three collinear libration points L i ( i = 1, 2, 3) in the classic restricted three-body problem, there appear four more collinear points L ni ( i = 1, 2, 3, 4). L n1 and L n2 result due to the potential from the belt, while L n3 and L n4 are consequences of the oblateness up to the zonal harmonics J 4 of the smaller primary. Owing to the mutual effect of all the perturbations, L 1 and L 3 come nearer to the primaries while L n3 advances away from the primaries; and L 2 and L n1 tend towards the smaller primary whereas L n2 and L n4 draw closer to the bigger primary. The collinear libration points L i ( i = 1, 2, 3) and L n2 are linearly unstable whereas the L n1 , L n3 and L n4 are linearly stable. A practical application of this model could be the study of motion of a dust particle near a radiating star and an oblate body surrounded by a belt.