Author(s)

Jagadish Singh^1*, Joel John Taura²

¹Department of Mathematics, Faculty of Science, Ahmadu Bello University, Zaria, Nigeria.
²Department of Mathematics and Computer Science, Federal University, Kashere, Nigeria.

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 J₄ 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 J₄ of the smaller primary. Owing to the mutual effect of all the perturbations, L₁ and L₃ come nearer to the primaries while L_n3 advances away from the primaries; and L₂ 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.

Circular Restricted Three-Body Problem, Photogravitational, Zonal Harmonic Effect, Potential from the Belt

Singh, J. and Taura, J. (2015) Collinear Libration Points in the Photogravitational CR3BP with Zonal Harmonics and Potential from a Belt. International Journal of Astronomy and Astrophysics, 5, 155-165. doi: 10.4236/ijaa.2015.53020.