Linear Stability of Equilibrium Points in the Restricted Three Body Problem with Perturbations

Abstract

We have considered the well known restricted three body problem under the influence of perturbations in the form of radiation pressure and lack of sphericity of the primaries, respectively. In the present article, author is interested to analyzed linear stability in case of three main resonances and hence, effect of perturbations on the stability regions. In order to achieve the goal, first, we have determined triangular equilibrium point then examined its linear stability and found that points are stable for the mass ratio 0 0.0396478,   c in the presence of perturbations. Perturbed mass ratio for three main resonance cases is obtained and noticed that it is increasing function of radiation pressure but it decreases with
respect to oblateness. It is also, observed that stability region expands with radiation pressure, in the presence and absence of oblateness but it contracts with oblateness. Again, effects of perturbations are analyzed and found that they affect the motion of restricted mass significantly, in space. Results are helpful to study more generalized problem in the presence of some other type of perturbations such as P-R drag and solar wind drag etc.