Stability of the Sitnikov's circular restricted three body problem when the primaries are oblate spheroid

Abstract

The Sitnikov's problem is a special case of restricted three body problem if the primaries are of equal masses (m 1 = m 2 = 1/2) moving in circular orbits under Newtonian force of attraction and the third body of mass m 3 moves along the line perpendicular to plane of motion of primaries. Here oblate spheroid primaries are taken. The solution of the Sitnikov's circular restricted three body problem has been checked when the primaries are oblate spheroid. We observed that solution is depended on oblate parameter A of the primaries and independent variable t. τ = η For this the stability of non-trivial solutions with the characteristic equation is studied. The general equation of motion of the infinitesimal mass under mutual gravitational field of two oblate primaries are seen at equilibrium points. Then the stability of infinitesimal third body m 3 has been calculated.