Effects of perturbations on the stability of equilibrium points in the CR3BP with luminous and heterogeneous spheroid primaries

Abstract

AbstractThis paper studies the position and stability of equilibrium points in the circular restricted three-body problem under the influence of small perturbations in the Coriolis and centrifugal forces when the primaries are radiating and heterogeneous oblate spheroids. It is seen that there exist five libration points as in the classical restricted three-body problem, three collinear $$L_{i} ,(i = 1,2,3)$$ L i , ( i = 1 , 2 , 3 ) and two triangular $$L_{i} ,(i = 4,5)$$ L i , ( i = 4 , 5 ) . It is also seen that the triangular points are no longer to form equilateral triangles with the primaries rather they form simple triangles with line joining the primaries. It is further observed that despite all perturbations the collinear points remain unstable while the triangular points are stable for $$ 0 < \mu < \mu _{c} $$ 0 < μ < μ c and unstable for $$ \mu _{c} \le \mu \le \frac{1}{2} $$ μ c ≤ μ ≤ 1 2 , where $$ \mu _{c} $$ μ c is the critical mass ratio depending upon aforementioned parameters. It is marked that small perturbation in the Coriolis force, radiation and heterogeneous oblateness of the both primaries have destabilizing tendencies. Their numerical examination is also performed.