Effect of oblateness on the non-linear stability of the triangular liberation points of the restricted three-body problem in the presence of resonances

The non-linear stability of the triangular libration points of the restricted three-body problem is studied under the presence of third and fourth order resonance's, when the more massive primary is an oblate spheroid. In this study Markeev's theorem are utilised with the help of KAM theorem. It is found that the stability of the triangular libration points are unstable in the third order resonance case and stable in the fourth order resonance case, for all the values of oblateness factor A₁. This revised version was published online in August 2006 with corrections to the Cover Date.