Non-linear Stability of Triangular Equilibrium Points in ER3BP Under Radiating Primaries in Presence of Resonance

The non linear stability of the triangular equilibrium points are studied considering the radiation pressure of both the primaries in the presence of third and fourth order resonance. Markeev (Libration points in celestial mechanics and cosmodynamics, 1978) method is applied throughout our analysis to study the non linear stability of the system. In order to do so, the Birkhoff’s normal form in the vicinity of the triangular equilibrium points up to fourth order terms of the Hamiltonian is computed. The normal forms of the Hamiltonian contains both the resonance cases \(\omega _{1}= 2\omega _{2}\) and \(\omega _{1}= 3\omega _{2}\). It is also observed that the triangular equilibrium points satisfying the conditions \(\mu \le \mu _\mathrm{c} =0.0385209\); are unstable in the third order resonance but stable in the fourth order resonance for different values of radiation pressure taken.