Abstract
In this research, we discussed the equilibruim points in the restricted three body problem (in brief RTBP) such as computing infinitesimal orbits. We investigated the dynamics of the orbits around the equilibrium points in the oblate restricted of three bodies problem. We costructed the problem formulation of infinitesimal orbit by applying the perturbation forces, the Hamiltonian of the dynamical problem is formulated. The transformed Hamiltonian near any one of the equilibrium points is obtained. A Lie operator method is applied to find the solution of the dynamical problem. The explicit first and second order solutions for the coordinates and their conjugate momenta of a particle in the infinitesimal orbit around equilibrium points are obtained. Numerical simulation of infinitesimal orbit around equilibrium points in the Earth-Moon (EM) system are deduced.