Abstract: A system and a method is disclosed for on board prediction of a trajectory for satellites, which can be implemented on a computer with a limited number of bits. The system includes a compact force model that approximate the forces that the satellite encounters in an earth orbit. The compact force model includes a two body force component, a non-spherical earth gravitational force component, a solar radiation pressure component and a lunar-solar perturbation force component. An adder is coupled to the force model for combining the force components to produce an equation of motion approximating the acceleration of the satellite. An integrator is included for integrating the equation of motion approximating the acceleration of said satellite to produce an equation of motion approximating the displacement of the satellite, wherein the equation of motion approximating the displacement of the satellite is a reference trajectory.