Numerical Methods of Orbital Dynamics

Different numerical integration algorithms are reviewed in their application to the many body problem, the determination of satellite orbits around the Earth, Moon and other planets. The integration in rectangular coordinates and in osculating elements are examined, as well as the computation of partial derivatives in trajectory estimation and physical parameters determination by differential correction (variational equations, Peano Baker method, numerical differences approximation). Besides, fast techniques for evaluating perturbations with respect to a mean reference orbit (which can be already disturbed) and specially the stroboscopic method, are described.