A procedure for the determination of the mean orbital elements of an earth satellite

The determination of the mean orbital elements of a satellite on the basis of two satellite position vectors and the corresponding time values involves mathematically the inversion of the functional system which indicates the dependence of the position vectors on the orbital elements. This task can also be considered as a boundary-value problem of the corresponding equation of motion. In the case of a pure Keplerian motion, the resulting problem has become known as the Lambert problem. The inversion becomes more difficult if the motion of the earth satellite is perturbed. The present investigation is concerned with an iterative procedure for solving the problem in the case of a perturbed Keplerian motion. The required mean orbital elements are approximated by the orbital elements of a sequence of Keplerian orbits. This approach makes it possible to reduce the required computational effort compared to other methods, and a real-time employment of the method is feasible even in the case of smaller computing systems.