Analytic formulation for J2 perturbed orbits

The paper deals with a technique developed along the years at the Scuola di Ingegneria Aerospaziale to provide an exact solution for J2 perturbed orbits, here applied to spacecraft formations. Analytic solutions are useful in the design phase and can help in operations to identify and to efficiently maintain a suitable configuration. The approach is based on the elaboration, conveniently performed by means of a symbolic software tool, of a set of equations analogous to the Lagrange planetary relations. Resulting parameters are expressed through Fourier series depending only on the initial conditions. Comparison with standard, longer to obtain and less accurate numerical propagation clarify the advantage of the technique, which is limited only by the number of terms taken into account in the expansion.