Exact Separation of Purely Short-Period Effects and Mean Variations in the Main Problem of Artificial Satellite Theory - Martin Lara (Aerospace)
It is well known that mean elements obtained by canonical perturbation theory only agree partially with the average dynamics of the osculating orbit. While this fact does not necessarily compromise the accuracy of corresponding perturbation solutions, the loose use of the terminology “mean elements” in artificial satellite theory may obscure the understanding of the variety of available solutions in the literature, and thus make the implementation of additional patches to increase their performance ambiguous. We resort to noncanonical perturbation methods, and, for the main problem of artificial satellite theory (the <semantics>J2</semantics>-problem), compute the purely periodic, noncanonical, mean-to-osculating transformation that yields the exact separation between short- and long-period variations up to the second order of the zonal harmonic of the second degree. To our knowledge this transformation is new and was long-awaited by software developers in order to improve operational orbit propagation tools based on semianalytical integration. It is also shown that this kind of noncanonical solution confines the long-period oscillations of the semimajor axis in the mean variation equations.