EXACT NORMALIZATION OF THE TESSERAL HARMONICS

An exact Delaunay normalization of the tesseral and sectorial harmonics using a nonconservative canonical transformation is presented. The main problem is reduced to a linear partial differential equation for the short-period generating function in two variables, mean anomaly and time, which is solved using the method of characteristics. This direct approach avoids the use of series expansions in the eccentricity and is unlike the iterative method of relegation. As a result, artificial satellite theories with tesseral and sectorial harmonics constructed using the proposed approach are valid for elliptic orbits of arbitrary eccentricity. Additionally, the proposed approach results in a significantly compact theory, valid for both subsynchronous and supersynchronous orbits simultaneously, and without singularities for resonant orbits. The analytic formulae for short-period and m-daily variations of classical as well as equinoctial orbital elements due to an arbitrary tesseral or sectorial harmonic are provided. The accuracy of the proposed satellite theory is compared with the solution obtained from numerical propagation and the results are presented for several types of orbits.