Approximate Analytical Solution to the Zonal Harmonics Problem Using Koopman Operator Theory

This work introduces the use of the Koopman Operator Theory to generate analytical solutions for the zonal harmonics problem of a satellite orbiting a non spherical celestial body. Particularly, the solution proposed directly provides the osculating evolution of the system and can be automated to generate any approximation order to the solution. Moreover, this manuscript defines a modified set of orbital elements that can be applied to any kind of orbit and that allows the Koopman Operator to generate stable and accurate solutions. In that regard, several examples of application are included, showing that the proposed methodology can be used in any kind of orbit, including circular, elliptic, parabolic and hyperbolic orbits.