Satellite orbits design using frequency analysis

We present here a new method for the efficient computation of periodic orbits, which are of particular interest for low-altitude satellite orbits design in high degree/order, non-axisymmetric gravity models. Our method consists of an iterative filtering scheme, that is itself based on ‘Prony’s method’ of frequency analysis, and is independent of the complexity of the gravity model. Applying this method to the case of a low-altitude lunar orbiter, we show that it converges rapidly, in all models and for all values of altitude and initial inclination studied. Thus, as demonstrated below, one could use it to correct the initial conditions of a desired mission orbit — usually defined within the framework of a simplified model (e.g. the ‘J2J2 problem’) — ensuring minimal orbital eccentricity variations and, for very low altitudes, collision avoidance. At the same time, an accurate quasi-periodic decomposition of the orbit is computed, giving a measure of the periodic fluctuations of the orbital parameters.