Design of low-altitude Martian orbits using frequency analysis

Nearly-circular Frozen Orbits (FOs) around axisymmetric bodies – or, quasi-circular Periodic Orbits (POs) around non-axisymmetric bodies – are of primary concern in the design of low-altitude survey missions. Here, we study very low-altitude orbits (down to 50 km) in a high-degree and order model of the Martian gravity field. We apply Prony’s Frequency Analysis (FA) to characterize the time variation of their orbital elements by computing accurate quasi-periodic decompositions of the eccentricity and inclination vectors. An efficient, iterative filtering algorithm, previously applied to lunar orbiters, complements the method and is used to accurately compute the locations of POs/FOs, for a wide range of initial conditions. By defining the ’distance’ of any orbit from the family of POs and using the relative amplitudes of the different components of the motion, we can build ’dynamical fate maps’ that graphically depict the survivability of low-eccentricity, low-altitude orbits at every inclination, and can be used for efficient mission planning. While lowering the altitude generally enhances the effect of tesseral and sectorial gravity harmonics, we find this to have less consequence for low altitude Martian satellites, in contrast with the Lunar case. Hence, a high-degree (≃20th) axisymmetric model is adequate for preliminary mission design at moderate altitudes, but should be complemented at low altitudes by the methods described here. All families of POs and their spectral decompositions can be accurately and effectively computed by continuation in arbitrarily complex Martian gravity models, as our filtering algorithm requires only short integration arcs.