* Astronomy

Title: Five Special Types of Orbits Around Mars
Authors: Xiaodong Liu, Hexi Baoyin, Xingrui Ma

The abstract is additional with respect to the paper published in JGCD. Ordinary Earth satellites are usually placed into five categories of special orbits: sun-synchronous orbits, orbits at the critical inclination, frozen orbits, repeating ground track orbits, and geostationary orbits. This paper investigates their counterparts around Mars and examines the basic nature of these orbits, which are of special interest for missions conducted around Mars, including Mars reconnaissance. Mars' gravity field is much more complicated, with relatively smaller J2, compared to Earth's, which makes the behaviours of these Martian orbits different from those of Earth. Analytical formulations and numerical simulations are used to analyse these Martian orbits and compare them with their Earth counterparts. First, mean element theory is employed to describe variations of orbital elements and give the constraint conditions for achieving these special orbits. Then, numerical verifications based on the PSODE algorithm (particle swarm optimisation combined with differential evolution) are adopted to provide more accurate conditions for achieving these orbits when considering an Mars gravity field. Using the numerical method can significantly improve the design in the full gravity field, and it is therefore possible to select these usable orbits for Mars that can reduce or eliminate the need for station keeping.

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