  The abstract is additional with repect 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 behaviors of
these Martian orbits different from those of Earth. Analytical formulations and
numerical simulations are used to analyze 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 optimization 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 stationkeeping.
