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In this paper we search for mid-range planar orbits for a spacecraft traveling in the neighborhood of Deimos. The first task is to perform a numerical search to find and classify mid-range natural orbits around Deimos that are dominated by Mars, using the idea of "Quasi Satellite Orbits" (QSO). The influence of the eccentricity of the orbit of Deimos around Mars and the irregular shape of Mars are considered in the mathematical model, allowing an assessment of their importance. Our approachdoi:10.22201/ia.01851101p.2019.55.02.16 fatcat:dqmw5iprlzbl3dkslzvv7cyb34