Keywords:Martian moons, asteroids
We have investigated the probability of temporary capture of asteroids in eccentric orbits by a planet in a circular or an eccentric orbit by analytical and numerical calculations. We found that in the limit of the circular orbit, the capture probability is ~0.1% of encounters to the planet's Hill sphere, independent of planetary mass and semimajor axis. In general, the temporary capture becomes difficult, as the planet's eccentricity (ep) increases. We found that the capture probability is almost independent of ep until a critical value (epc) that is given by ~5 times of Hill radius scaled by the planet's semimajor axis. For ep> epc, the probability decreases approximately in proportional to ep-1. The current orbital eccentricity of Mars is several times larger than epc. However, since the range of secular change in Martian eccentricity overlaps ep, the capture of minor bodies by the past Mars is not ruled out.