When planetesimals encounter a planet, they can be temporarily captured by the planet's gravity and orbit about it for an extended period of time before escaping from the planet's vicinity. Such a process may have played an important role in the origin of irregular satellites or the dynamical evolution of short-period comets. Using three-body orbital integration, we study the temporary capture of planetesimals by a planet from their heliocentric eccentric orbits. We examine the dependence of the orbital characteristics during temporary capture as well as the rate of capture on the pre-capture heliocentric orbital parameters. We find that typical orbital size and direction of revolution around the planet change depending on planetesimals' initial eccentricity and energy. When initial eccentricity is so small that Kepler shear dominates the relative velocity between planetesimals and the planet, temporary capture typically occurs in the retrograde direction in the vicinity of the planet's Hill sphere, while large retrograde capture orbits outside the Hill sphere are predominant for large eccentricities. Long prograde capture occurs in a very narrow range of planetesimal eccentricity and energy. We obtain the rate of temporary capture of planetesimals and find that the rate of long capture increases with increasing eccentricity at low and high eccentricities, but decreases with increasing eccentricity in intermediate values of eccentricity. We also examine the dependence of capture rate on the duration of capture and find an approximate power-law dependence.
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