We present the time evolution of orbital elements of the Centaur asteroid 2009 HW77, discovered by KC and IE, forwards and backwards in time over a 10-Myr period. The dynamical behaviour is analysed using three software packages: the OrbFit, the swift and the Mercury integrators. Changes in the orbital elements of 2009 HW77 clones are calculated using the classification of Horner et al. It is shown that close approaches to the giant planets significantly change the asteroid orbit. Our computations made with the swift software and with the Mercury software give similar results. The half-life is about 5 Myr in both the forward and backward integrations.
Moreover, our computations suggest that the Centaur asteroid will be temporarily locked as a periodic asteroid connected with Jupiter with a Tisserand parameter smaller than 3. Hence it is dynamically similar to the Jupiter Family Comets. The mean duration in this state is about 82 kyr, but the behaviour and lifetime depend on whether capture occurs after a few hundred thousand years or a few hundred million years.
Several clones of this dynamically interesting Centaur asteroid are temporarily locked up to four times as periodic asteroids connected with Jupiter, after which they are ejected from the Solar system. According to Bailey and Malhotra, asteroid 2009 HW77 may belong to the diffusing class of Centaurs, which can evolve into Jupiter Family Comets.