Trojan Capture by a Growing proto-Jupiter

F. Marzari (Univ. Padova), H. Scholl (Observatoire de Nice)

We have numerically studied the capture of planetesimals in Trojan orbits by a growing proto-Jupiter in a 4-body problem Sun-Jupiter-Saturn-planetesimal. The masses of Jupiter and Saturn increase exponentially with time. Nebular gas drag on small planetesimals is taken into account. We show that a fraction of the planetesimals near Jupiter's orbit and almost all planetesimals originally in horseshoe orbits are trapped into stable Trojan orbits. This mechanism was probably an important factor together with collisional diffusion (E.M. Shoemaker et al., 1989), for delivering a large amount of planetesimals into stable Trojan orbits during the final growth of Jupiter. We find also that the libration amplitude of trapped Trojans is damped by the increase of Jupiter's mass reinforcing the stability of the resonance lock.

For planetesimals small enough to be perturbed by nebular gas drag, we find an asymmetry between the trapping rate in L5 as compared to L4. We present here a simple semi-analytical explanation for both trapping and stability asymmetry (Peale, 1993).