NEBULAR GAS DRAG AND PLANETARY ACCRETION .2. PLANET ON AN ECCENTRIC ORBIT

We study the trajectories of planetesimals whose orbits decay starward as a result of gas drag and are perturbed by the gravity of a massive planet on an eccentric orbit. Each planetesimal ultimately suffers on e of three possible fates: (1) trapping in a mean motion resonance wit h the planet, (2) accretion by the planet, or (3) passage by the plane t and continued orbital decay. At moderate to large planetary eccentri city, numerical 3-body integrations of the motion of a planetesimal in the solar nebula demonstrate that migrating planetesimals can become trapped in the 1/1 resonance. These bodies initially have large librat ion amplitudes (approaching 2 pi) which decay down to 0 at the trailin g Lagrange point. With some combinations of drag rate and planetary ec centricity, over 15% of the planetesimals which encounter the planet a re trapped in the 1/1 resonance. Bodies trapped in the this way could be the precursors of the Trojan asteroids. Migrating planetesimals can be caught in both pure Lindblad and combined Lindblad/corotation reso nances exterior to the planet's orbit. Trapping has been found in seve ral j/(j + k) resonances with k's ranging from 1 to 4. As one consider s larger planetary eccentricities, corotation resonances become more i mportant than Lindblad resonances, and (for a given drag rate) trappin g can occur at higher k's and farther from the planet. At large planet ary eccentricities, planetesimals can also be caught in (j + 1)/j Lind blad/corotation resonances interior to the planet. Interior trapping, which is dynamically forbidden in the case of a planet on a circular o rbit, requires planetary eccentricity to increase both the planetesima l's semimajor axis and its eccentricity near conjunction to counter ga s drag. Provided the planetesimal's and planet's apoapses are roughly aligned, and conjunction occurs while both bodies are approaching apoa pse, then the planetesimal can become trapped in an interior resonance . The probability of a planetesimal avoiding accretion while migrating past the planet can be described as the probability of not being accr eted in a single conjunction to the power of the number of conjunction s that a planetesimal has with the planet while passing through its fe eding zone. In the nongravitating planet limit (which is valid for a l ow mean density planet on a highly eccentric orbit), the accretion pro bability increases with planetary eccentricity due to the growth of th e planet's feeding zone. When the planet's gravity is considered using the 2+2-body approximation (which is valid for a dense planet on a mo derately eccentric orbit), the accretion rate is nearly independent of planetary eccentricity. Numerical simulations show that at small plan etary eccentricities, the 2+2-body approximation breaks down, and the accretion probability gradually increases with decreasing eccentricity in this regime. (C) 1995 Academic Press, Inc.