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.