  As part of our ongoing initiative on accurately calculating the accretion
rate of planetesimals in the core-accretion model, we demonstrated in a recent
article that when the calculations include the gravitational force of the Sun
(the original core-accretion model did not include solar gravity), results
change considerably [ApJ, 899:45]. In this paper, we have advanced our previous
study by including the effect of Saturn. To maintain focus on the effect of
this planet, and in order to be consistent with previous studies, we did not
include the effect of the nebular gas. Results demonstrated that as expected,
Saturn's perturbation decreases the rate of accretion by scattering many
planetesimals out of Jupiter's accretion zone. It also increases the velocities
with which planetesimals encounter the envelope, which in agreement with our
previous findings, enhances their break-up due to the ram-pressure. Results
also show that, because the effect of Saturn in scattering of planetesimals
increases with its mass, this planet might not have played a significant role
in the accretion of planetesimals by proto-Jupiter during the early stage of
its growth. Finally, the late accretion of planetesimals, as obtained in our
previous study, appears in our new results as well, implying that combined with
the rapid in-fall of the gas, it can result in the mixing of material in the
outer regions of the envelope which may explain the enhancement of the
envelope's high-Z material.
