  The migration history of Jupiter in the sun's natal disk remains poorly
constrained. Here we consider how Jupiter's migration affects small-body
reservoirs and how this constrains its original orbital distance from the Sun.
We study the implications of large-scale and inward radial migration of Jupiter
for the inner solar system while considering the effects of collisional
evolution of planetesimals. We use analytical prescriptions to simulate the
growth and migration of Jupiter in the gas disk. We assume the existence of a
planetesimal disk inside Jupiter's initial orbit. This planetesimal disk
received an initial total mass and size-frequency distribution (SFD).
Planetesimals feel the effects of aerodynamic gas drag and collide with one
another, mostly while shepherded by the migrating Jupiter. Our main goal is to
measure the amount of mass in planetesimals implanted into the main asteroid
belt (MAB) and the SFD of the implanted population. We also monitor the amount
of dust produced during planetesimal collisions. We find that the SFD of the
planetesimal population implanted into the MAB tends to resemble that of the
original planetesimal population interior to Jupiter. We also find that unless
very little or no mass existed between 5 au and Jupiter's original orbit, it
would be difficult to reconcile the current low mass of the MAB with the
possibility that Jupiter migrated from distances beyond 15 au. This is because
the fraction of the original disk mass that gets implanted into the MAB is very
large. Finally, we discuss the implications of our results in terms of dust
production to the so-called NC-CC isotopic dichotomy.
