  The impact cratering record of the Moon and the terrestrial planets provides
important clues about the formation and evolution of the Solar System.
Especially intriguing is the epoch 3.8-3.9 Gyr ago (Ga), known as the Late
Heavy Bombardment (LHB), when the youngest lunar basins such as Imbrium and
Orientale formed. The LHB was suggested to originate from a slowly declining
impactor flux or from a late dynamical instability. Here we develop a model for
the historical flux of large asteroid impacts and discuss how it depends on
various parameters, including the time and nature of the planetary
migration/instability. We find that the asteroid impact flux dropped by 1 to 2
orders of magnitude during the first 1 Gyr and remained relatively unchanged
over the last 3 Gyr. The early impacts were produced by asteroids whose orbits
became excited during the planetary migration/instability, and by those
originating from the inner extension of the main belt (E-belt; semimajor axis
1.6<a<2.1 au). The profiles obtained for the early and late versions of the
planetary instability initially differ, but end up being similar after ~3 Ga.
Thus, the time of the instability can only be determined by considering the
cratering and other constraints during the first ~1.5 Gyr of the Solar System
history. Our absolute calibration of the impact flux indicates that asteroids
were probably not responsible for the LHB, independently of whether the
instability happened early or late, because the calibrated flux is not large
enough to explain Imbrium/Orientale and a significant share of large lunar
craters. Comets and leftovers of the terrestrial planet formation provided
additional, and probably dominant source of impacts during early epochs.
