  Evidence in the Solar System suggests that the giant planets underwent an
epoch of radial migration that was very rapid, with an e-folding timescale
shorter than 1~Myr. It is probable that the cause of this migration was that
the giant planets experienced an orbital instability that caused them to
encounter each other, resulting in radial migration. Several works suggest that
this dynamical instability occurred `late', long after all the planets had
formed and the solar nebula had dissipated. Assuming that the terrestrial
planets had already formed, then their orbits would have been affected by the
migration of the giant planets. As a result, how did the orbits of the
terrestrial planets change? And can we use this migration to obtain information
on the primordial orbits of the terrestrial planets? We directly model a large
number of terrestrial planet systems and their response to giant planet
migration. We study the change in the Angular Momentum Deficit (AMD) of the
terrstrials. We conclude that the primordial AMD should have been lower than
~70\% of the current value, but higher than 10\%. We find that a scenario with
five giant planets better satisfies the orbital constraints of the terrestrial
planets. We predict that Mars was initially on an eccentric and inclined orbit
while the orbits of Mercury, Venus and Earth were more circular and coplanar.
The lower primordial dynamical excitement and the peculiar partitioning between
planets impose new constraints for terrestrial planet formation simulations.
