We use the current orbital structure of large ( > 50 km ) asteroids in the main asteroid belt to constrain the evolution of the giant planets when they migrated from their primordial orbits to their current ones .
Minton & Malhotra ( 2009 ) showed that the orbital distribution of large asteroids in the main belt can be reproduced by an exponentially-decaying migration of the giant planets on a time scale of \tau \sim 0.5 My .
However , self-consistent numerical simulations show that the planetesimal-driven migration of the giant planets is inconsistent with an exponential change in their semi major axes on such a short time scale ( Hahn & Malhotra , 1999 ) .
In fact , the typical time scale is \tau \geq 5 My .
When giant planet migration on this time scale is applied to the asteroid belt , the resulting orbital distribution is incompatible with the observed one .
However , the planet migration can be significantly sped up by planet-planet encounters .
Consider an evolution where both Jupiter and Saturn have close encounters with a Neptune-mass planet ( presumably Uranus or Neptune themselves ) and where this third planet , after being scattered inwards by Saturn , is scattered outwards by Jupiter .
This scenario leads to a very rapid increase in the orbital separation between Jupiter and Saturn that we show here to have only mild effects on the structure of asteroid belt .
This type of evolution is called a jumping-Jupiter case .
Our results suggest that the total mass and dynamical excitation of the asteroid belt before migration were comparable to those currently observed .
Moreover , they imply that , before migration , the orbits of Jupiter and Saturn were much less eccentric than the current ones .