The dynamical structure of the Solar System can be explained by a period of orbital instability experienced by the giant planets .
While a late instability was originally proposed to explain the Late Heavy Bombardment , recent work favors an early instability .
Here we model the early dynamical evolution of the outer Solar System to self-consistently constrain the most likely timing of the instability .
We first simulate the dynamical sculpting of the primordial outer planetesimal disk during the accretion of Uranus and Neptune from migrating planetary embryos during the gas disk phase , and determine the separation between Neptune and the inner edge of the planetesimal disk .
We performed simulations with a range of ( inward and outward ) migration histories for Jupiter .
We find that , unless Jupiter migrated inwards by 10 AU or more , the instability almost certainly happened within 100 Myr of the start of Solar System formation .
There are two distinct possible instability triggers .
The first is an instability that is triggered by the planets themselves , with no appreciable influence from the planetesimal disk .
About half of the planetary systems that we consider have a self-triggered instability .
Of those , the median instability time is \sim 4 Myr .
Among self-stable systems – where the planets are locked in a resonant chain that remains stable in the absence of a planetesimal ’ s disk– our self-consistently sculpted planetesimal disks nonetheless trigger a giant planet instability with a median instability time of 37-62 Myr for a reasonable range of migration histories of Jupiter .
The simulations that give the latest instability times are those that invoked long-range inward migration of Jupiter from 15 AU or beyond ; however these simulations over-excited the inclinations of Kuiper belt objects and are inconsistent with the present-day Solar System .
We conclude on dynamical grounds that the giant planet instability is likely to have occurred early in Solar System history .