Dynamical Effects of Planetary Migration on the Primordial Asteroid Belt

The effect of the hypothetical early Solar System migration of Jupiter and Saturn on primordial asteroids is investigated. Based on a linear theory, the positions of the secular resonances nu_6 and nu_ {16} are noticed to shift by around 0.6 AU, yielding considerable excitation to the eccentricities and inclinations of primordial asteroids orbits. Numerical integrations of the complete equations of motion show an even longer range of semimajor axes swept by the migrating secular resonances, thus affecting the eccentricities of asteroids initially placed on the present main belt (2.1 AU to 3.2 AU). The inclinations are not however affected by secular resonance for asteroidal semimajor axes above 2.7 AU for the assumed range of migrating planetary semimajor axes. In a primordial Solar System, this hypothetical phenomenon could have contributed to hamper the formation of a planet in the asteroidal region. Today's asteroidal eccentricities and inclinations may be the final product of a process started at the time of planetary migration.