Dynamical Effects of Planetary Migration on Primordial Trojan-Type Asteroids

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Abstract
The hypothesis of planetary migration is tested by numerically integrating orbits of Trojan-type asteroids in the gravitational field of the Sun, the migrating parent planet, and at least one extra migrating planet. A linear model and an exponential model for migration are used. Migration speeds are defined by several total migration times for the linear model and by two different timescales for the exponential model. The migration process is found to develop great instability on Saturn Trojans. It is a much more stable process for Jupiter and the two outermost major planets' Trojans. The instability produced by migration is also found to be strongly dependent on the initial orbits of the planets. Migration can explain why Saturn Trojans have not been found up to date. It can also explain the absence of these bodies for Uranus and Neptune if initial positions for Neptune closer to the Sun are assumed. In order that migration does not create too much instability for Jupiter Trojans, initial positions for the pair Jupiter-Saturn should not be as close as usually supposed. For the exponential model and timescale 2.5 × 106 yr, there is a significant trend of Jupiter Trojan survivors to the L4 point. The results of this work and previous ones about planetary migration can impose some constraints on possible initial positions for the major planets.