Some effects of mean motion resonance passage on the relative migration of Jupiter and Saturn

We look for clues to the amount and direction of Saturn's migration relative to Jupiter in their current orbits, specifically, from the fact that the former lies barely sunward of their 5 : 2 mean motion resonance. Numerical simulations suggest that Saturn has moved in the same direction (presumably inward) as has Jupiter but that the pair has never passed through their more distant 3 : 1 resonance. Thus, their relative migration has been less than about 1.5 AU. Passage through 5 : 2 is consistent with their current orbits and could have contributed to their present eccentricities, e (and especially to their large periodic variations), but it probably cannot generate their e's if both, and particularly Jupiter's, were initially less than about 0.03. In fact, it is most likely that their initial e's were both close to the current values. Very long term capture into 5 : 2 for the Sun-Jupiter-Saturn case occurs with a remarkably high frequency.