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D.P. Hamilton (U. Maryland)
Large swarms of Trojan asteroids currently oscillate around Lagrange points located 60 degrees ahead of and behind Jupiter. These points are stable now, but were they also stable in the past when significant amounts of nebular gas still orbited the Sun? One dissipative process that can systematically damp or increase the libration amplitudes of small Trojans about the equilibrium points is gas drag, which has been studied in detail by Peale (1993) and Kary and Lissauer (1995). In this work, I investigate another potentially-important process that affected Trojans of all sizes: the gravitational tugs from Jupiter-induced disturbances in the gas disk, Perturbations to the nebular gas, or disk tides, act back on Trojan asteroids, adding or removing energy from their orbits. In response, the position of the equilibrium points shift slightly from their usual ±60\circ locations. In fact, the equilibrium points shift by just the right amount that, when averaged over one librational cycle, Jupiter adds/removes exactly the same amount of energy that the tides remove/add. Thus there is no energy loss or gain and, somewhat surprisingly, no systematic orbital evolution. The analysis is very simple and powerful, is backed by numerical integrations, and can be generalized to other related systems including, for example, tides raised on a central planet.