The spacecraft Lucy is en route to explore Jupiter's trojan asteroids. Lucy is so named because the trojan asteroids are believed to be fossil remnants from the formation of the solar sytem. Presumably this means that the astroids have been occupying the Lagrange points for a very long time.
At Saturn's closest approach to Jupiter's Lagrange points, it is actually slightly closer than Jupiter (~650 million km vs. 780 million km). Saturn has only 30% the mass of Jupiter, so its gravitational effects are smaller. Nevertheless, for periods of many months, Saturn will exert on the asteroids a force of up to 43% of the gravitational force of Jupiter. So how do these asteroids manage to remain in the vicinity of the Lagrange points given such large perturbing forces?
I suppose the reality of their apparent longevity must be supported by simulations, but are there some simple arguments or observations that give some insight into why, given the presence of Saturn, the trojans are still there after five billion years?