jamie found an article at the NY Times about the extreme orbital mechanics
gyrations required to extend the Cassini mission at Saturn by seven more years. Here's a graphic of the mission extension
, which NASA took two years to arrive at. "The plans are for Cassini to keep working for seven more years, but it currently has only 22 percent of the maneuvering propellant it had when it started. Figuring out how to more than double the duration of the mission with less than a quarter of the fuel is hard. Cassini's orbital mechanics present an astonishingly complex exercise in Keplerian physics and geometry. The enormous array of science objectives and targets — moons, rings, Saturn itself — makes it one of the most complex missions ever flown. ... 'Without Titan,' Mr. Seal [Cassini's mission planning supervisor] said, 'we would go into one orbit around Saturn and be stuck there.' Thus Titan, in the argot of orbital mechanics, is Cassini's 'tour engine.' [T]he final 'reference trajectory' ... now includes 56 passes over Titan, 155 orbits of Saturn in different inclinations, 12 flybys of Enceladus, 5 flybys of other large moons — and final destruction."