The New York Times has an interesting piece on the machinations required to extend the Cassini probe for another 7 year mission at Saturn.
With only 22% of it’s original fuel left, getting the probe around the Saturn system’s 53 moons, the rings, and the planet itself – without coming so close as to hit anything – “… present[s] an astonishingly complex exercise in Keplerian physics and geometry. The enormous array of science objectives and targets Ã¢â‚¬â€ moons, rings, Saturn itself Ã¢â‚¬â€ 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 Ã¢â‚¬â€ and final destruction.”
Click the image to see the full sized graphic.