Several spacecraft have had really interesting trajectories, and explaining those is much easier with a little animated help.
Let’s start with the twin Voyagers, which were not the first to use gravity assist, but certainly the first to use it so extensively:
MESSENGER required 1 Earth flyby, 2 Venus flybys, and 3 Mercury flybys to step its heliocentric orbit down enough to slip into Mercury orbit with the available spacecraft engine:
Rosetta’s journey isn’t that complicated, but takes a lot longer — when it finally reaches its target it will have already been in space for 12 years. Flyby of Earth, flyby of Mars, two more flybys of Earth, and then finally it was ready to go into the outer solar system and meet up with its cometary target; rendezvous is scheduled for next month.
Solar observing can call for some interesting orbits; here’s the twin STEREO probes, out in heliocentric orbit and gradually receding from Earth — in both directions, allowing study of the Sun over 360 degrees.
Going to Mars is usually a very straightforward matter of launching into the Hohmann Transfer Orbit, but that wasn’t an option for Mars Orbiter Mission (Mangalyaan); the PSLV just didn’t have enough power to launch something as large as that onto an escape trajectory. So they had to get clever instead, using a series of burns after launch to pump their original parking orbit up to an Earth escape orbit that also happened to be a Mars transfer orbit.
And we’ve all heard the fuss about ISEE-3 (which, by the way, has now successfully fired its engine! hooray!), so why was it such a big deal to try to talk to it *now*? This orbit animation helps illustrate how much time it takes for it to come back around to Earth again, even though it’s actually pretty close (in cosmic terms) to our orbit.
This one, meanwhile, is pretty simple — just one gravity-assist. But it’s going so far I figured it was worth including. New Horizons, on its trip to Pluto.