Cassini arrived in Saturn's neighborhood in 2004 for a four-year mission, but it performed so well and remained in such good shape, its mission was extended for two more years. In that time it's made countless discoveries, generated a wealth of scientific data and spawned well over 1,000 academic papers. It's also burned three quarters of its fuel.
For the NASA Jet Propulsion Lab mission designers tasked with extending Cassini's mission for an extra seven years, the project became a convoluted whirl of math and politics. Here, The New York Times explains the orbital mechanics of the new Cassini mission, which has to more than double the length of the mission using just a quarter of the craft's original propellant, all while appeasing opposing scientific interests.