At closest approach, Rosetta skimmed the Earth at a distance of just 6000 km (3600 miles) above the surface! Close enough to feel the breeze from it... if it weren't for that whole "vacuum of space" stuff. As it was, the spacecraft accelerated by about 13 km/sec (8 miles/sec), enough to boost it on its way to meet up with a comet. When it arrives, it will deploy a lander that will touch down on the surface of the comet and study it up close and personal, giving us our best view yet of these objects.
Related post: Rosetta Takes some home pictures
Credit: ESA © 2005 MPS for OSIRIS Team MPS / UPD / LAM / IAA / RSSD / INTA / UPM / DASP / IDA