Why does a gear rotating around another gear rotate twice as fast around its own center?

Take two gears: One is fixed, the other rotates around it. If the gears are the same size the rotating gear has to rotate around its center twice as fast as it rotates around the other gear. I'm looking for intuition or reasoning why this is the case.

• @Sarien Because a rolling gear will always rotate exactly as much as its centre moves. If the centre moves 1 unit, the gear will have to rotate 1 unit too. If it didn't, it would mean the gear either deform or slip. In this case, the centre moves (2rπ)*2 units, therefore the gear has to rotate (2rπ)*2 units, which is (2π)*2 radians = 2 full rotations. – biziclop Oct 26 '14 at 23:35