Hidden Red Star
The Red Star in Super Mario Galaxy gives Mario the ability to literally fly around. It acts as a timed power-up, and lasts quite a while. This hidden star is not related to the Hidden Green Stars in Super Mario Galaxy.
Unfortunately, the Red Star is not available until pretty far into the game (You’ll need to have the “Gate Observatory” available, which requires quite a few Grand Stars). The “Gate” observatory is actually the planet on which you first start off the game on (Bunny Hide and Go Seek). Instead of searching for bunnies this time, you’ll need to talk to Rosalina, followed by a Red Luma.
The Red Luma will present a challenge of collecting 100 Purple Coins scattered around the planet. In order to collect the coins, you’ll need to use the Red Stars scattered about to fly to them. After collecting all 100 purple coins, Red Stars will be scattered throughout the main lobby, allowing you to freely fly around at will!