Super Mario Galaxy/Green Stars and Trial Galaxies

To get to the three Trial Galaxies, you first have to find the green Power Stars. After you find the green stars, you play the Trial Galaxies by using the Green Launch Star in the Comet Observatory near the three green Lumas, which are the three green Power Stars of course.

Green Stars
Go to the Hungry Luma under the platform in the Dusty Dune Galaxy. Feed it some star bits to turn it into a new planet. Take the Pink Launch Star to the planet that looks like a pyramid. Find the five silver stars by controlling where the sand moves. Don't get crushed! Once you find all five stars, the sand disappears and at the very bottom is your first green Power Star.
 * Star 1

Go to Buoy Base Galaxy and swim underwater. Lure the Torpedo Ted into a glass cage that has a pipe in it. Once you go in the pipe, avoid the Bullet Bills and lure one into the glass cage that has the second green Power Star.
 * Star 2

You can get this star when you've received a message from Luigi. Go to Battlerock Galaxy. Go to the saucer with a glass cage with Luigi trapped in it. Lure the Bullet Bills into the cage that Luigi is inside. Once you set him free, he will give you the third and final green Power Star. Jump on Luigi's head to bounce into the star.
 * Star 3