The luna's secret

You have to have gotten pretty far into the game to get this. It's a flying ability that let's you fly as long as it lasts. If you complete the mission, you can use it at the observatory.

The secret is that you can use a red star to transform to soar mario/soar luigi.

Go to the Gate, which is unlocked after the 5th Dome: The Engine Room. Go to where you meet Rosalina and talk to her again, then the red Luma will give you a test. Fly around with the red star and collect all the purple coins. Then get the red power star, you will go home, and find the red luma on the library. There will be a red flying star right next to him, and one near the garage.

TThe secret is the red luma knowing the "Flying Ability" Find a red star around the castle and you'll fly with Mario/Luigi.

Go to a place called "the gate" that leads to gateway galaxy, available after unlocking "the garden" and select the mission "gateway's purple coins" When Mario enters the galaxy, Rosalina will meet. A Red Luma notices how much Rosalina trusts Mario, so he gives Mario the challenge of collecting 100 Purple Coins scattered around the planet to earn his trust as well. There are seventy coins on the planet and thirty in the air. Mario must use the new Red Star power-up(that's the luma's secret) that gives him the ability of flight to reach the thirty purple coins in the air. Completion of this mission will award Mario with the game's sole Red Power Star. One collected, it allows for use of the Red Star power-up in the Comet Observatory. Sadly, it cannot be use in other places apart from the obserbatory. It would be awesome, don't you agree?
Hope this helps! Btw, the little stars are called lumas, not lunas. Good luck getting the soar star!

When you get the last stage the one after the garden, (gate) you will unlock a level that is the second one. Collect all the purple coins and it will be a red star. It allows you to fly once you spin in midair! You have to break the dimond and run into it first!

When you unlock the new dome "The Garden" an extra dome will appear. This leads back to the very first level of the game. When you go in that dome, pick the new level available. You will need to collect 100 purple coins on the planet. You will be able to use the secret the luma has been telling you about. The secret is to be able to fly when you spin next to red stars. Collect all 100 purple coins and you will get a red star. Then when you are back at the observatory, there will be 2 red stars that you will be able to use to fly.