Answer
The answer is as follows. 
Katrielle and the Millionaires' Conspiracy walkthrough
When the star moves, it leaves a trail in its wake.
Can you fill the whole night sky with its trail?
The mysterious objects floating in the sky are warp holes.
They are paired according to their appearance, and when the star goes into one of them, it reappears out of the other.
Touch a square to move to it, and make sure the star moves through all of the squares.
You are not allowed to go through a square that already has a trail on it.
The answer is as follows.