Unlock shooting stars when viewing a particular constellation on the Prince's homeworld (the view constellation option) by meeting the katamari's diameter within the following time limits:

Star 1 - Under 1 minute
Star 2 - Under 3 minutes
Star 3 - Under 4 minutes
Star 4 - Under 6 minutes
Star 5 - Under 8 minutes
Star 6 - Under 8 minutes
Star 7 - Under 8 minutes
Star 8 - Under 12 minutes
Star 9 - Under 15 minutes
Moon - Under 20 minutes