"I use an old laptop-charger (19.4V, 4,5 amps, not all used ;)) to power tthe LED's. Here is a test-setup of the breadboard powering all the leads. I have every constellation seperately wired. Eventually I want to make a 'switchbox' so you can illuminate the constellation of your choice!"
examples:
http://www.instructables.com/howto/planetarium/
commercial home planetariums go from around $30 up and have features like changeable skies and rotating in sync with the earth's orbit.