How long did galileo watch the moons before he realized they were orbiting jupiter?

Galileo turned his telescope peacefully to the skies. He started by observing the Moon, on which he discovered mountains and craters, not an even surface as was believed at the time. Then, on January 7th, 1610, while looking at Jupiter, he saw three small stars close to it, two to the east of the planet and one to the west. The next night he looked at them again and all three were to the west. Watching on subsequent nights he saw them in varying positions and realised that they were ‘wandering’ round Jupiter, as he later put it, moving around it in orbit. On January 13th he discovered a fourth satellite or moon. 

Every statement this is because of the same law