By observing the sunspots, Galileo concluded that the sun rotated on its own axis.
Explanation:
Galileo with the help of his telescope, observed that the sunspots were blackish spots found in the sun which is irregular, uneven and often with unique shapes. These cannot be any satellites or particles moving round the sun. Rather these observations consolidated the fact that the sunspots were denotations of the sun's surface and the irregularity in shapes points towards the fact that the sun rotate in its own axis.
