Galileo found out how fast the Sun spins by following the movement of sunspots.
Even though it is made of gas the Sun does spin around (rotate). Because it is not solid, like the Earth, the equator of the Sun spins round faster than the poles. It takes 27 Earth days for the Sun's equator to turn once round. Near the North and South poles it takes longer, nearly 35 Earth days.
This animation shows one rotation of the Sun as it appears when pictured
in X-rays (image from the Yohkoh Public Outreach Project).
The image below shows differences in the speed of rotation of material not only on the solar surface, but also inside the Sun. It was made using SOHO observations from MDI. Isn't it just amazing that by analysing data from instruments on board spacecraft scientists can find out how the gas is moving deep inside the Sun as well as on the surface?
Image courtesy of the Stanford Solar Center
The false colors represent speed; red material is rotating the fastest, dark blue, the slowest. Red material at the Sun's equator is moving approximately five thousand kilometres per hour faster than the blue material at the poles.
(Photo Credit: Stanford University)