The right image is from today at 2100 UTC (4:00 pm EST) and the left image is 4 days earlier. Note how the sunspots move because the Sun is rotating on its axis. It takes about 25 days for a rotation (at the equator, it takes longer as you move toward the poles due to the fact that the Sun is a big ball of gas, not a rigid body). One can observe sunspots and easily work out this rotational period.
While there are scattered references to sunspot observations with the naked eye from ancient Chinese and Greek observers, Galileo was one of the first to observe them with a telescope starting in 1610 and he was able to show that they were actual features on the surface of the Sun and moved as the Sun rotated.
In the Aristotelian cosmology which still ruled in the early 1600s, and which was backed by the Roman Catholic Church, the Sun was a perfect and unblemished celestial body. In was inconceivable to some that it had darks spots on it. Christoph Scheiner (1573-1650), a Jesuit priest/astronomer, was one and he argued that these dark spots represented small satellites orbiting the Sun.
Careful observations by Galileo, however, showed that the sunspots moved more slowly when they were near the limb of the Sun and more quickly when they were in the center of the Sun. This was due to foreshortening as shown in the diagram below. A sunspot moving from A to D would travel the same distance as from D to C. From the Earth, however, the A-D distance looks shorter than the D-C distance. That makes it appear as if the sunspot was moving faster between D and C.
The idea that heavenly objects like the Sun were perfect and unblemished held sway for over 1,500 years because people philosophically liked the idea and it conformed to their religious beliefs. A few simple observations, however, was all that was needed to topple this incorrect view. No wonder the religious authorities of the day (and even some today) hated science.