How did astronomers prove the earth revolves around the sun?
The parallax is one of the proves.
In ancient times, some thinkers realized that if the Earth rotated around the Sun, we would see an oscilation of the "fixed" stars. They didn't realized the enormous distances that the other stars are from us, and the parallax is far to be seen with naked eyes. The parallax after all exists, but the larger parallaxes are about 1 arc second.
Of course the problem of what rotates about what is a no-problem after the discovery of the gravity laws. Everything in the solar system rotates around the mass center. But the Sun is so massive, that the mass center of the solar system is inside the Sun.