What are the accepted proofs that Earth revolves around the Sun? When did this realization take place?

Original Article

This article contains a smoking gun quote which demonstrates the circular nature of using stellar parallax to prove heliocentricity.

“If an astronomer measures the position of a nearby star, and then measures it again six months later”

The assumption that the earth is moving is made before the measurements are taken, it is not a conclusion which may be deduced.

Proofs

1. Aristarchus
2. Phases of Venus
3. Stellar Parallax
4. Bessel and 61 Cygni
5. Aberration of starlight