The original article is a dead link.
Fortunately I have a screen shot of a smoking gun quote which illustrates the circular reasoning necessary in the use of stellar parallax to prove heliocentricity.
“If the earth moves around the Sun, then the apparent positions of the stars must change between January and June.”
This is an inductive rationalization of the premise of heliocentricity, not proof of it.
Proofs
- Stellar parallax
Matty's Paradigm 