After giving this some more thought, perhaps the point you are missing is the heliocentrists always ignore the gravitational effects of the rest of the universe and geocentrists always include it.
When you appeal only to the gravatational 'pull' of the sun, you are by definition ignoring the gravitational effects of the rest of the universe.
In the geocentric universe, the stars are centered on the sun, not on the earth and the universe has an annual wobble offsetting the orbit of the sun around the earth.
I'm sure you can understand that the earth doesn't orbit the center of the sun, but the center of mass of the system as impacted by the other planets in the solar system. Geocentrists make the point that the rest of the solar system is not the only mass that must be accounted for, but the entire universe.
Since the solar system is basically a point when compared to the rest of the universe, the gravitational offset caused by the annual wobble of the universe with the stars centered on the sun is more than enough to shift the center of mass from the sun out to the earth.
This is basically what Einstein and Hoyle understood that modern heliocentrists do not.
?
Where did you ever get that idea? That's completely inaccurate . . .
'heliocentrism' simply means that you understand the gravitational physics. And that after you understand that the sun, as the greatests mass in the solar system, has the dominant gravitational effect on the solar system.
So anyone who observes the motion of the planets, moons and sun is observing direct evidence of heliocentrism.
Which is as proven as almost anything.
Y'know?