Markus6 said:
Our understanding of gravity explains why a heliocentric solar system is simplest. The sun is far more massive than any other body in the solar system so we can neglect the gravitational forces between the planets and get a fairly accurate model. If there was another body about as massive as the sun then heliocentric wouldn't cut it. If the Earth was the most massive we'd all be geocentrists. We can still use a geocentric model, in fact it's still used in navigation.
It is not enough for the earth to be the most massive. For the sun to orbit the earth every 365 days, the earth would have to be the same mass as the sun to have the same gravitational effect on a body at that distance. If the earth had that mass, gravitational acceleration on the surface of the earth would be 3,265,062 m/s
² or 332,830g. We would not be having this conversation.
This does not depend on heliocentrist calculations of the Suns mass, but on Newton's law of Gravity
F=G*m1*m2/r²
The acceleration on a body is
a=G*m1/r²
To pull an object into a 365 day orbit at a radius of 150,000,000km you need a mass of
1.989×10³° kg. Either the sun has that mass or the earth has. Of course we know from the orbit of mercury that the Sun does exert that force, and if the earth exerted that force it would pull all the other planets out of their orbit around the sun and into orbit around the earth because all of the planets including Venus are closer to the earth than the sun.
For the sun to rotate around the earth every day, the earth would need a mass 365 times greater still.