Galileo's observations of the phases of Venus do not prove that
the Copernican model is correct. But they do show that the Ptolemaic
model is wrong, for in that model Venus does not go through the full
range of phases.
As to whether a geocentric or heliocentric model is correct -
Tycho Brahe proposed a compromise model in which the sun orbits
the earth & all the other planets orbit the sun. It's generally
recognized that this is _kinematically_ equivalent to the Copernican
model. What doesn't seem to be so widely recognized - though I think
most general relativists will agree if they think about it - is that a
SEMI-Tychonic model is valid. I emphasize SEMI because two important
changes have to be made in Tycho's model.
1) Tycho wanted the earth non-rotating but that won't work. If
everything rotated around the earth once in 24 hours, objects beyond
Neptune would have to be moving faster than light.
2) The "fixed stars" have to be "fixed" with respect to the
sun, rather than the earth, so that there will be stellar parallaxes.
But the major point - that the earth is stationary at the center
of the planetary system - remains.
This semi-Tychonic model can be worked out consistently in
general relativity. Though I think there is nothing really new about
this claim, I have never actually seen it treated in the literature, &
some relativists (e.g., Fock) have disagreed with the idea that one can
have a valid geocentric model. I have a brief paper on this which (as
coincidence would have it) I hope to be able to give at the Ohio Section
meeting of the American Physical Society in May.
George L. Murphy