To add another consideration to JD's point about the planets orbiting Earth, it would be difficult to posit a first-order neo-gravitational interaction with Earth which would provide for their orbits without having the gravity of the Sun. The Sun is definitely the gravitational king of the solar system, not the Earth. If you demand to have a true geocentric **model** with the Earth dominating at (or near) the center, you also need a planet/Earth interaction which dominates.
I'm wondering now, whether a Tychonian picture with elliptical orbits could be nicely drawn. Of course, it all comes back to what is the first-order interaction which keeps the planets in the system: the Sun's gravity, not the Earth's.
-> -----Original Message-----
-> From: Phys-l [mailto:phys-l-bounces@www.phys-l.org] On Behalf Of John
-> Denker
-> Sent: Wednesday, March 25, 2015 10:02 AM
-> To: Phys-L@Phys-L.org
-> Subject: Re: [Phys-L] Sun going around the Earth?
->
-> On 03/25/2015 05:59 AM, Brian Blais wrote:
-> > So, I was having an argument with someone about establishing that the
-> > Earth goes around the Sun, and he claimed that he could write down a
-> > perfectly consistent general relativistic framework where the Sun
-> > would be going around the Earth. Not having the time, I didn't get a
-> > chance to see this done, but I was wondering whether it *could* be
-> > done - even in principle.
->
-> Sure it "could" be done. It's not even hard. It's not even what I would
-> dignify as a general relativity exercise; high-school Newtonian mechanics
-> suffices.
SNIP
-> > If so, then is the geocentric model "just as good" as the
-> > heliocentric model - in the sense of "just as consistent with reality"
-> > - as opposed to the "just as convenient"
-> > sense?
->
-> That's a slightly different question. "The" heliocentric model posits that the
-> /planets/ go around the earth. You "could" write an equation of motion for
-> the planets in a frame comoving with the earth -- using the techniques
-> outlined above -- but it would be monumentally inconvenient.
->
-> As a matter of principle, you can choose any reference frame you like. The
-> physics doesn't care.