Re: [Phys-L] Sun going around the Earth?

[John Denker <jsd@av8n.com>]

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.

Pick a reference frame instantaneously comoving with the
earth.  Write the equations of motion in this frame.
  The interesting bit is this:  Since this is an accelerated 
  reference frame (accelerated w.r.t the barycenter) i.e.
  not a freely-falling frame, there  will be gravitational
  pseudoforces in this frame.  This isn't much of a challenge,
  since people have been using non-freely-falling reference
  frames for as long as they've been doing physics.  The
  prosaic "lab frame" is in this category.

At the next level of detail:  The acceleration of your chosen
frame changes over the course of the year ... but you don't
need to worry about this.  There are no x dot-dot-dot terms
in the equation of motion;  x dot-dot (acceleration) appears,
but x dot-dot-dot (the derivative of acceleration) does not.
So you can get away with using the /instantaneously/ comoving
reference frame.  That gives you an integrand that you can
integrate to get the equations of motion.  People have been
doing this for hundreds of years without even questioning it
at this level of detail.

Accelerated reference frames tend to get little coverage
(or outright wrong coverage) in introductory physics classes,
but still they exist, and techniques for dealing with them
are well known and rather widely used.  In particular, I'm
thinking of centrifugal and Coriolis effects, which everybody
knows are real and useful, even if your physics book says 
they don't exist.
  https://www.av8n.com/physics/rotating-frame.htm

>  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.