Geocentric frame of reference and superluminal speeds I have a couple of questions on frames of reference.
From my understanding, we can do math in an accelerating frame of reference as long as "fictitious" force terms are correctly added. From this point of view, is there anything wrong with viewing the Earth as stationary, and the rest of the universe rotating around it, at least kinematically? And, if so, wouldn't several cosmological objects move faster than light in this frame of reference? How can this be?
I'm sorry if this is a dumb question, I'm not asking this from a religious perspective I just want to understand how frames of reference work.
 A: You're right - but so too are the photons. They're moving "faster than light", too, in this frame!
You see, talking of "light speed limits" is really just pseudo-Newtonian mechanical heuristics on top of the actual gist of relativity theory, which is that information can transmit between some places in space-time and not others. These relations, or predicates on events, are what must not be violated.
However the predicates that tell you "yes or no" to "Can you send a message from A to B?" take different forms depending on the coordinate system. For "flat" spacetime, in a certain special class of coordinate systems, they show up as a "speed limit", but are more subtle in others. This is why the theory here is called "special" relativity (SR).
All the "weird" effects - time dilation, length contraction, and so forth can be thought of as what a Universe with minimum imposed communication latencies looks like from the viewpoint of someone inside it subject to those constraints.
A: Take a simple example: You are standing on a conveyor and a friend is running behind you to try to reach you, 10m away. He is walking 1m/s and it will take him 10 seconds to reach you.
The conveyor may be moving at 2m/s and that would not change the situation. but you could work out what happens using the ground as a reference. Your speed would be 2m/s your friends' speed 3m/s and the outcome would be the same.
So no, there is nothing wrong with a geocentric reference frame if you calculate these kinds of problems. in fact we do it all the time. Your car doesn't care about the angular speed of the milky way spirals, it just shows you km/s with respect to the ground. 
But that is cutting short the actual problem with a geocentric world model, where gravity would be hard to explain.
And no, things would not move at above light speed, when you use a geocentric frame of reference, it's just that you would observe things in a different time scale than from other reference frames, because speed is dilating time. What is important to keep in mind concerning reference frames is that at non-relativistic speeds, we can use them interchangeably, but actually, this is "wrong" in the sense that any relative motion is relativistic.
