Scott,
In the rotating earth model, the zero sum is obtained by means of a fictitious force called "centrifugal force" that is provided by the tangential velocity of the satellite. The centripetal force - pointing inward - is provided by gravity. The two are set equal (or equivalently, summed to zero) and the radius is calculated, just as you did above. In the geocentric model, instead of a fictitious centrifugal force, you have a real force provided by the rotation of the aether. You want an equation, but I don't know what else to tell you other than that the equation is the same. It is literally the exact same equation. The only difference is what accounts for the outward force that balances gravity. The answer is that it's a real force allegedly caused by the rotation of the aether, just as in the model in which the earth is rotating, the gravity is balanced out by a fictitious centrifugal force that is really provided by the tangential velocity of the satellite. That's it. That's all there is to it.
Regarding your claim to Lynnie that there would be no sidereal day in a geocentric model, that is not accurate, either. The revolution of the earth around the sun does not just disappear in a geocentric model. It is accounted for in the same way, just with the earth defined at rest and all other motion defined relative to it.
I have enjoyed the interaction with you gentlemen, but I think I've had my fill for now. Besides, I would rather see a hermeneutical discussion of this subject. Perhaps after the dust has settled on this thread, I'll eventually start another one for hermeneutical considerations only, as I think it is essential to separate the two.
I know you are likely done, but you are not correct in your analysis of even the rotational model. The net force is not zero according to the rotational model. There is no outward force. If there was, the satellite would stay on the same velocity vector and fly off into space. The centripetal force provided by gravity is a net force that is always accelerating the satellite towards the Earth. This has the effect of continually changing the velocity vector so that the satellite follows a circular path around the Earth. You can't change direction without a net force. If you review the equations I wrote down you won't find any outward force.
This is not the case with the geocentric model which requires zero acceleration and hence a net force of zero (F = ma). I'm going to try something different and invent a dialogue between me and a geocentrist. Lynnie, it will have to be a geocentrist that does not believe in the rotation of the Earth as I simply can't address every variation of geocentrism out there. I hope that is acceptable. This is mostly to identify where I seem to have the geocentrist position wrong. If you feel it is a straw man then kindly correct the dialogue where appropriate.
Scott: You are a geocentrist?
Geocentist: Why yes. The Earth is fixed and immovable.
S: So you don't believe the Earth moves up or down?
G: No.
S: You don't believe the Earth moves sideways?
G: No.
S: You don't believe the Earth move in or out?
G: No.
S: You don't believe the Earth spins like a top?
G: No.
S: So the Earth is truly stationary?
G: Yes.
S: What of the stars?
G: Well they move with an orbital period of 86,164 seconds.
S: And the sun?
G: It moves with an orbital period of 86,400 seconds.
S: And the planets?
G: They are more complicated.
S: What about that geostationary satellite?
G: It doesn't move at all. You can watch it all day every day and it won't budge. And since we are standing on the Earth which is fixed and immobile, anything that doesn't move from our perspective doesn't move at all.
S: It doesn't move up or down?
G: No, it does not get closer nor further away.
S: It doesn't move side to side?
G: No, it stays above the same spot on the Earth.
S: It doesn't spin like a top?
G: Well I suppose it could, but that doesn't matter. It would be geostationary regardless.
S: I agree. So if it is not moving side to side it can't be moving around the Earth.
G: That's right.
S: So it can't have an angular speed around the Earth.
G: True.
S: You wouldn't mind me just dropping the centripetal force factor from the left side of the equation. It just comes out to zero.
G: Right. Zero times anything is zero.
S: Well now I'm left with a strange result. That means that the gravitational force on the right has to equal zero. But the only way that could be true is if the satellite is at an infinite distance from the Earth which it is not.
G: Actually you are overlooking something...
And that is where I am stuck. Either the geocentrist wants to add an additional term to one side of the equation,or he wants to mess around with Newton's law of gravitation (or both). In any case, he needs the net force to equal zero at precisely the right altitude.