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The mathematics used to describe how geocentrism works is the same mathematics that can describe how any other point in our solar system can be thought of as stationary, or motionless. It makes no difference to the physics of the theoretical system being considered.
Using the identical gravitational formulas and those for elliptical orbits (such that the area traced out by the arc of orbit by a satellite is the same area for each unit of time, regardless of the distance from the presumed stationary focal point), the sun could be thought of as stationary (but nobody thinks that it is anymore, unlike Galileo), or Jupiter could be thought motionless, or Mars, or Venus, or Earth's moon, or even Halley's comet.
In fact, any point in space, even one not occupied by any planet, sun or asteroid (or a particle of space debris or dust), could be imagined motionless and the center of rotation around which all other objects rotate. The math is the same.
The way planets and/or the sun appear to a viewer located at any particular point is likewise the same, regardless of whether one presumes that one spot or another is "motionless."
An analogy could be a merry-go-round, where someone standing on the rotating floor could be the "motionless" one, and the world around the merry-go-round is in motion (relatively speaking). From the standpoint of physics and mathematical calculation, the way the world around appears to the rider is the same whether the rider believes he is moving or not.
When engineers figure how large framework beams and columns in a bridge have to be to make the bridge safe, they use a system called "taking moments of inertia" which requires presuming some point to be stationary, or "point zero." To do so, they can choose any point on the bridge, and "take moments" around that "zero point," most often using two or more points in successive calculations, to double or triple check their work for accuracy. When all the numbers are correct, they'll get the same results for member forces regardless of which point is held as "zero" (or "motionless"). If you know an engineer, ask him this question. And don't be surprised if he has to stop and think when you ask him how this applies to geocentrism, because they do not make the connection (which is simple logic) in engineering schools. That's another topic, really.
Many misunderstandings about the discussion around geocentrism arise from a failure to recognize the simple principle described above.
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