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Even if Newtonian physics, geocentrism is a valid choice as long as the Earth rotates to account for centrifugal forces.
All other planets also circle around the sun, the most massive object in our solar system.
How can you change the frame of reference to make them circle the earth, too, without crossing their orbits?
change the frame of reference
the notion of a frame of reference is independent of that of the center of any given orbit. "frame of reference" simply means choosing some origin for your coordinate system1; although a stationary frame of reference is easier to work with, in practice the convenient frames of reference all track either the sun or the earth.
there is also the question of whether to use an inertial frame, or a rotating one. a properly rotating frame of reference2 can have coordinates of locations on the surface of the earth remain fixed; and in these coordinates, the sun would indeed appear to orbit the earth, because the addition of the virtual rotation requires a "fictitious" force3.

Footnotes

  1. Some of the common choices.
  2. I link directly into the middle of the article, although you might want to skim the introductory section as well: https://en.wikipedia.org/wiki/Inertial_frame_of_reference#Inertial_frames_and_rotation
  3. After posting I found that there's an entire article about these.
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