[fjsolwmv]

It's not arbitrary. The only two choices that work are the real center of gravity, and the observer's position with the real center of gravity orbiting the observer and everything else orbiting the real center of gravity. If Tycho chose Jupiter as the center of the orbits, the planetary orbits would have the same problem of epicycles as the older models.

[goto11]

You can claim that any arbitrary point is "the center of the universe" if you acknowledge that the planets rotate around the sun, not around the designated "center". If you choose Jupiter as the "center", there would still be no observable difference and you wouldn't need additional epicycles.

[Armisael16]

What precisely do you mean by “the same problem with epicycles”? You can fix Jupiter at the origin. You use exactly the same equations, except that the sun is using the equation that used to describe Jupiter (with an extra negative sign) and the other planets add in the term describing the Sun’s motion.

Earth is no different than any other planet (or other celestial body in a stable orbit relative to the solar system) in this respect. Hell, you could make the Moon the center of the solar system - the math works just fine.

[rimliu]

If observer is on the Earth then equations for Jupiter will not work for describing the apparent motion of the planets.