How was the Tychonic system mathematically related to the Copernican system?

The Tychonic system, proposed by the Danish astronomer Tycho Brahe in 1583, is mathematically equivalent to the heliocentric model developed by Nicolaus Copernicus.1

While Copernicus placed the Sun at the center of the solar system with Earth orbiting it as a planet, Tycho Brahe retained a geocentric model where the Sun and Moon orbited a stationary Earth, while all other planets orbited the Sun. Because the relative motions of the bodies remain the same in both schemes, they are mathematically interchangeable.21

Despite this equivalence, the Tychonic system is considered an unnecessary complication compared to the Copernican model. Tycho’s model was developed in part to address the lack of observed stellar parallax and to reconcile his observations with a stationary Earth, though it ultimately failed to provide a physically correct description of the universe.12