Equivalence of Hypotheses
Claudius Ptolemy / Nicolaus Copernicus / Tycho Brahe
Unlike the normal equivalence page, this web page has exaggerated equants and eccentricities to make clearer that the equivalence between the three forms of hypothesis comes not from the eye's being fooled by nearly circular motion, but from the very nature of the hypotheses.
With these large eccentricities, the green line in the Brahean model looks absurd. This is because the planets are not actually tied to the apparent sun, but rather to the mean sun. Click here to see a full animation of the Brahean model. The mean sun is added in green, moving around the earth at a constant distance. The center of Mars's orbit is red. Its equant is magenta.