Observations made with ESO's Very Large Telescope have for the first time revealed the effects predicted by Einstein's general relativity on the motion of a star passing through the extreme gravitational field near the supermassive black hole in the centre of the Milky Way. This long-sought result represents the climax of a 26-year-long observation campaign using ESO's telescopes in Chile.
[...] The new measurements clearly reveal an effect called gravitational redshift. Light from the star is stretched to longer wavelengths by the very strong gravitational field of the black hole. And the change in the wavelength of light from S2 agrees precisely with that predicted by Einstein's theory of general relativity. This is the first time that this deviation from the predictions of the simpler Newtonian theory of gravity has been observed in the motion of a star around a supermassive black hole.
(Score: 3, Interesting) by AthanasiusKircher on Thursday August 02 2018, @06:07PM
Well, the historical epicycle model is definitely wrong, because (contrary to popular belief) there were no "epicycles upon epicycles." You can read more about that in the link someone already gave above. The mathematics required to build models of epicycles upon epicycles simply didn't exist in medieval times, and there's no historical evidence that they were ever used.
If I remember correctly, Owen Gingerich (science historian) traced the error to some ignorant 19th-century historian who didn't understand how the epicycle system worked, and mistook other aspects of the theories as "epicycles upon epicycles."
So yes, if we build a theory of epicycles that is completely divorced from the method used historically, one can approximate motion to an arbitrary level of precision. But why would you? At best, it serves to perpetuate a scientific urban legend.