Some may find this graphic illustration interesting:
http://www.astro.utoronto.ca/~zhu/ast210/both.html
Here are a few quotes from Hans Reichenbach, who was Einstein’s student in Berlin, when he lectured on the theory of relativity. (In 1926, with the help of Albert Einstein, Reichenbach became assistant professor in the physics department of Berlin University. After Hitler came to power he left Germany, eventually moving to the United States and accepting a professorship at the University of California):
The cosmologies of Copernicus [Heliocentrism] & Ptolemy [Geocentrism] are kinematically equivalent; both of them are descriptions of the same facts, and Ptolemy’s epicycles of the planets are the kinematic equivalents of the circular orbits of Copernicus.
Reichenbach, Hans- Philosophy of Space and Time- p210-211
The Copernican conception is indeed simpler, but this does not make it any “truer” since this simplicity is descriptive… One description may be simplest for some phenomena while a different description may be simplest for others; but no simplest description is distinguished from other descriptions with regard to truth. The concept of truth does not apply here, since we are dealing with definitions.
Reichenbach, Hans- Philosophy of Space and Time- p219
He [Copernicus] was able, in fact, to cite as a distinct advantage only the greater simplicity of his system. … Here lies one of the reasons which led scientists to accept the Copernican system, even though it must be conceded that, from the modern standpoint, practically identical results could be obtained by means of a somewhat revised Ptolemaic system.
Hans Reichenbach- From Copernicus to Einstein- p18
Motion is change in position; it is clear, however, that it cannot be observed unless it is a change in position relative to a certain body and not relative to an ideal space point. Is it meaningful, under these circumstances, to speak of absolute motion or of motion relative to space, if motion relative to other bodies only can be observed? According to this principle there exists only a motion of bodies relative to other bodies, and it is impossible to distinguish one of these bodies as being at rest, because rest means nothing but rest relative to another body, i.e. rest is itself a relative concept.
Hans Reichenbach- Philosophy of Space and Time- p210
And here are quotes from some others:
The commonly held view is that Copernicus’s heliocentric model vanquished the competition, especially the geocentric view of Ptolemy, because it yielded better predictions of the positions of the celestial bodies. In actual fact, the predictions of the Copernican model were a little worse than those obtained via the complicated series of epicycles… the real selling point of the Copernican model was that it was much simpler than the competition yet still gave a reasonably good account of the observational evidence.
Today we cannot say that the Copernican theory is ‘right’ and the Ptolemaic theory ‘wrong’ in any meaningful physical sense.
Fred Hoyle, Nicolaus Copernicus, Heinemann Educational Books Ltd., 1973, p78
And hence this affirmation: “the earth turns round” has no meaning, since it cannot be verified by experiment; … such an experiment … cannot even be conceived of without contradiction …
Henri Poincare- Science and Hypothesis- p117
There is one more implication that modern science has perceived in the work of Copernicus. The same observational data that Ptolemy organized in his geocentric theory of deferent and epicycle can also be organized under the heliocentric theory of Copernicus. Despite the belief of the latter that the new theory was true, the modern view is that either theory will do and that there is no need to adopt the heliocentric hypothesis except to gain mathematical simplicity. Reality seems far less knowable than Copernicus believed, and today scientific theories are regarded as human inventions.
Morris Kline- Mathematics and the Search for Knowledge, p85
… in fact simplicity of the mathematical theory was the only argument Copernicus & Kepler could advance in favor of their heliocentric theory as opposed to the older Ptolemaic theory.
Is the path of the earth around the sun an ellipse? No. Only if the earth & sun are regarded as points and only if all other bodies in the universe are ignored. Do the four seasons on earth repeat themselves year after year? Hardly. Only in their grossest aspects, which are about all men can perceive anyway, do they repeat.
Morris Kline- Mathematics: The Loss of Certainty- p 344, 350