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If we assume a geocentric model of the universe (like ancient astronomers did) how could we ever find out (again, like ancient astronomers did) the right distances of the planets? For example, how did they know that Jupiter is further than Mars, if Jupiter is brighter?

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    $\begingroup$ Can you back up your claim that ancient astronomers [knew] the right distances of the planets? $\endgroup$ – Jan Doggen Oct 18 '16 at 12:55
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According to the Cambridge Concise History of Astronomy (p 33 of my edition), essentially the Greeks took the (not unreasonable) view that the planets that moved more slowly were further away and were orbiting on larger spheres.

That's obviously not the same as suggesting they knew "the right distances" to the planets, merely the order. They did develop a mathematically sound means of estimating the distance to the Moon, though their observational data let them down on a correct estimate.

They also thought the Sun was in the fourth sphere around the Earth (to explain the observed behaviour of Mercury and Venus).

Not all Greeks thought the Sun revolved round the Earth and those who argued for a heliocentric universe said the reasons the stars did not move as the Earth did was because they were very, very far away.

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  • $\begingroup$ I found the mathpage site mathpages.com/home/kmath639/kmath639.htm to be an interesting account of the Ptolomy's model. It notes "Lacking any definite means of ordering the distances, the ancients basically guessed that the planets were ordered according to their overall orbital periods, i.e., the time taken to completely circle the Earth" $\endgroup$ – James K Oct 15 '16 at 11:59
  • $\begingroup$ How does that order of planets based on orbital periods hold up, given that the Sun orbits Earth more often than any other object, but still Ptolemy put the Sun between Venus and Mars? It was obviously not at all as simple as those late Cambridgeans tried to make it look like. $\endgroup$ – LocalFluff Oct 17 '16 at 20:34
  • $\begingroup$ They didn't propose that the world was flat or not spinning - ie they did not propose that the Sun moved round the Earth daily. $\endgroup$ – adrianmcmenamin Oct 17 '16 at 21:02
  • $\begingroup$ @LocalFluff At a guess they observed the analemma and concluded that the Sun had a 1 year orbital period; that's consistent with the ranking. $\endgroup$ – j-g-faustus Oct 17 '16 at 21:22
  • $\begingroup$ @adrianmcmenamin Aristotle, and Ptolemy who ordered the planets, argued that the Earth did not spin. Otherwise everyone would drop their hats as if riding a horse (which was dangerous before the stirrup) at 465 meter per second. They knew the size and shape of the Earth. And j-g-faustus, a 1 year Solar orbital period assumes a daily rotating Earth, which was like criticizing the global warming doomsday belief until Copernicus, Kepler, Galileo mid 1500s to early 1600s. $\endgroup$ – LocalFluff Oct 18 '16 at 11:06

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