I'm aware that it was known to the ancient Greeks that the planets were somehow different from the stars. But in what depth did they know the solar system? In particular, did they know:

  • that the sun was an ordinary star?
  • the motion of the planets?
  • the difference size of the planets (this is the part that started the whole question: Jupiter is big, while Mercury is small and fast. I suppose they chose the names knowing this, but the calculations aren't that simple)?

If any of the answers is yes, how did they? What math did they use?

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    $\begingroup$ Who exactly are the "ancient Greeks"? Is Ptolemy who lived in the African part of the Roman empire in the second century AD but wrote in Greek, is he considered an "ancient Greek"? 90% of what is known about "ancient Greek" astronomy comes from his books because very little before him survived. $\endgroup$ – Alexandre Eremenko Sep 18 '20 at 1:22
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    $\begingroup$ The Sun was not an ordinary star, it was not a star at all, stars were luminous bodies attached to a crystal sphere with regular rotation. The irregular motion of the planets across the night sky was plain to see, and the Sun was moving more like them. The naming of Jupiter and Mercury had nothing to do with their real sizes. Mercury was the fastest moving planet, and Jupiter was visibly the brightest other than Venus. And there were problems with the status of Venus at the (very ancient) time of the naming. $\endgroup$ – Conifold Sep 18 '20 at 6:43
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    $\begingroup$ They know the “celestial facts” by observation. This they thinked that planets (wandering stars) and fixed stars were very different objects. $\endgroup$ – Mauro ALLEGRANZA Sep 20 '20 at 6:52
  1. No they did not know this.

  2. The motion of the Sun, Moon and planets (as seen from the Earth) was known, in the sense that it could be predicted with reasonable accuracy. To do this, they used an ingenious model, approximating the periodic motions by combinations of circular motions, the same principle that is used nowadays for predictions of celestial motions.

  3. The sizes of the planets and distances to them were not known, except for the Moon but the order (Mercury, Venus, Mars, Jupiter, Saturn was known, or better to say "correctly guessed"). About the Moon, they new approximate distance, so they could compute the size. They had no means to estimate the distance to the Sun and planets, thus no means to estimate their sizes. There were attempts to do this but they came with wrong answers by the orders of magnitude. But Ptolemy understood that "The Earth is like a point in comparison to distances to planets and stars".

They understood that stars and planets must be at an enormous distance since they experience no visible parallax. But they could not imagine how really enormous these distances are. (The absence of parallax was the strongest argument against the heliocentric system which they proposed and then rejected.)

All this reflect the knowledge at the time of Ptolemy, 2-nd century AD, Egypt, Roman empire. He is considered a Greek because he wrote in Greek, as all other astronomers in the Roman empire. Most of the earlier work is lost, and we know about it only from mentioning in the secondary sources and Ptolemy himself.

What math did they use? Arithmetic (they did complicated calculations in sexagesimal system), Geometry and Trigonometry. Trigonometry was actually invented for this very purpose, and the earliest surviving source on trigonometry is also Ptolemy. (Ptolemy mentions Hipparchus, but the work of Hipparchus did not survive. There is also strong indirect evidence that the tables of sines existed before Ptolemy.)

  • $\begingroup$ What do you mean with point 2? Did they know that the motion was planar? Did they know that the trajectories were elliptical? Maybe only circular? $\endgroup$ – Mauro Giliberti Sep 20 '20 at 10:53
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    $\begingroup$ It is not strictly planar, but almost planar. And they knew this. They did not know that they are elliptic, but approximated them with combinations of circular motions, like nowadays we approximate any periodic motion with a combination of circular motions (Fourier expansion). If you take into account that they are not exactly elliptic but only approximately, they did the same that what we do now. $\endgroup$ – Alexandre Eremenko Sep 20 '20 at 12:15

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