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When ancient Greeks could not observe any parallax, what were the two bodies they were looking at to determine this? I imagine the stars (or a specific star) would have been one of these, but what was the near body they used?

Normally, when explaining parallax, we tell a person to close an eye, hold a finger up at arms length (the near body) and align this to an object across the room (like the stars in the example above). What "finger" did the Greeks use to try to measure parallax?

They cannot have been measuring the angle between stars as these were believed to be all at the same distance on a hollow sphere.

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    $\begingroup$ They were trying to measure position of celestial bodies from two different locations on the Earth. They were able to discover only Moon's parallax in this way. For the Sun and planets it was too small for them to measure, not speaking of the stars. So the role of "two eyes" was played by two remote positions on Earth. $\endgroup$ Jul 15, 2023 at 7:18
  • $\begingroup$ Thank you, @AlexandreEremenko, what did they use as the finger? $\endgroup$ Jul 15, 2023 at 8:05
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    $\begingroup$ Moon, of course. $\endgroup$ Jul 16, 2023 at 5:41

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They tried to find parallax between pairs of stars. First of all, they didn't "believe" that stars were on the same distance. That was their hypothesis. And one of the reason why they accepted it is because they didn't find any parallax. If you don't have parallax then the sphere of fixed stars is the simplest model. But they tried to find deviation from this model even after they failed to measure parallax. For example, one of the reason for Hipparchus' star catalogue was to attempt to find proper motion of fixed stars. This is why he focused on triplet of stars that lies on one line. It would be easier to find if they would move in the feature.

By the way, theoretically you can find parallax even between two objects at the same distance, but of course it would be much smaller and harder to measure.

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