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Who first measured the distance to the Moon? How was it done? I think it had to happen after Newton, but I am not sure.

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It happened long before Newton. In the second century BC Hipparchus used lunar parallax to calculate a value for the minimum and maximum distance of the earth and moon. His results are very close to the modern calculation of this distance.

You can read about it here: Toomer G.J. (1974), "Hipparchus on the Distances of the Sun and Moon." Archives for the History of the Exact Sciences 14: 126–142.

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    $\begingroup$ "Who first measured..." If that means absolute terms, it was Hipparchus. But if relative measures, then Aristarchus did it before Hipparchus. He only got a relative value, saying that the Moon was 18 to 20 times closer than the Sun. (That is wrong because of a bad angle measurement, but his trigonometry was correct.) $\endgroup$ – DrZ214 Feb 19 '17 at 11:23
  • $\begingroup$ I read that Aristarchus measured in absolute terms by measuring the duration of a lunar eclipse. $\endgroup$ – timur Aug 12 '17 at 19:13
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This is an ill defined question. It can be interpreted as "Who was the first to TRIED to measure the distance to the Moon", or "Who was the first to give a correct number", and what is counted as correct number.

And even this does not define the question precisely. The crucial question: "in what units"? It is relatively easy to measure the distance in terms of the radius of the Earth. But it is another matter, if you want the answer in miles, kilometers or stadia.

The earliest written evidence that survived is a purely theoretical work of Aristarchus where he explains some mathematics involved. One can conclude from the book that he hardly measured anything in practice.

Hipparchus who lived later, had already the idea of the order of magnitude of Moon's parallax (this is equivalent to measuring the distance in terms of the Earth radius). However most ancients did not discuss the distance as we understand it, but only ratios, for example the ratio of the distance to the Sun and to the Moon, or the Moon's parallax which is sufficiently large to be measured by primitive tools. To pass from the Moon parallax to the distance in some conventional length units one needs to know the size of the Earth. The size of the Earth was measured by Eratosthenes, but it is still subject of discussion how accurate his measurement was.

The problem is that he gives the answer is stadia, and nobody knows how long his stadium was. Few other measurements were made after him, but still when Newton was a student he was taught that the degree of the meridian is 60 (British) miles. There was no way to measure the distance to the Moon without knowing the radius of the Earth.

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    $\begingroup$ The point is that the ancients had a valid mathematical and astronomical basis for calculating the radius of the earth (Eratosthenes) and for determining the distance to the moon in earth radii (Hipparchus). If you have a broadly correct figure for these two things you can express the distance to the moon in whatever units you like. $\endgroup$ – fdb Jan 10 '15 at 9:30
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    $\begingroup$ I agree that "the ancients" (more precisely, Hellenistic Greeks) had a valid mathematical basis for all of this, but their actual measurements were rare, and when we have a record, they were mostly of poor quality. $\endgroup$ – Alexandre Eremenko Jan 13 '15 at 0:01
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Just was at Pulkovo Astronomical Observatory last year, they definitely said that, first time the distance was measured, after the Lunokhod 1 delivered the Corner reflectors to the Moon. There are also atomic clocks, made with lamps in museum

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  • $\begingroup$ It probably was the first high precision measurement (to the cm I guess. I’d have to check is no radar measurement where made befor Lunokhod 1), but the knowledge of approximate distance is much older than that $\endgroup$ – Frédéric Grosshans Jan 8 '18 at 18:13
  • $\begingroup$ @Frédéric Grosshans You are right. Question was about first, which was made by Hippocrates in -4' century. However this modern one was made with laser, not a radar $\endgroup$ – Oleg Skripnyak Jan 19 '18 at 16:30
  • $\begingroup$ I know. To male a laser measurement, you need a mirror on the Moon, which was impossible before Lunokhod. But radar measurement could have been made before Lunokhod $\endgroup$ – Frédéric Grosshans Jan 20 '18 at 9:20
  • $\begingroup$ Indeed, this 1965 paper is about a US measurement campaign in 1959-1960, done to improve the result of a 1957 US campaign. $\endgroup$ – Frédéric Grosshans Jan 20 '18 at 9:26
  • $\begingroup$ @Frédéric Grosshans I see, never knew about this, thank you for the info. There also mentioned that peak to peak amplitude variation is about 3km. I think its more preferable than just distance to a corner reflector in cm precision, so its averaged distance to the whole moon. But not suitable for distance variations. That strange, i thought that only metal can reflect microwaves $\endgroup$ – Oleg Skripnyak Jan 20 '18 at 22:13

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