Talk:On the Sizes and Distances (Aristarchus)

Untitled
Any feedback on this page would be greatly appreciated, especially verification of my numbers, both those of Aristarchus and the modern values. The images should be improved, but I don't have the programs to do it right now. --Dantheox 08:07, 20 December 2005 (UTC)

Typo: in the second construction, the label "t-s" should read "s-t". --Dantheox 08:09, 20 December 2005 (UTC)

Distance to Sun and Moon
According to van Helden (1985, pp. 8-9) "Aristarchus did not calculate these absolute distances, however! After a determination of the ratio of volumes of the Moon and Earth, the tract ends abruptly."

Since the distances given in the table are apparently not in Aristarchus, they should be described clearly as modern reconstructions. Interestingly, van Helden gives two possible reconstructions, one (drawing on a value of the Moon's apparent diameter found in Aristarchus) yields your distances to the Moon of 20 earth radii, to the Sun of 380 e.r.; the other puts the Moon at 80 e.r, the Sun at 1,520 e.r. --SteveMcCluskey 15:29, 15 June 2006 (UTC)


 * Please make a note of this in the article as you see fit. That information certainly belongs in the article! --Dantheox 16:52, 15 June 2006 (UTC)

I suggest the article could use some editing to simplify it slightly. It is no major thing just that I find it unnecessarily difficult to read and one needs to re-read it a bit too much. It could for be stated for example that θ is the angular radius of the moon seen from earth and that d is the radius of the cone which represents the earths shadow. --83.226.131.224 14:13, 14 August 2006 (UTC)

Also the most important hypothesis of Aristarchus, though very obvious but which he nevertheless stated, is that the moon receives its light from the sun. (Thomas L. Heath, Greek Astronomy, Dover Publications, 1991, p.100)

Furthermore Aristarchus could have underestimated the anglular distance between the sun and the moon as his result was amazing even as it was. Anaxagoras had to leave Athens for claiming that the sun was greater then the Peloponnese. Had he discovered that the distance to the sun was 380 times that of the moon he would surely have a hard time accepting it himself. --83.226.131.224 14:33, 14 August 2006 (UTC)

Radius of moon compared to earths
Please note that there is no need for formulas to compare the sizes of earth and moon, just simple observation of the earths shadow as it appears on the moon surface during the beginning or the end of a lunar eclipse. —Preceding unsigned comment added by 77.49.11.149 (talk) 20:28, 24 July 2008 (UTC)

Bugs in Picture
The picture is missing the segment marking t-d on the Earth radius line and the line 90 degrees to it forming the triangle between the earth, the shadow of Earth on the moon, and the ray from the sun. I don't know how to amend the picture. --TryingToUnderstand11 (talk) 07:08, 15 July 2023 (UTC)

I think the quantity t-s in the picture under "Lunar Eclipse" should be s-t. 69.124.189.188 05:47, 4 December 2007 (UTC)

Observable quantities in measurement of moon's size
"The above equations give the radii of the Moon and Sun entirely in terms of observable quantities."

I am not clear how n = d/ℓ is measured. I believe that this might be done using the duration of the lunar eclipse. Could some one elaborate on this point?

Trebauchet1986 (talk) 05:56, 17 August 2010 (UTC)

Possible explanations
There are a thousand possible explanations of the 2 degrees for the angular diameter of the sun. A scribe might have used it in error for 1/2. — Preceding unsigned comment added by 86.176.7.150 (talk) 15:58, 7 December 2011 (UTC)

Removed dubious paragraph -- is there another citation for similar conclusions?
Removed:


 * However, since the time of Voltaire questions have existed as to whether the work is genuinely Aristarchus'. In 2009, it was revealed that misunderstanding the ancient angular unit "meros" appears to have introduced an error by a factor of 4 into several calculations, which explains the work's bizarre demands that central lunar eclipses last ½ a day, and that the Moon retrogrades against the stars every day. The testimony of Archimedes indeed disagrees on the solar diameter by a factor of 4. In 2011, it was first pointed out that the work's best-known data, its 87° half-Moon solar elongation-limit and 2° solar diameter, are mathematically incompatible with each other, given the precision of human vision.

The references lead to a personal web page and to references to Vol. 1	No. 1 of "DIO & The Journal for Hysterical Astronomy". This stuff looks like a joke, and certainly not a credible source. A credible citation for corrections to Aristarchus interpretations would be welcome. As for Voltaire... likewise. — Preceding unsigned comment added by 86.140.51.175 (talk) 21:43, 5 March 2013 (UTC)
 * The above removal is arguably somewhat unsatisfactory. Though it presumably does not qualify as a RS (indeed it looks like OR), there is little or no reason to think that the blog is a joke, as distinct from an occasionally slightly humorous but scholarly look (backed up by some scholarly citations) at some of the pseudo-scientific absurdities occasionally still found in contemporary astronomy. In other words there is every reason to think that what was said was quite likely to be true and should at least arguably have initially been left in the article, with some or all of the citations replaced by "citation needed" requests, and only removed if no RS citations had turned up after whatever our rules describe as a reasonable period of time. After a little further thought I may well soon decide to at least temporarily restore it with such citations needed added. Tlhslobus (talk) 00:46, 13 August 2015 (UTC)
 * Further research indicates that Thomas Heath (1913) mentions and rejects some early doubters, notably Voltaire, and that these should probably be mentioned in the article, perhaps in a section called Authenticity, or perhaps Authorship, along with a few other citations showing that most RS today do not have such doubts. I may or may not eventually get around to doing that myself. Meanwhile the rest of the removed stuff is not RS, and I have found no RS backing online, so it should probably stay removed. Tlhslobus (talk) 02:55, 13 August 2015 (UTC)

New image
I don't see how this fits into your excellent article, but this diagram is intended for Astronomy students at a more conceptual (introductory level)--Guy vandegrift (talk) 14:41, 5 June 2017 (UTC)


 * Hey, I just found a home for it! Quadrature (astronomy)-Guy vandegrift (talk) 14:41, 5 June 2017 (UTC)


 * The link to the 2011 effort of Alberto Gomez Gomez does not work, at least with me, now. — Preceding unsigned comment added by 36.70.3.227 (talk) 08:29, 24 October 2017 (UTC)
 * Is the description for that image correct? Dichotomy (half-lit) occurs at 89.85 degrees, 0.15 degrees before what I thought was the definition of the 1st quarter moon which occurs at 90 degrees at quadrature. But in trying to find a scientific definition I'm finding none, just pages that conflate dichotomy, quadrature, quarter and/or half. So I don't know, and nobody has citing sources either way.
 * As a side note: the dark light side and the light dark side bugs me... Skintigh (talk) 23:22, 9 December 2022 (UTC)

Absolute size of the sun
The lunar eclipse method relies upon knowing s, the absolute radius of the Sun. But there is no explanation as to how that could be known. If one knows s then the distance to the sun can be trivially calculated by observing the apparent angular size. Determining s is the crux of the problem.

Consider a smaller sun moved closer to the earth so that the apparent size is the same. The observation of its shadow would also be the same.

If I have missed something, then others will have too and it should be noted in the article. I believe this is a case of the maths obscuring the main point. Tuntable (talk) 21:15, 13 October 2019 (UTC)