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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)
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)
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)
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)
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)
"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)
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:
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)
References
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)
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)
This article is rated C-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | |||||||||||||||||||||||||||||||
|
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)
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)
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)
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)
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)
"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)
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:
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)
References
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)
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)