Editing Aristarchus of Samos (section)

== Size of the Moon and Sun ==
In ''On the Sizes and Distances of the Sun and Moon'', Aristarchus discusses the size of the Moon and Sun in relation to the Earth. In order to achieve these measurements and subsequent calculations, he used several key notes made while observing a [[lunar eclipse]].<ref name=":0">{{Cite journal|last=Hirshfeld|first=Alan W.|date=2004|title=The Triangles of Aristarchus|url=https://www.jstor.org/stable/20871578|journal=The Mathematics Teacher|volume=97|issue=4|pages=228–231|doi=10.5951/MT.97.4.0228|jstor=20871578|issn=0025-5769}}</ref> The first of these consisted of the time that it took for the Earth's shadow to fully encompass the Moon, along with how long the Moon remained within the shadow. This was used to estimate the [[Angular diameter|angular radius]] of the shadow.<ref>{{Cite journal|last=Batten|first=Alan H.|date=1981|title=Aristarchos of Samos|url=https://adsabs.harvard.edu/full/1981JRASC..75...29B|journal=Journal of the Royal Astronomical Society of Canada|volume=75|pages=29–35|bibcode=1981JRASC..75...29B}}</ref> From there, using the width of the cone that was created by the shadow in relation to the Moon, he determined that it was twice the diameter of the Moon at the full, non-central eclipse. In addition to this, Aristarchus estimated that the length of the shadow extended around 2.4 times the distance of the Moon from the Earth.<ref name=":0" />[[File:Aristarchus and Herodotus craters Apollo 15.jpg|thumb|240px|right|Aristarchus (center) and [[Herodotus (crater)|Herodotus]] (right), from [[Apollo 15]], [[NASA]] photograph]]

Using these calculations, along with his estimated distances of the Sun from the Earth and Moon from the Earth, he created a triangle. Employing geometry similar to that he had already used for the distances, he was able to determine that the diameter of the Moon is roughly one-third of the Earth's diameter. In order to estimate the size of the Sun, Aristarchus considered the proportion of the Sun's distance to Earth in comparison to the Moon's distance from Earth, which was found to be roughly 18 to 20 times the length. Therefore, the size of the Sun is around 19 times wider than the Moon, making it approximately six times wider than the Earth's diameter.<ref name=":0" />