<Tr> <Td> L / t </Td> <Td> Earth - Moon distance in Earth radii </Td> <Td> 20 </Td> <Td> 60.32 </Td> </Tr> <Tr> <Td> S / t </Td> <Td> Earth - Sun distance in Earth radii </Td> <Td> 380 </Td> <Td> 23,500 </Td> </Tr> <P> The error in this calculation comes primarily from the poor values for x and θ . The poor value for θ is especially surprising, since Archimedes writes that Aristarchus was the first to determine that the Sun and Moon had an apparent diameter of half a degree . This would give a value of θ = 0.25, and a corresponding distance to the moon of 80 Earth radii, a much better estimate . The disagreement of the work with Archimedes seems to be due to its taking an Aristarchus statement that the lunisolar diameter is 1 / 15 of a "meros" of the zodiac to mean 1 / 15 of a zodiacal sign (30 °), unaware that the Greek word "meros" meant either "portion" or 7 ° 1 / 2; and 1 / 15 of the latter amount is 1 ° / 2, in agreement with Archimedes' testimony . </P> <P> A similar procedure was later used by Hipparchus, who estimated the mean distance to the moon as 67 Earth radii, and Ptolemy, who took 59 Earth radii for this value . </P>

On the sizes and distances of the sun and moon