Results
The above formulae can be used to reconstruct the results of Aristarchus. The following table shows the results of a reconstruction using n = 2, x = 19.1 (φ = 87°) and θ = 1°, alongside the modern day accepted values.
| Quantity | Relation | Reconstruction | Modern |
|---|---|---|---|
| s/t | Sun's radius in Earth radii | 6.7 | 109 |
| t/ℓ | Earth's radius in Moon radii | 2.85 | 3.50 |
| L/t | Earth-Moon distance in Earth radii | 20 | 60.32 |
| S/t | Earth-Sun distance in Earth radii | 380 | 23,500 |
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 Aristarchos 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.
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.
Read more about this topic: Aristarchus On The Sizes And Distances
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