Symbols
The work's method relied on several observations:
- The apparent size of the Sun and the Moon in the sky
- The size of the Earth's shadow in relation to the Moon during a lunar eclipse
- The angle between the Sun and Moon during a half moon is very close to 90°.
The rest of the article details a reconstruction of Aristarchus' method and results. The reconstruction uses the following variables:
| Symbol | Meaning |
|---|---|
| φ | Angle between the Earth and the Sun during a half moon (directly measurable) |
| L | Distance to the Moon |
| S | Distance to the Sun |
| ℓ | Radius of the Moon |
| s | Radius of the Sun |
| t | Radius of the Earth |
| D | Distance from the center of Earth to the vertex of Earth's shadow cone |
| d | Radius of the Earth's shadow at the location of the Moon |
| n | Ratio, d/ℓ (a directly observable quantity during a lunar eclipse) |
| x | Ratio, S/L = s/ℓ (which is calculated from φ) |
Read more about this topic: Aristarchus On The Sizes And Distances
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