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
Famous quotes containing the word symbols:
“There are those who would keep us slipping back into the darkness of division, into the snake pit of racial hatred, of racial antagonism and of support for symbols of the struggle to keep African-Americans in bondage.”
—Carol Moseley-Braun (b. 1947)
“For all symbols are fluxional; all language is vehicular and transitive, and is good, as ferries and horses are, for conveyance, not as farms and houses are, for homestead.”
—Ralph Waldo Emerson (1803–1882)
“If the Americans, in addition to the eagle and the Stars and Stripes and the more unofficial symbols of bison, moose and Indian, should ever need another emblem, one which is friendly and pleasant, then I think they should choose the grapefruit. Or rather the half grapefruit, for this fruit only comes in halves, I believe. Practically speaking, it is always yellow, always just as fresh and well served. And it always comes at the same, still hopeful hour of the morning.”
—Johan Huizinga (1872–1945)