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:
“Luckless is the country in which the symbols of procreation are the objects of shame, while the agents of destruction are honored! And yet you call that member your pudendum, or shameful part, as if there were anything more glorious than creating life, or anything more atrocious than taking it away.”
—Savinien Cyrano De Bergerac (1619–1655)
“Many older wealthy families have learned to instill a sense of public service in their offspring. But newly affluent middle-class parents have not acquired this skill. We are using our children as symbols of leisure-class standing without building in safeguards against an overweening sense of entitlement—a sense of entitlement that may incline some young people more toward the good life than toward the hard work that, for most of us, makes the good life possible.”
—David Elkind (20th century)
“As usual I finish the day before the sea, sumptuous this evening beneath the moon, which writes Arab symbols with phosphorescent streaks on the slow swells. There is no end to the sky and the waters. How well they accompany sadness!”
—Albert Camus (1913–1960)