Question

How do you find a circumference if given altitude of sun and equinox?

Answer 1

The formula is 2`pi` X (Sun-Earth distance) X (cos (latitude) `-` sin (latitude) X tan (altitude))

Explanation:

At equinox instant, Sun S is overhead at equinox Q of the Earth's equator.
At the same instant, it is noon at Q's longitude, at all latitudes. L is one with latitude `theta`,
The Sun's altitude from L, at noon, is `alpha`.
Using that sides are proportional to opposite angles in the `triangle` SEL, E being the Earth's center ans S Sun's, the formula for Earth's radius EL is
EL = ES ( cos `theta` `-` sin`theta` tan `alpha`).
I thank the questioner for making me think on this handy formula. .