Assuming that the earth is a perfect sphere, in units of the earth's radius, how high must one be to see exactly one half of the earth's surface?

Okay... okay... how about exactly one third of the earth's surface?

(In reply to off on a tangent by Tristan)

Actually the bending of light due to earth's relatively tiny gravity is insignificant compared to the bending of light due to the refraction by the atmosphere.  Something, say the sun or the moon or more pertinantly the observer in this puzzle, that looks as if it were on the horizon is really 1/2 degree below the horizon.  It is only atmospheric refraction that brings it visually above the horizon.  And of course light will travel over the same path in both directions.

So we seek csc 1/2 deg = 114.593....  Therefore the observer standing 113.6 earth radii above the surface would see 1/2 the earth's surface, if it's clear enough to see down to the surface. This is almost twice the distance to the moon.

Posted by Charlie on 2004-09-30 10:25:29