Bending Light From Sun

If the gravity of the earth bends the light from the sun at sunrise so that the sun appears on the horizon before it has actually "risen", how many radians (or degrees) does the light from the sun cover of Earth's crust at a given point in time. Also, is this measure a constant for all the planets or does it vary between them.
- Noah (age 16)
Pittsburgh, PA, 15044

The gravitational bending is really small. Roughly, it must be about gR/c² radians, where g is the acceleration near the surface, R is the Earth's radius, and c is the speed of light. That's roughly 10^-9 rad. The number will end up different for different planets, being bigger for say Jupiter.

There's a much bigger effect from the light bending as it goes through the atmosphere. Unlike the gravitational bending, the atmospheric bending depends on the frequency of the light. When I was a student at La Jolla, there was a sort of cult of trying to see a "green flash" just as the sun was setting over the ocean. The idea is that the bluish light bends more and thus sets after the reddish light. It's not a blue flash, though, because the bluest light scatters a lot. So it's supposed to end up kind of green.

Mike W.

(published on 03/09/2015)