[froggerexpert]

Very cool. What program is that?

It'd also be nice if the colour was not just day/night, but the actual predicted daylight at the time of day, which would result in a continuously changing colour.

I guess at that point, the sine approximation from OP would no longer apply, and https://en.m.wikipedia.org/wiki/Sunrise_equation would have to be used.

[Centigonal]

It's Blender! Great OSS project.