Given a latitude how many miles is the corresponding longitude? OK so lines of longitude (the distance/circumference around the earth horizontally) differ based on what latitude you are at (0 at north and south poles up to ~25k at the equator.)
So given a latitude, how can I determine how many miles it would be to go directly east/west around the earth until I was back at the starting point.
If it is easier mathematically to treat the earth like a perfect sphere, then that is fine. I do not need it to be precise, just close enough.

The parallel of latitude is actually a circle of radius $r\cos(\alpha)$
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Thus, the length of the parallel of latitude $\alpha$ is $2\pi r\cos(\alpha)$, where $r$ is the radius of the Earth.
