Winter is coming

The long days of summer are behind us now -- as we get closer to the equinox, the days get shorter and shorter faster and faster. No more bright sun at 10pm.

So... I wanted to calculate the times of sunrise and sunset. If you assume a spherical earth going around a circular orbit at uniform velocity, then it's easy enough. I made the plot above using the simple sunrise equation that makes those assumptions. It seems to agree with the US Naval Observatory times to within a few minutes.

But if you want to be a little more attentive to detail, it gets pretty complicated. The earth's orbit is not circular but elliptical, and the positions of the solstices and the equinoxes don't correspond to the axes of the elliptical orbit. There are many other effects, too: it's not the earth orbiting the sun, but the earth+moon system; parallax; etc.

I confess, I didn't notice this before: the equinoxes and solstices are not equally spaced. There are 185 days from the vernal equinox (March 20th) to the autumnal equinox (Sept 21), but there are only 180 days from the autumnal equinox to the next spring equinox. So it turns out that the northern hemisphere summer is something like 5 days longer than the northern hemisphere winter for this reason -- during summer we are farther away from the sun, so our angular position changes more slowly.

This effect doesn't show up when you assume a circular orbit.