This is the time of year when I’m most surprised by darkness, either in the morning or evening, and there’s a good reason for that: The first derivative of sunset/sunrise times is at its highest.

The two equinoxes – this coming Monday is the autumn equinox – are the days when daylight & not-daylight are equal, hence the name. If you’re graphing daily hours of daylight vs. hours of darkness over the course of the year, they are when the graph crosses the X-axis. And also when the slope is steepest.

In other words, right now the amount of daylight is changing (shrinking, because it’s autumn) faster from day to day than at any other time of year. Years ago when I wrote about this I had to get sunrise/sunset charts from the the US Naval Observatory and do hand calculation but now it’s online – this fine chart from shows that the amount of daylight in mid New Hampshire will shrink by 2 minutes and 54 seconds between Sept 22 and Sept 23, more than any other time of year.

That’s why you’re surprised at how dark it is when you get up or get home from work, assuming you’re able to leave your house.

This variation is a function of the fact that Earth’s orbit isn’t a perfect circle and out axis isn’t at 90 degree to the plane of the ecliptic.

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