The Dark Days of December

At latitude 40 degrees north, earliest sunset occurs on about December 8 and latest sunrise on about January 5. The shortest day of the year, the winter solstice, is December 21 or 22. Why are all these dates not the same?

Answer

There are two effects that, together, determine the local times of sunrise and sunset. One is called the equation of time; the other is the Sun’s declination.

Earth’s orbit around the Sun is slightly elliptical. As a result, the speed of the Sun’s apparent motion across the sky is a bit faster in winter than in summer. Clocks, however, run at a constant speed, so there is usually a discrepancy up to 16 minutes between clock time and the solar time shown by a sundial. We refer to this discrepancy as the equation of time.

The Sun’s declination, its angular distance above or below the celestial equator, determines the maximum height of the Sun in the sky on any given day, thus causing our seasons. In late December, the daily rate of change of the Sun’s declination is rather small. It is, in fact, exactly zero at the December solstice (“solstice” means “sun stationary”). Hence in late December, or more precisely from about December 8 to January 5 at latitude 40 degrees north, the equation of time has the dominant influence over the changes in sunrise and sunset times. Prior to December 8, however, the declination effect is dominant, pulling the sunset to its earliest time on December 8. Then the equation of time takes over, and during the two weeks before winter solstice all the shortening of the day comes from the later clock time of sunrise. After winter solstice the days lengthen, even as the sunrises continue to get later until January 5.

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