The Winter Solstice and the Time of Sunrise and Sunset

You may have missed it, but the winter solstice happened today, Wednesday 21st December 2016, at 10.44am GMT (10.44 UTC). This marks the shortest day of the year: days will get longer from now until the Summer Solstice next June. As we were discussing in the pub last night, however, this does not mean that sunrise will happen earlier tomorrow than it did this morning. In fact, sunrise will carry on getting later until the new year. This is because there is a difference between mean solar time (measured by clocks) and apparent solar time (defined by the position of the Sun in the sky), so that a solar day does not always last exactly 24 hours. A description of apparent and mean time was given by Nevil Maskelyne in the Nautical Almanac for 1767:

Apparent Time is that deduced immediately from the Sun, whether from the Observation of his passing the Meridian, or from his observed Rising or Setting. This Time is different from that shewn by Clocks and Watches well regulated at Land, which is called equated or mean Time.

The discrepancy between mean time and apparent time arises because of the Earth’s axial tilt and the fact that it travels around the Sun in an elliptical orbit in which its orbital speed varies with time of year (being faster at perihelion than at aphelion).

In fact if you plot the position of the Sun in the sky at a fixed time each day from a fixed location on the Earth you get a thing called an analemma, which is a sort of figure-of-eight shape whose shape depends on the observer’s latitude. Here’s a photographic version taken in Edmonton, with photographs of the Sun’s position taken from the same position at the same time on different days over the course of a year:

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The winter solstice is the lowermost point on this curve and the summer solstice is at the top. The north–south component of the analemma is the Sun’s declination, and the east–west component is the so-called equation of time which quantifies the difference between mean solar time and apparent solar time. This curve can be used to calculate the earliest and/or latest sunrise and/or sunset.

Using a more rapid calculational tool (Google), I found a table of the local mean times of sunrise and sunset for Cardiff (where I live) around the 2016 winter solstice. The table shows that today is indeed the shortest day (with a time between sunrise and sunset of 7 hours 49 minutes and 55 seconds). The duration of the shortest day this year is 8 hours and 48 minutes shorter than the longest day (the summer solstice). The table also shows that sunset already started occurring later in the day before the winter solstice (although the weather has been too overcast to notice this), and sunrise will continue to happen later for a few days after the solstice. In fact the earliest sunset this year in Cardiff was on 12th December, and the latest sunrise will be on 30th December.

I hope this clarifies the situation.

One Response to “The Winter Solstice and the Time of Sunrise and Sunset”

  1. […] in the sky (on average) than in winter. From this argument you can infer that the winter solstice (which passed on 21st December), not the perihelion, is the relevant astronomical indicator of […]

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