In the Dark

The winter solstice in the Northern hemisphere happens tomorrow, Monday 21st December, at 10.02 Irish Time. Among other things, this means that tomorrow is the shortest day of the year in the Northern hemisphere. Days will get steadily longer from then until the Summer Solstice next June.  The longest night – defined by the interval between sunset and sunrise – is tonight and the shortest day – defined by the interval between sunrise and sunset – will be tomorrow. The day tomorrow will be two seconds shorter than today, while the interval between sunrise and sunset on Tuesday 22nd December will be four seconds longer than tomorrow.

This does not, however,  mean that sunrise will happen earlier tomorrow than it did this morning. Actually, sunrise will carry on getting later until the new year, the length of the day nevertheless increasing because sunset occurs later. Sunrise this morning (20th December was at 08.37 Dublin Time while tomorrow it will be at 08.38. Sunset tonight will be at 16.07 and sunset tomorrow will be at 16.08.

These complications arise 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:

The winter solstice is the lowermost point on this curve and the summer solstice is at the top. These two turning points define the time of the solstices much more precisely that the “shortest day” or  “longest night”.

Incidentally, the Tropic of Capricorn is the circle of latitude (about 23.5°, the declination of the Sun at the Winter Solstice) that contains the subsolar point at the December solstice. This is therefore the most southerly latitude on Earth where one can see the Sun directly overhead.

Anyway, 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 Dublin around the 2020  winter solstice. This shows that tomorrow is indeed the shortest day (with a time between sunrise and sunset of 7 hours 29 minutes and 57 seconds).  The table also shows that sunset already started occurring later in the day from 17th December,  before the winter solstice, and sunrise will continue to happen later  after the solstice, notwithstanding the fact that the interval between sunrise and sunset gets longer from tomorrow onwards.

I hope this clarifies the situation.