Latest Sunrise, Earliest Sunset, and the “Equation of Time”



Dr. David McNaughton

People are often puzzled by the fact that the dates of earliest sunset and latest sunrise do not coincide with the shortest day of the year (which is on or around 21st December in non-tropical northern latitudes). At latitude 25N, latest sunrise occurs just before mid-January, and earliest sunset is around the end of November. And at 50N, the date of earliest sunset is approximately 13th December, while latest sunrise is experienced at the end of December.

Two quite separate factors contribute to this apparently strange behaviour:

1. The Earth’s speed of movement round the sun is not uniform. This causes variations in the sun’s apparent rate of passage through the constellations – which is fastest during December/January, and slowest around June/July. Thus, sometimes the sun goes ahead of what may be called its ‘normal’ or ‘mean’ position; at other times it falls behind. (Here, ‘ahead’ and ‘behind’ need to be carefully defined; see below*).

2. The sun’s week-to-week migration across the starry firmament is tied to the Ecliptic Line. However, times of sunrise, noon and sunset (being determined by Earth’s daily rotation) relate more easily to the sun’s Celestial Longitude – whose labels (along the Celestial Equator) are direct projections out from Earth’s equator. But the 23½-degree angle between our equatorial plane and the ecliptic – usually modifies the sun’s speed of progress parallel to the (more important) Celestial Equator. The greatest reductions occur in late March and late September. These seasonal fluctuations can cause dawn and dusk to come early (or late).

Adding together those two contributing influences, produces a double-waved curve with a minimum near 11th February (when the sun is said to be 14 minutes ‘behind schedule’), and a maximum near 3rd November (when it is just over 16 minutes ‘ahead of schedule’). Thus, times of sunrise (and indeed sunset) from January to March are later than they would be if Earth’s orbit was circular and if our spin-axis was ‘upright’. And from September till late December, those times are earlier than they ‘should’ be. (*However, remember that when sunset is ‘later than normal’, the sun is actually further ahead than ‘normal’ in its migration across the firmament – which is from west to east).

There is also a secondary maximum and minimum in May and in late July respectively. This graph is known as the Equation of Time – which may be described as the daily and seasonal difference between sundial time and clock time. The various curves are shown in URL Over a period of thousands of years the shape of the Equation of Time will change.

THE ECLIPTIC is the plane containing Earth’s orbit round the sun. It can be extended indefinitely in all directions, so the ECLIPTIC LINE is where that plane intersects the Celestial Firmament**. This line occupies a well-defined position in the sky (during the day as well as the night), being the ‘track’ followed by the sun (whose departure from it is never more than 1.2″ of arc). It is usually marked on star charts.

** THE CELESTIAL FIRMAMENT is the inside surface of an enormous imaginary sphere surrounding the Earth. Positions of stars and planets etc. may be projected onto this surface as if it were a screen – just as in the interior of a gigantic planetarium. The CELESTIAL EQUATOR is where Earth’s extended equatorial plane cuts through the firmament. Values of CELESTIAL LONGITUDE are also called Right Ascension; (their labels lie vertically above our equator, but are fixed with respect to the constellations).

David McNaughton