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| Sunrise on the morning of the winter solstice, at Coliemore Harbour, Dalkey, Co Dublin. Photo: Eric Luke |
Today is the winter solstice, the
shortest day of the year. We might expect that the latest sunrise and
earliest sunset also occur today. In fact, the earliest sunset, the
darkest day of the year, was on December 13th, over a week ago, and the
latest sunrise is still more than a week away. This curious behaviour is
due to the unsteady path of the earth around the sun. Our clocks, which
run regularly at what is called mean time, move in and out of
synchronisation with solar time.
The difference between clock time
and solar time is encapsulated in a mathematical expression called the
Equation of Time. The extent of the discrepancy between apparent solar
time, following the sun, and mean solar time, with noons always 24 hours
apart, can be up to about 15 minutes. Technically, the difference is
due to the eccentricity of the earth’s orbit and the obliquity of the
ecliptic. In plain language, the orbit of earth is not perfectly
circular, but is slightly elongated and the axis of rotation of earth
has a tilt.
Imagine that the path of earth
around the sun were a perfect circle, and the axis of rotation were
perpendicular to the plane of the orbit. Then there would be a symmetry
in the day: the time between sunrise and noon would equal the time
between noon and sunset. Thus, if sunrise is at 7am, five hours before
noon, sunset should be at 5pm, five hours after noon. But suppose now
that your watch is one hour fast. Then sunrise is at 8am by your watch,
four hours before noon. And sunset is at 6pm, six hours after noon. The
symmetry is broken.
As a result of this asymmetry, noon is not normally halfway between
sunrise and sunset. This happens on only four days every year, when mean
time and solar time agree. One of those days is Christmas Day. Just
before Christmas, the sun is running fast so that, by our clocks, both
sunrise and sunset seem slightly early.
