Milankovich's angle on a moving circle

The Arctic Circle is defined as the parallel of latitude north of which the sun does not rise at the winter solstice

The Arctic Circle is defined as the parallel of latitude north of which the sun does not rise at the winter solstice. Moving north from this latitude the period of continuous night gradually increases to reach a full six months at the North Pole itself. And the Arctic Circle, as every schoolchild knows, lies at 661/2 degrees north.

But does it? About 60 years ago the Norwegian government erected an impressive monument to mark the position of the circle, but it was noted recently that now the monument was in the wrong place: the Arctic Circle had been edging northwards at about 40 feet a year, and so the monument had to be moved about half-a-mile to regain its correct position.

This requirement, of course, was not entirely unexpected. The exact position of the Arctic Circle is regulated by the angle which the Earth's axis of rotation makes with the plane of the Earth's orbit around the Sun. In 1920, a Yugoslav physicist, Milutin Milankovich, established that this angle is not constant at its current value of about 221/2 degrees, but varies from about 25 to 22 degrees in a regular cycle of about 41,000 years - the so-called Milankovich Cycle. The Earth is like a spinning top that has a wobble; as a consequence of this wobble the Arctic Circle moves northwards on a 200-mile journey for 20,000 years, and then begins a gradual retreat southwards again.

Today, December 13th, is a fitting day to contemplate such matters. It is Lucy Day, the feast of St Lucia, who has assumed great importance in Scandinavian countries for two reasons. Firstly, her name means "light", a very scarce commodity in those northern latitudes in wintertime. More importantly, Lucia's feast day fell on what was in olden times the shortest day of the year. By the old Julian Calendar, the winter solstice occurred on December 13th, rather than around December 21st as it does by our Gregorian reckoning. Lucy Day, therefore, was an appropriate time to announce to the demons of winter that their reign was broken, and that light would return with the now lengthening days.

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Thus it is that throughout Scandinavia today is celebrated as a festival of light. In each village, early in the morning, a young local woman, dressed in a white gown and wearing a crown of twigs adorned with blazing candles, goes from farm to farm carrying a torch to light her way, and brings gifts of food. She symbolises the light of the returning Sun, and food aplenty with the anticipated fertility of the coming spring.