The illuminating analemma

The what?  No, the analemma isn’t some strange pet that Hagrid keeps well-chained in his hut, rather it’s something that many of us are familiar with, especially if you, like me, have trouble getting out of bed in the morning.

It’s nearly two months since the longest day (21 December), but you may have noticed that the evenings are not all that much darker than they were back at Christmas. The same cannot, however, be said of the mornings. No more being woken by the birds at quarter to five – it is now noticably darker in the mornings, and, as we know, is destined to get a lot darker still.

So how come the difference between the evening and the morning?  It’s because the earliest sunrise, and the latest sunset, do not occur on the same day.  The former occurs early December; the latter comfortably into January. The ‘longest day’, being the day with greatest difference between sunrise and sunset, falls between those two.

Now, imagine doing the following experiment. Put a big stick (the taller the better) vertically into the ground. (Trees are no good because they grow.) Now, at exactly noon by your watch (or 1 pm in daylilght savings time), put a peg in  the ground at the position of the tip of the shadow of your stick. Repeat the next day. And the next, for a whole year.  What shape do you think the pegs will mark out?

At first thought you might think you’ll have a straight line running exactly southwards from the stick (isn’t the sun in the north at midday?), but actually, you don’t. You’ll get a rather elongated figure-of-eight shape. This is called the analemma. Try it as a year-long project at school, or, if you can’t wait that long, and are lucky enough to live near Hamilton, have a look at the noon-sundial in Hamilton Gardens, where the analemma is clearly marked for you on the ground.

So why isn’t the sun exactly in the north at exactly midday. Simply, it’s because the earth does not move in a circular orbit. It’s an ellipse, which by Kepler’s second law means that sometimes it is moving a bit faster along its orbit, and sometimes it moves a bit slower. That causes the clocks to run either a bit fast or a bit slow compared to the position of the sun, depending on time of year. This is called the ‘equation of time’.

So, what do we have in store for the coming months? We’ll now notice the evenings will get darker, very quickly. By the start of June, we’ll be at our darkest evening, but the darkest morning will wait until after the shortest day.

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