diamond geezer

 Friday, December 12, 2014

For years I've been aware that the earliest sunset of the year isn't on the day of the winter solstice, it's a few days earlier. More specifically for London, the earliest sunset of the year isn't on December 21st (3:53pm), it's today December 12th (3.51pm). [data] [full data] [interactive map]

DateLength of day Sunset 
Nov 19h 3916:34
Nov 119h 0516:17
Nov 218h 3516:04
Dec 18h 1115:55
Dec 117h 5515:51
Dec 217h 4915:53
Dec 31  7h 5416:01

But I'd never quite got my head around why this discrepancy should arise. It seems entirely counter-intuitive that the shortest day and earliest sunset don't coincide, so some other factor must be at play to cause the difference. And so I dug around a bit, and I think I finally understand what's going on. Bear with me on this one.

First of all you need to understand this next table, based on data for central London. The amount of daylight each day is fixed, decreasing from almost 10 hours at the start of November to less than 8 hours throughout December. Half of that daylight occurs before noon and half after, so if we halve the total amount of daylight we get the length of the afternoon. And if the afternoon starts at noon, then it's possible to work out at what time the sun sets. Noon + afternoon = sunset. Like so...

DateLength of day      Noon      Length of afternoon* Sunset 
Nov 19h 3912:004h 4916:49
Nov 119h 0512:004h 3216:32
Nov 218h 3512:004h 1716:17
Dec 18h 1112:004h 0516:05
Dec 117h 5512:003h 5715:57
Dec 217h 4912:003h 5515:55
Dec 31  7h 5412:003h 5715:57
* half the length of the day

But those aren't the actual sunset times, as you can see if you compare them with the first table. And that's because the middle of the day, the time the sun is highest in the sky, isn't twelve o'clock. This so-called 'solar noon' changes throughout the year, wobbling over fifteen minutes away from 12:00 at different times of the year. For example at the start of November the sun is highest in the sky at quarter to twelve, but by the end of January it's quarter past. You'd never spot this, day to day, but it's true.

Date Solar noon* 
Nov 111:44
Nov 1111:44
Nov 2111:46
Dec 111:49
Dec 1111:54
Dec 2111:58
Dec 3112:03
* the time the sun is highest in the sky

The reasons for solar noon changing are quite complicated. It's to do with the Earth's orbit not being a circle, but an ellipse. It's to do with the Earth travelling at different speeds at different points in its orbit. It's to do with the Earth being tilted on its axis at an angle of 23½°. It's to do with all three of these things combining to create something called The Equation Of Time, which you can read all about here - I'm not going to go into the details. But The Equation Of Time is why the sun isn't always at its highest at noon. It's why sundials only tell the right time four days a year. And it's why the middle of the day today is at 11.54, but the middle of the day on December 21st will be at 11.58.

To find out what's really happening to sunset times, you have to start counting the afternoon from solar noon, not from twelve o'clock. Solar noon + afternoon = sunset. Like so...

DateLength of day Solar noon Length of afternoon Sunset 
Nov 19h 3911:444h 4916:34
Nov 119h 0511:444h 3216:17
Nov 218h 3511:464h 1716:04
Dec 18h 1111:494h 0515:55
Dec 117h 5511:543h 5715:51
Dec 217h 4911:583h 5515:53
Dec 31  7h 5412:033h 5716:01

At the moment solar noon is at 11.54 and the afternoon lasts 3h 57, which means sunset is at 3.51pm. By the winter solstice the afternoon is two minutes shorter at 3h 55, but solar noon is four minutes later at 11.58, making sunset two minutes later at 3.53pm. And that's why the earliest sunset is now rather than next week... because the sun is highest in the sky earlier in the day.

Here's how the next ten days pan out, sunset-wise.

DateLength of day Solar noon Length of afternoon  Sunset  
Dec 117h 5511:543h 5715:51:49
Dec 127h 5411:543h 5715:51:43
Dec 137h 5311:543h 5615:51:44
Dec 147h 5211:553h 5615:51:46
Dec 157h 5211:553h 5615:51:53
Dec 167h 5111:563h 5615:52
Dec 177h 5011:563h 5515:52
Dec 187h 5011:573h 5515:52
Dec 197h 5011:573h 5515:52
Dec 207h 4911:583h 5515:53
Dec 217h 4911:583h 5515:53

A few caveats. Times have been rounded and may not be 100% accurate. All times are for central London. Locations further north and east see sunset earlier, and locations south and west see sunset later [see map]. Locations well to the south of London have already had their earliest sunset (New York's was on December 6th), while locations north of London haven't had theirs yet.

And if all of this has gone completely over your head, don't worry. All that's important is that the earliest sunset of the year is today, at around eight minutes to four. And from tomorrow, second by second, then minute by minute, the evenings start getting longer and longer.

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