Solstice Drift
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I was looking up the time of the Solstice, which i do every year, and i thought, 'i should REALLY build a database for this!' To download data i went to the USNO website and it's STILL DOWN -- Covid has extended the upgrade period! So i went to which i quite like. However they 'only' have 2,100 years worth of data (i was hoping for 6,000 or more) and it's all in 50 year chunks which is time consuming to process. I was feeling lazy so i only collected back to the year 1500.

I figured since i had the data temporarily in a spreadsheet i should make a graph. I love the way a good graph can make interesting parts of the data stand out -- but i usually have to massage that data for a couple hours to make a really good graph. I quickly popped the December solstice times of day into a graph without much effort. (This works the same for both solstices and both equinoxes, i just chose this one.) I don't know what i was expecting -- maybe a sine wave?

Exact time of the December Solstice over 600 years

click images to enbiggen

The moment i saw this it knocked my socks off. It's beautiful, but more than that there are about a dozen natural cycles, human decisions and historical events that become instantly apparent at a glance. I even understand these systems better now.

First, of course, you can see that a year is not exactly 365 days as the solstice advances a quarter day each year. The years are arranged in fours -- so you can immediately see leap years resetting the drift. And you can see the extended drift in the Julian calendar as the solstice moves earlier and earlier in December.

You can clearly see the correction in 1752 when they dropped 10 days from the year. (Pope Gregory announced it in 1582 but the protestant English were slow to adopt it!) In addition to dropping days to make up for historical drift, the change to the Gregorian calendar said we would skip leap years in years divisible by 100 except if they are divisible by 400 so we get that obvious stair step after that. Skipping the 100 year correction in 2000 (which is divisible by 400) makes an extended step which we can see.

And the anomaly in 1943 1944 and 1945? Year-round daylight savings time during World War II!!

This amazing graph got me so excited that i downloaded the remaining 1500 years of data. I was pretty sure i knew what this would show, and it did, exactly: a long slow drift earlier in the month due to over correction.

Exact time of the December Solstice over 2 millennia.

Since a year is 365.242199074 days, not 365.25000 days, the drift continued. (The solstice moves 5 hrs & 48 minutes, not an exact 6 hours.) If the calendar drifts too far from the seasons, the crops get planted at the wrong time and you have big problems. But tweaking the year to fit the day is a problem because the day is an indivisible unit -- you can't add a partial day to a calendar!

By simply adding a day every four years, the Julian calendar was over adjusting. The Gregorian rules are better, they drop 3 leap year days every 400 years, but not perfect. Astronomers and mathematicians have discussed this; for the calendar to be precise we need to eliminate 4 more leap days every 10,000 years. I did the math in the 1970s when i was twelve and determined that 2000 should NOT be a leap year -- i was a bit surprised when it was! In about 5,000 years the solstice will drift a day because of that.
Add a day every 4 years.    

In years divisible by 4, add a day.
But if the year is divisible by 100, don't add the day.    
But if the year is divisible by 400, add the day.

  (This drops 3 leap days every 400 years.)
In years divisible by 4, add a day.
But if the year is divisible by 100, don't add the day.
But if the year is divisible by 400, do add the day.
But if the year is divisible by 2,000, don't add the day.
But if the year is divisible by 10,000, do add the day.

Finally we can see some evidence about where in the month the solstice is arbitrarily pegged. At the start of the calender during the early days of Rome, the solstice was, of course, on January 1st. That was the definition (and it's why we celebrate on that day). By the time of Julius Caesar when the calendar was reformed and a leap day added to try to prevent the solstice from drifting, it had been almost 600 years and the solstice had already drifted to December 25th. That date then got pegged as a holiday too, but the Julian calendar was not precise enough to prevent the solstice from drifting away even further.

By 325 CE when the Council of Nicaea defined Easter, the solstice had drifted up to the 21st. When Scandinavia converted to Christanity, the solstice had drifted all the way to the 13th - St Lucy's day - and that date got pegged as a holiday of light as well! In 1582, when the calendar was adjusted, the Pope chose to peg the solstice, not on Jan 1 where it originally was, but instead returned it to the 21st, the date it had drifted to after 900 years of errors!
We call it solstice drift, but actually the calendar was drifting past the solstice, which doesn't change. All these holidays are like a chain of volcanic islands, a Hawaii of holidays! As the tectonic plate of the calendar has moved around on top of the static hot spot of the solstice, various holiday islands have popped through where the plate was at that moment and then drifted off in a chain from that spot. And we can see that drift on these graphs.

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