Trivia 081: Padding out the year

I have not one, but two new timelapses! A view of the Seattle skyline and waterfront from Hamilton Viewpoint Park, and a short one of the moon rising over some of the skyscrapers. Be sure to subscribe to my YouTube channel if you want to know when I upload.

As promised with last week’s post, today we’ll be discussing leap days. After all, an opportunity like this only rolls around every 4 years after all. Or does it? You see, a leap day is more complicated than many people realize.

First of all, how long is a day? Seems like a simple enough question. We can simply define a day by the amount of time it takes for the Sun to reach the highest point in the sky on two consecutive days. However, here we immediately run into an issue. Because the Earth’s orbit around the sun is elliptical, not circular, sometimes it is moving faster than average, and sometimes it is moving more slowly. This does have small effects on the length of a day (to the tune of 51 seconds at most). And that’s besides the fact that a solar day does not actually match the Earth’s rotation (that’s what a sidereal day is for). But if we just take the average, we get 24 hours (within a few milliseconds).

Okay, so far so good. So then how do we define a year? That can be done more easily. Using the positions of the stars in the sky, we can figure out how long it takes the Earth to go around the sun. And it turns out that it takes us 365.2422 days to orbit once. And here we see the problem. Since the rate of the Earth’s rotation and the rate of its orbit are independent of each other, they do not sync up. This is the problem with trying to build a system for measuring time out of a bunch of rates which are unrelated to each other. (And then there’s the fact that the months are based on the moon’s orbit around the Earth, which isn’t related to any of these other rates. But that’s a different story.)

These sorts of discrepancies do not have much effect on us in the short term. However, when these errors are propagated over centuries, they build up, resulting in things like Christmas happening in the spring. So we need to periodically adjust the calendar to make sure that the seasons keep in line with dates. Ancient civilizations had various different ways of doing this, such as inserting a whole week or month periodically. Nowadays, the majority of the world follows the Gregorian Calendar, which mandates that one extra day be inserted every four years. Normally, that rule serves well enough, but there are a few caveats. However, if the year is a multiple of 100, it will not be a leap year (i.e. 1900 did not have a leap day). However however, if the year is a multiple of 400, it will be a leap year (i.e. 2000 was a leap year). And that’s it! So, more complicated than you may have thought, but not all that bad.

Occasionally, we have also introduced “leap seconds” to keep Universal Coordinated Time (UTC) and solar time in line with International Atomic Time (TAI). This is because geologic events, such as major earthquakes, ocean movements, and climate shifts can all affect the speed of Earth’s rotation. However, in 2022 the 27th General Conference on Weights and Measures decided that by 2035 this practice will be abandoned. This is so that computer systems with timestamps will not experience discrepancies if some systems are updated but not others.

One final question: Where does the term “leap day” or “leap year” come from? I mean, we’re adding an extra day, not skipping one, so shouldn’t it be “long year” or something? Well, since a standard year has 365 days, there are 52 weeks and one extra day in a standard year. This means that dates will advance one day of the week per year – i.e. January 1st, 2023 was a Sunday, but January 1st, 2024 was a Monday. However, when a leap year happens, you end up “leaping over” a day: January 1st, 2025 will be a Wednesday instead of a Tuesday.

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