When I was a little kid, I had a friend who was born on February 29, the “leap day” we add to that month every four years. I remember we used to tease him by saying he was only three years old. I’ve lost touch with him over the years, but I think now he’s tired of the joke.
And here we are once again on the cusp of our quadrennial exercise in timekeeping: Leap Day 2024 is upon us. A handful of traditions are associated with it. Someone thought that this was the only acceptable day for women to propose marriage to men. Some people like to treat this day as a free day that gives them time to pursue something they have been putting off for a long time.
I think this is a very good idea because, after all, catching up is what a leap day means – in astrological terms.
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There are two basic units of time that we use based on astronomical events. One is the day, which is the length of time it takes the Earth to rotate once on its axis. The other is the year, which is the time it takes the Earth to complete a revolution around the sun. Although this sounds simple, these two modules are actually very complex. For example, the Earth rotates once relative to what? You need some frame of reference to measure that movement.
In our daily life, we use the sun. The time it takes for the Sun to set southward and then rise again and reach the southern meridian again is one solar day, which we define as 24 hours, or 86,400 seconds. This is actually it He means Solar day, which uses the center of the sun’s disk as a reference point and is the average of each day of the year. Using an average value is useful in setting time because the Earth moves at different speeds and at different points in its orbit, changing the exact length of any given day.
There are several different ways to measure the length of the year as well. Our current calendar uses the tropical year, the time from vernal equinox to vernal equinox, to calculate subtle effects such as precession. Otherwise, the date of the equinox would slowly change over the years, and eventually the December solstice would fall in July, which would be very confusing.
The tropical year has an average length of 365.2422 solar days. Since the Earth’s rotation and orbital period are not related in any way, they are not divided equally. We are left with 0.2422, and this is the key for leap days.
If we started measuring the day and year at the exact same moment, at the end of one year, the Earth would have rotated 365 times, plus an additional 0.242 rotations when the new year begins. After four years, this amounts to 0.9688 days, almost a full day. We’ve built an extra day into the year!
This was known even to ancient peoples, and when Julius Caesar decided to change the basis of the Roman calendar from using the moon to the sun, he also decreed that an extra day would be added every four years to keep everything in sync. Congratulations! Happy Leap Day! This is technically called an interpolated day, which is the day that is added to the calendar to synchronize.
Except the math doesn’t quite work. By adding a full day every four years, we add a lot: after four years, we have only 0.9688 days left, not one. This difference is 0.0312 days, or about 45 minutes. This means that every four years we still have about three-quarters of an hour to count. Over time, this will accumulate, and the calendar will be turned off again.
Enter Pope Gregory no It is a leap year, so no leap days will be added. There are 25 leap days in a century, so that’s how it works Removes 25 x 0.0312 = 0.78 days, and the calendar syncs a little better in the long run, but again, not quite.
Using this algorithm, the calendar would run every 100 years at a rate of 1 – 0.78 = 0.22 days. This adds up too! Therefore, as part of his papal decree, Pope Gregory XIII also declared that every 400 years would gain a leap day again. By then, there are 4 x 0.22 = 0.88 extra days, so adding one day brings us very close to catching up with Earth’s non-integrated daily annual rate.
This is the rule we use now. Every four years, i.e. every year whose number is evenly divisible by 4, is a leap year and is given an extra day – that is, except every 100 years, when we skip a leap day, Excludes Every 400 years, when we reverse the rule and add a leap day again. So the years 1700, 1800, and 1900 were not leap years. The year 2000 was because although it is equally divisible by 100, it is equally divisible by 400. The year 2100 will not be a leap year, but the year 2400 will be, and so on.
This actually puts us very close to being in sync. However, I have sometimes wondered why Pope Gregory XIII did not use the time period of 500 years instead of 400 years. That would be better because the amount remaining after 100 years is closer to one-fifth of one day. But here we are.
For this reason, our current rules still leave the calendar a bit off. We add a full day every 400 years, but that’s too much at 1 – 0.88 = 0.12 days. If we wanted to, we could adjust the rule again and say that every 3,200 years no Make that year a leap year. Why 3200? Well, 8 x 0.12 = 0.96, so we can skip a leap year every eighth 400-year cycle, which is every 3,200 years. This means that the year and day would be separated by only 0.04 days – just under an hour – every 3,000 years, which is very close.
As usual, when dealing with astronomy, numbers and the calendar, things seem simple, but they are not.
Anyway, happy Leap Day, and if you have something you’ve been putting off for four years, now is the time to do it. And to my old friend Ted, if you were there and saw this: Merry Christmas!