Why are the years like 1900 and 1800 not leap years when they are divisible by 4. I know in centuries we see whether the given century is divisible by 4 or not. But why, if we keep subtracting 4 from 2000, wouldn’t it make 1900 a leap year too?
Why are the years like 1900 and 1800 not leap years when they are divisible by 4. I know in centuries we see whether the given century is divisible by 4 or not. But why, if we keep subtracting 4 from 2000, wouldn’t it make 1900 a leap year too?
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Because there aren’t 365.25 days in a year, so the leap year correction is too much and has to be accounted for.
Leap years being divisible by 4 is just an approximation, the error compounds, some years that are divisible by 4 not being considered leap years cancels out some of the error
That’s just the rule – years divisible by 100 but not by 400 are not leap years. 1896 was a leap year, 1904 was a leap year, but 1900 was not a leap year.
Leap years are necessary because the earth doesn’t rotate an integer amount of times per revolution around the sun.
The reason it skips every 100 years but not every 400th is to match up the fraction of days per year as cleanly as possible
Edit (2): yeah i commented, closed, realized it didn’t answer the question, and then edited. I did not see the reply until after the edit. Unlucky with the timing on the reddit server flushes it would seem as someone saw the original comment in the couple minutes it was unedited.
The astronomical year (how long does it take for Earth to make full orbit around the sun) isn’t a round number of days – which means you have to fudge things a bit once in a while to match them.
The once every 4 years would make the average calendar year (365 days 1/4) a wee little bit too long – retaining the leap year for only one century in 4 brings the value closer to the astronomical years and reduces drift between calendar and astronomical year.
You have to understand why we have leap years to begin with. It’s because each year is not 365 days. It’s closer to 365 and 1/4. So every 4 years you just add an extra day.
Notice I said closer to 365 and 1/4, I didn’t say it’s 365.25. That’s because it’s not. Skipping those additional years you are confused about gets us even closer to the actual value. It’s still not exactly right, but by little enough that we don’t worry about it.
A full year isn’t exactly 365 days. It’s somewhere around. 365.2422. it’s this way because the rate at which the earth spins around itself ( a day ) is not related to the orbit of the earth around the sun.
If you want to count years in terms of days and use the same amount each year, your calendar is going to be “out of sync”. This is mostly a problem for the seasons. You want to know that January 100 years ago was the same season as the January you know.
To solve this issue, you start with leap year. 365.2422 is pretty close to 365.25 , and you can get that 1/4 by adding a day every fourth year.
The not divisible by 400 rule is just to get our 365.25 ( number of days in a year with a leap day every fourth year) just a little further down, closer to the real thing.
Ultimately, it’s really impractical to make a “perfect” calendar that doesn’t go out of sync. So we add these easy to remember leap day rules to get it to go out of sync that much slower.
Because a year is not quite exactly 365 and a quarter days, but taking away one in 25 leap days (by making the centuries not leap years), which would make the average year be 365 and 6/25 days long is a little bit too short. Add in the leap day on the 400s, and you have an average year length of 365 and 97/400 days, which is very close to the real year.
With the simple leap year every four years rule, the calendar year is longer than the real year by 0.00718 days on average, an error of one day every 128 years. Skipping every century would make it shorter by 0.00219 days, an error of one day every 457 years. Skipping only three out of every four centuries reduces the error to 0.00031 days, one day in 3226 years.
Leap years are just an approximation to keep the year aligned with the calendar year, accounting for the fact that the length of the year isn’t a whole number of days, or even any clean fraction. There are something like 365.24217 days per year. Each rule for leap years is to get the long term average number of days in a year closer to the actual year length.
Basically, there’s no gear train keeping earth’s rotation correlated with its orbital period around the sun.
It’s so the math works out. If 1800, 1900, 2100, etc. were leap years, we would have slightly too many leap days. If 2000, 2400, etc. were not leap years, we would have slightly too few leap days. This would eventually result in the calendar getting ever so slightly out of sync with the seasons, which is seen as undesirable, especially in relation to calculating the date of Easter. The exact rule was chosen because it is easy to memorize and calculate.
The Julian calendar, named for Julius Caesar in 46 BC, had the simple “leap year every four years” method. It worked great and no one noticed a problem in their life rime.
Over the centuries, people noticed the seasons were starting to drift. By the Middle Ages, they noticed that spring was starting a week and a half early. So, in 1582, Pope Gregory, made a correction so that only one out of every four “century” years is a leap year. This fixed the season drift for now.
Maybe in 10,000 years they notice a slight drift again but we’re OK for a long time. Astronomers probably already know what the next correct would be.
Because the century is 18 and 19, not 1800 and 1900.
Pope Gregory’s leap year rules keep the seasons from creeping earlier and earlier due to a solar year being slightly longer than 365 days. (it’s actually 365.2422 days) The previous calendar (Julian calendar) was in use since Roman times and it already had leap years, but only the simplest leap year rule of one leap year every four years.
Since the year is very close to but slightly less than 365 and 1/4 days long, if you’re only using the simple leap year rule of one leap year every four years, that very small difference of 0.0312 days means you are over-correcting with each leap year and adding about 45 min too much. Over hundreds of years this turns into several days of extra time so you are effectively starting the year late, ie the calendar says Jan 01 but it should be Jan 11. (This was exactly the case when the Gregorian calendar replaced the Julian – the date was ten days behind the solar year)
So, the Gregorian calendar makes additional less frequent adjustments to compensate for those extra 45 min per leap year; once per century we skip a leap year. But this too is imperfect because now we are under-compensating ever so slightly, so finally every 400 years we DON’T skip the leap year on the turn of the century.
It’s still not perfect, but it’s precise enough such that now it only drifts one day out of sync for every ~3200 years!
Extremely short version: Easter
Longer reason:
That was how the Julian Calendar worked.
The problems arose from the fact that Easter is held on the first Sunday on or after the Spring Equinox/March 21st after the Paschal Full Moon, which is on the 14th day of a lunar month as determined by tables and is supposed to be correlated with Passover because that’s when Jesus was supposed to have been crucified.
The problem of solving that each year is called computus paschalis and is where we get the word “Compute” as a general term for mathematical problem solving from whence we got Computer as a job title from whence we got Computer the device you’re using to read this post (mobile phones just being specialized computers)
Using 365.25 days per solar year caused drift between the Solar and Lunar calendars of ~7 days per millennium, which isn’t a huge amount but was enough to throw off those calculations when you are using a calendar system devised over a millennia ago, since the Julian was in effect since 45 bc, the problem was noticed in the 700s, calculated at ~a week in the 1200s, the astronomer who was going to figure it out in the 1470s died before much work could be done, work was done throughout the 1500s, and a reform was signed into Catholic doctrine in 1575 by Pope Gregory 13 (for whom it is named), which required Catholic countries to skip 10 days as a correction.
Because there was the Protestant reformation, not everyone did that at the same time
The length of a year is approximately 365.2422 days. So an average of every year of 365, but every 4 years we have built up enough “extra day” we need to burn off the excess (.2422 x 4 = 0.9688) but we are actually overestimating that a tiny bit (1 – 0.9688 = 0.0312) so every century it adds up to ignore a leap year (0.0312 25 leap years = 0.78) but then we are overestimating again so we skip it every 400 years (0.78 4 leap centuries = 3.12) because we haven’t built up enough calendar excess to need to rebalance it by the 400th year. However, every 400 years this leaves us with a remaining excess of 0.12 day, so (1/0.12 = 8.333 x 400 = 3333.333) every 3333 years or so we need to have a leap millennium where February actually has 30 days, but we have never done so yet, and every 10000 years or so we ignore the leap millennium.
Here’s a pretty cool chat with Neil de Grasse Tyson that explains it pretty well in detail:
https://youtu.be/WkhrL8NMycU?si=FscrG9gZ4dSDaBmb
Having a leap day every 4 years gives us an average of 365.25 days a year.
But we skip it every 100 years, so it’s actually 365.24 days.
But we don’t skip it every 400 years, so it’s actually 365.2425 days.
Which is 27 sec off of how long it takes to make a revolution, 365.24219 days. Which is what an actual year is, astronomically speaking.
Here’s a really good video by Matt Parker (yt stand-up maths) where he explains it well and even posits a better version (iirc, it’s been almost 10 years since I’ve seen it)