What is a Leap Year?
A calendar year is made of three hundred and sixty-five days -- a number that refuses to be divided nicely, which is why we end up with uneven months of either 30 or 31 days. Except for February -- the runt of the litter -- which only gets 28... except when it gets 29, and then the year is 366 days long. Why does that happen? What kind of crazy universe do we live in where some years are longer than others? To answer this, we need to know: just what is a year?
Way oversimplifying it: a year is the time it takes Earth to make one trip around the sun. This happens to line up with the cycle of the seasons. Now, drawing a little diagram like this, showing the Earth jauntily going around the sun is easy to do, but accurately tracking a year is tricky when you're on Earth because the universe doesn't provide an overhead map.
On Earth, you only get to see the seasons change, and the obvious way to keep track of their comings and goings is to count the days passing, which gives you a 365-day calendar. But as soon as you start to use that calendar, it slowly gets out of sync with the seasons. And with each passing year, the gap gets bigger and bigger and bigger. In three decades, the calendar will be off by a week, and in a few hundred years, the seasons would be flipped -- meaning Christmas celebrations taking place in summer -- which would be crazy.
Why does this happen? Did we count the days wrong? Well, the calendar predicts that the time it takes for the Earth to go around the sun is 8,760 hours. But, if you actually timed it with a stopwatch, you'd see that a year is really longer than the calendar predicts by almost six hours. So our calendar is moving ever-so-slightly faster than the seasons actually change.
And thus, we come to the fundamental problem of all calendars: the day/night cycle, while easy to count, has nothing to do with the yearly cycle. Day and night are caused by Earth rotating about its axis. When you're on the side facing the sun, it's daytime, and when you're on the other side, it's night. But this rotation is no more connected to the orbital motion around the sun than a ballerina spinning on the back of a truck is connected to the truck's cruising speed.
Counting the number of ballerina turns to predict how long the truck takes to dive in a circle might give you a rough idea, but it's crazy to expect it to be precise. Counting the days to track the orbit is pretty much the same thing, and so it shouldn't be a surprise when the Earth doesn't happen to make exactly 365 complete spins in a year. Irritatingly, while 365 days are too few, 366 days are too many and still cause the seasons to drift out of sync, just in the opposite way.
The solution to all this is the leap year: where February gets an extra day, but only every four years. This works pretty well, as each year the calendar is about a quarter day short, so after four years, you add an extra day to get back in alignment. Huzzah! The problem has been solved. Except, it hasn't.
Lengthening the calendar by one day every four years is slightly too much, and the calendar still falls behind the seasons at the rate of one day per hundred years. Which is fine for the apathetic, but not for calendar designers who want everything to line up perfectly. To fix the irregularity, every century the leap year is skipped. So 1896 and 1904 were leap years, but 1900 wasn't. This is better, but still leaves the calendar ever-so-slightly too fast with an error of 1 day in 400 years.
So an additional clause is added to the skip the centuries rule that if the century is divisible by 400, then it will be a leap year. So 1900 and 2100 aren't leap years, but 2000 is. With these three rules, the error is now just one day off in almost eight thousand years, which the current calendar declares "mission accomplished," and so calls it a day.
Which is probably quite reasonable because eight thousand years ago humans were just figuring out that farming might be a good idea, and eight thousand years from now we'll hopefully be using a calendar with a better date tracking system. But perhaps you're a mathematician, and a 0.0001 percent error is an abomination in your eyes and must be removed.
"Tough luck," says The Universe because the length of a day isn't even constant. It randomly varies by a few milliseconds and on average, and very slowly decreases by about 1 millisecond per hundred years. Which means it's literally impossible to build a perfect calendar that lasts forever. In theory, the length of a day will expand to be as long as a current month -- but don't worry, in practice it will take tens of billions of years, and our own expanding sun will destroy the Earth long before that happens.
Sorry, not quite sure how we got from counting the days of the months to the fiery unavoidable end of all human civilization -- unless of course we have an adequately funded space program (hint, hint) -- but there you have it. For the next eight millennia, leap years will keep the calendar in sync with the seasons, but in a surprisingly complicated way. You can learn a lot more about orbits, different kinds of years, and supermassive black holes over at Minute Physics. As always, Henry does a great job of explaining it all in his new video. Check it out.