# An Extra Leap Day

I decided to take my own personal leap day on writing about the leap day.  Partly due to being busy at work, and partly due to lack of mental faculties.  All that aside, it’s only another 1,459 days until the next leap day, so we better start preparing.

A leap year occurs because the solar system seems to slightly disagree with the way we manage time.  Earth’s trip around the Sun, a year, doesn’t take exactly 365 days each lasting 24 hours.  It takes a bit longer.  A year is actually 8,765 hours, or 525,949 minutes, which is 365 days, 5 hours, 48 minutes.  We could just ignore the extra five hours and go about our business, and we wouldn’t notice any difference. At least until Winter started to creep into September.

The extra five hours a year means that the seasons shift by a day every 4 years, or astronomically speaking the Earth ends up a day behind in its orbit.  We wouldn’t really notice it, but every few generations the seasons would be all gummed up, and we don’t really like that.  We like to be accurate, to have everything nice and neat and tidy.  We want the Earth to be at the same point in its orbit every July 12th, every October 6th, and to a lesser degree, every January 16th (stupid Winter).

And so we take that 5 hours and 48 minutes, add it up, and then every four years we just have an extra day! Now you might naturally be thinking, 5h48m + 5h48m + 5h48m + 5h48m = 23 hours and 12 minutes, not the 24 hours in a day.  So by taking an entire extra day every leap year, we actually overcorrect by 48 minutes each time.

At this point, most of you would say “Alright we’re good, close enough, who cares?” Astronomers care! Mathematicians care! And to a lesser extent engineers care!  We fixed this one too!  Here’s how!

If we add up 48 minutes every 20 leap years, we end up 16 hours behind per century. Or to extrapolate a bit more, 96 hours = 4 days every 600 years.  The way we deal with this is the golden rule that nobody gives a damn about.

The golden rule nobody gives a damn about: No leap years on centuries (2100, 2200, 2300) unless they are divisible by 400 (2000, 2400).

And magically it works out! I could go through the table of values and show you how it lines up, but I am far too lazy to calculate all that, just as you are far too lazy to try and follow along with it.  So there.

But even with all these fixes, the calendar will still lose a day every 8,000 years. At this point, everyone says screw it! Definitely the engineers, and even the astronomers and mathematicians.

So this is the reason, lots of math and Earth taking its damn time getting around the Sun.  Leap seconds have nothing to do with this…that’s another story.

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