Friday, February 29, 2008

Jump for joy, it's Leap Day!

Apollo astronaut John Young leaps and salutes the flag on the moon
Image Credit: NASA

Today is Leap Day, February 29. Every four years, February gets to last an extra day, and the year is 366 days long. (Does this mean that places that say they are open 24/7/365 get to close for the day?) But why do we even have leap years?

First, we need to define what we mean by a "year." Forget the calendar for a minute. Why would we even want to define a year? Well, the year is one of the most fundamental cycles in our lives here on Earth. The seasons run through one full cycle in a year. The constellations appear to make one full circuit through the sky. The days get longer and shorter. And then it all repeats again.

This year, also known as the "tropical year," (yes, there are other kinds, but that's not really important for most people), is the amount of time it takes the sun to complete one full circle in the sky, due to the Earth finishing one full orbit around the sun. But the Earth doesn't take an exact number of days to finish its orbit. The tropical year is 365.24219 days long. So, in a "normal" year of 365 days, the Earth needs an extra 0.24219 days (about 1/4 day) to finish its orbit. Over four years, this almost adds up to one complete day. So, in order to keep the sun aligned with our calendar, we add an extra day to the year.

But if you do a little math, you find that the calendar still doesn't quite work. Three years of 365 days and one year of 366 days averages out to 365.25 days per year -- a little too much. Over a century, this cycle adds up to almost one full day. So, every century, we skip one leap year. 1896 was a leap year, 1904 was a leap year, but 1900 was not a leap year.

But even this scheme doesn't work out. Over a century, the average length of the year is 365.24 days, or 0.00219 days shorter than the real year. Over 400 years, we've lost almost one full day! So, every 400 years, we keep the leap day that would have been thrown out. That's why the year 2000 was a leap year, even though 1700, 1800 and 1900 were not leap years, and even though 2100, 2200 and 2300 won't be leap years. (At least they shouldn't be; I don't expect to be around to find out if we stick to our calendar or not.)

Over 400 years, the average length of our calendar year works out to 365.2425 days. That's an accuracy of one day every 3200 years. That's not too bad for a calendar that was developed 445 years ago! The astronomer John Herschel pointed out that we should consider not having a leap year in the year 4000, but most people aren't too worried about that quite yet!

Update: After posting this, I noticed that yesterday the Bad Astronomer posted a very similar blog entry, although he goes through the math in a bit more detail and with a bit more clarity. I guess Leap Day makes an easy target for us bloggers!

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