Written by Kelly Herbst, Astronomy Curator for the Virginia Living Museum. Updated every two weeks, more or less.

Wednesday, February 29, 2012

Four Small Orbits for the Earth, One Giant Leap Day for Mankind

Happy Leap Day!  It's February 29th, a day that comes only once every four years.  Well, almost once every four years.  Sometimes we skip it.  Do you know the rule for Leap Years?  It gets pretty complicated.  Let's pick it apart, shall we?

Leap Year Rule, Part I: If the year is evenly divisible by four, add one day to the end of February.

Why would we need any kind of rule at all?  Everyone knows that a year is 365 days, right?

Except it's not.

We use a calendar which has 365 days, because that is the number of days it takes the Earth to make one complete trip around the Sun.  But unfortunately, the Earth doesn't quite complete a revolution in 365 days.  In order for the Earth to return to exactly the same spot in its orbit around the Sun, the Earth actually moves for 365 and 1/4 days.  Our calendar ignores this quarter-day, so every 4 years, we need to add a day to our calendar to keep everything lined up correctly.  If we didn't add this day, over time, the extra days would build up, and we'd find ourselves celebrating New Year's in the middle of summer.  So adding a day once every four years helps to keep our calendar days in synch with the seasons as we expect them.
The reason why we need Leap Day.  Credit: Kelly Herbst

Leap Year Rule, Part II: If the year is evenly divisible by four, add one day to the end of February, unless the year is divisible by 100, then don't add a Leap Day.

Okay, so we had a nice simple rule.  Why add this extra bit?  Well, because once again, our math is slightly off.  That extra bit of time it takes for the Earth to truly complete one revolution?  It's not really exactly one quarter of a day.  A year is actually about 365.24 days long...almost one-quarter day but not quite.  So every four years we're adding just a little too much to the calendar.  Over a long period of time, this drift begins to add up again, and your seasons start getting out of synch.  So by the time you've been following the part one rule for about 100 years, you've added about one whole extra day to the calendar that you didn't need.  So skip Leap Day in years that are divisible by 100.

Leap Year Rule, Part III: If the year is evenly divisible by four, add one day to the end of February, unless the year is divisible by 100, then don't add a Leap Day, unless the year is also divisible by 400, then keep the Leap Day.

Okay, now things are just getting silly.  Another adjustment?  Yep, sorry to say it, but 365.24 days isn't the exact time for the Earth to revolve around the Sun once either.  The actual length of a year is really about 365.2425 years.  So if you've been following the part two rule for about 400 years, you've subtracted off one too many leap days and you have to add one back in again to keep the calendar in synch with the seasons.

Notice I said "about 354.2425 years"?  Yes, someday, the leap day rule may grow even more.  The problem here really lies in the fact that we are able to make more and more precise measurements of the actual length of a year.  The basic "once every four years we need an extra day rule" was well-known to the ancient Romans.  In about 45BC, this idea was codified into the Julian calendar, and the concept of the regular Leap Day was first put into practice.  But by 325AD, the Council of Nicaea was already wrestling with the problem that the celebration of Easter was drifting from the season where the church had determined it should be celebrated.  But calendar reform is not easy, and it took another 1300 years before Pope Gregory XIII was able to get the majority of the world to agree to shift to a new calendar, one that included both parts II and III of the leap year rule.  We use this Gregorian calendar today, and even this modern calendar accumulates one day of error in 8000 years.

Pope Gregory XII.  Source: Wikipedia

Will the year 8000AD see another adjustment to our leap year system?  Maybe.  Because something else is happening that we haven't discussed - the length of Earth's year is not constant.  It changes ever so slightly over time.  So by the time we get to 8000AD, we might not need to make any adjustment at all!  Or...we might need to adjust things in the other direction!  But whatever happens, don't worry about it.  Just enjoy this extra day in February - take the opportunity to do something fun!  Subway is giving away free cookies today...sounds like a fun thing to me!

And a special Happy Birthday to my friend Eric, who turns 6 (24) today!  Happy Leap Day everyone!
Until next time,
Carpe noctem!

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