Are our calendars inaccurate (even with leap years)?

[Bob55]

I was going through Cecil's archives and came across When do leap-day babies celebrate their birthdays? (http://www.straightdope.com/classics/a960209.html) .

Cecil states "One year = one complete revolution by the earth around the sun = 365 days, 5 hours, 48 minutes, and 46 seconds."

This got me thinking (since one year did not equal 365 days 6 hours), don't we gain a few minutes on leap years? Will our calendars one day be horribly out of sync with the earth? According to

this site (http://www.bibarch.com/Concepts/Calendrics/MarkingTime.htm) :

"A solar year (365.2422 days) consists of the period of time (365 days, 5 hours, 48 minutes, and 46 seconds) spent by the sun in making its apparent passage from vernal equinox to vernal equinox. In fact, a solar year is the time it takes the earth to make one orbit about the sun using the instant in the spring when the sun’s center crosses the equator as a reference point. The earth, however, does not circle the sun at a constant rate, nor does the earth rotate on its axis at a fixed rate. The earth revolves faster when it is nearer the sun during the northern winter. The solar year, or the year of the seasons, is about 20 minutes shorter than the true period of the earth’s revolution. The difference is the result of the precession of the earth."


OK so there's a bunch of numbers flying around...my basic question is if a year is 365.2422 days, then the extra day added every 4th year is .0312 days longer (1 -.2422*4), or 44.928 minutes longer than the actual year, how do we account for this extra time?

[Captain Amazing]

You know, the same thing bothered Pope Gregory XII. Here's what he did about it.

http://www.geocities.com/calendopaedia/gregory.htm

[Caught@Work]

Isn't that why we don't have a leap year unless the centruty is also divisible by 400?
eg. 1900 didn't have a leap year, so everything that was out of whack, was whacked back in.

[Fear Itself]

You forgot about leap centuries (http://www.abc.net.au/2000/mill/leapyear.htm) :2000 is not only a leap year but also a leap century. 1900 and 2100 are not leap years and the next '00 leap year is not until 2400, so we'd better make the best of February 29, 2000. The rules are:

To be a leap year, a year's number must be divisible by 4 unless the year is a century year
If it is a century (that is, an '00 year) the number of the year has to be divisible by 400.
Hence 1600 was a leap year, and so is 2000 and 2400.


and
One of the far-sighted Gregorian calendar reforms in 1583 was the addition of the "century rule" to the leap years. Over a repeating cycle of 400 years, this made the average year length 365.2425 days per calendar year. That means the Gregorian Calendar drifts out of sync with the true solar year by one day in about 2,500 years. For Gregory XIII, near enough was good enough.