# Gregorian calendar off by 26 seconds a year

1. Dec 17, 2007

### Scraff

I just read that the Gregorian calendar is off by 26 seconds a year from the solar calendar. That adds up to about 43 minutes ever 100 hundred years.

Does this mean that if it starts to get dark at 5:30 pm on the East coast on December 1st, that it got darker 43 minutes earlier or later 100 years ago and that it will be off by another 43 minutes 100 years from now?

2. Dec 17, 2007

### mgb_phys

The gregorian calender is much more accursate than that (1 day in 6000 years)
In fact random changes in the Earth's rotation due to weather / climate etc have a bigger effect.

We currently add leap seconds (to allow for both the Earth's predicatable slowdown due to tidal friction and random changes) to keep clocks in sync with the seasons. There is a proposal to stop adding leap seconds since reseting computers every year is a pain but nobody needs to know the seasons to an accuracy of a few seconds.

3. Dec 18, 2007

### D H

Staff Emeritus
That error is equivalent to 1 day per 3300 years, which is indeed the error in the mean Gregorian year as compared to the mean tropical year. mgb_phys cited an error about half that (1 day in 6000 years), which is the error in the mean Gregorian year compared to the mean equinoctical year.

It is better to express the error over a very long term rather than over one year. Most years in the Gregorian calendar are not leap years and are thus 365 days long. These years have an "error" of about -6 hours, not 26 seconds. Leap years are even worse, with an error of about 18 hours. The careful balance of normal years and leap years in the Gregorian calendar makes the long term error in the Gregorian calendar very, very small.

4. Dec 18, 2007

### D H

Staff Emeritus
This is the danger of looking at the Gregorian calander error as "26 seconds per year". A day is 86,400 seconds long, exactly. We occasionally add or subtract one leap second to keep local midnight at the Greenwich meridian within one second of 00:00 UTC. A normal Gregorian year is 365 days long, exactly. We occasionally add one leap day to keep the vernal equinox within one day of March 21. The formula for adding a leap year is very well defined. The formula for adding a leap second is not. We know we need to add a leap second by observation only.