Most famous rounding error

As all you know 2008 is a leap year. This led me to think about the most used and common rounding error: the rounding of the number of days in a year. The current standard calendar in most of the world is the Gregorian calendar, which establishes that the year is 365.2425 days long. Using a calendar with 365 days would result in an error of 5 hours, 49 minutes, and 12 seconds per year.

The leap year makes up for this error by adding one day to the month of February every four years, except to those years divisible by 100 unless they are divisible by 400, but still isn’t enough:

The Gregorian calendar was developed to keep the vernal equinox, moment when the Sun is over the Earth’s equator, close to March 21, so that the date of Easter remains correct with respect to the vernal equinox. The vernal equinox year is about 365.242374 days long (and increasing).

Illumination of the Earth by the Sun on the day of equinox, (ignoring twilight).

Illumination of the Earth by the Sun on the day of equinox.

The insignificant difference of 0.000125 days means that in around 8,000 years, the calendar will be approximately one day behind where it is now. But by that time, the length of the vernal equinox year will have changed by an amount that cannot be predicted. Therefore, the current Gregorian calendar suffices for practical purposes

References:

http://en.wikipedia.org/wiki/Leap_year

http://www.timeanddate.com/date/leapyear.html

http://en.wikipedia.org/wiki/Vernal_equinox

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