Gregorian Calendar - Accuracy

Accuracy

The Gregorian calendar improves the approximation made by the Julian calendar by skipping three Julian leap days in every 400 years, giving an average year of 365.2425 mean solar days long. This approximation has an error of about one day per 3,300 years with respect to the mean tropical year. However, because of the precession of the equinoxes, the error with respect to the vernal equinox (which occurs, on average, 365.24237 days apart near 2000) is 1 day every 7,700 years. By any criterion, the Gregorian calendar is substantially more accurate than the 1 day in 128 years error of the Julian calendar (average year 365.25 days).

In the 19th century, Sir John Herschel proposed a modification to the Gregorian calendar with 969 leap days every 4000 years, instead of 970 leap days that the Gregorian calendar would insert over the same period. This would reduce the average year to 365.24225 days. Herschel's proposal would make the year 4000, and multiples thereof, common instead of leap. While this modification has often been proposed since, it has never been officially adopted.

On time scales of thousands of years, the Gregorian calendar falls behind the astronomical seasons because the slowing down of the Earth's rotation makes each day slightly longer over time (see tidal acceleration and leap second) while the year maintains a more uniform duration. Borkowski reviewed mathematical models in the literature, and found that the results generally fall between a model by McCarthy and Babcock, and another by Stephenson and Morrison. If so, in the year 4000, the calendar will fall behind by at least 0.8 but less than 1.1 days. In the year 12,000 the calendar would fall behind by at least 8 but less than 12 days.