Gregorian calendar

==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 [[solar time#Mean solar time|mean solar days]] long.{{sfnp|Seidelmann|1992|pages=580–581}} This approximation has an error of about one day per 3,030 years{{efn|Using value from Richards (2013, p. 587) for tropical year in mean solar days, the calculation is {{nowrap|1/(365.2425-365.24217).}}}} with respect to the current value of the [[mean tropical year]]. However, because of the [[Axial precession (astronomy)|precession of the equinoxes]], which is not constant, and the movement of the [[perihelion]] (which affects the Earth's orbital speed) the error with respect to the ''astronomical'' vernal equinox is variable; using the average interval between vernal equinoxes near 2000 of 365.24237 days{{sfnp|Meeus|Savoie|1992|page=42}} implies an error closer to 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 4,000 years, instead of 970 leap days that the Gregorian calendar would insert over the same period.<ref>{{cite book| first1= John |last1= Herschel |url=http://visualiseur.bnf.fr/Visualiseur?Destination=Gallica&O=NUMM-94926 |title= Outlines of Astronomy | year=1849 | page= 629}}</ref> 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.<ref>{{cite book |last1=Steel |first1= Duncan |title=Marking Time: The Epic Quest to Invent the Perfect Calendar|year=2000|publisher=John Wiley & Sons|isbn=978-0-471-29827-4| page=185 |url=https://books.google.com/books?id=rxvVdXyr_hMC&pg=PA185}}</ref>

On time scales of thousands of years, the Gregorian calendar falls behind the astronomical seasons. This is because [[Earth's rotation#Changes|the Earth's speed of rotation is gradually slowing down]], which makes each day slightly longer over time (see [[tidal acceleration]] and [[leap second]]) while the year maintains a more uniform duration.

===Calendar seasonal error===
[[File:Gregoriancalendarleap solstice.svg|frameless|upright=3.65|Gregorian calendar seasons difference]]

This image shows the difference between the Gregorian calendar and the astronomical seasons.

The ''y''-axis is the date in June and the ''x''-axis is Gregorian calendar years.

Each point is the date and time of the [[Solstice|June solstice]] in that particular year. The error shifts by about a quarter of a day per year. Centurial years are ordinary years, unless they are divisible by 400, in which case they are leap years. This causes a correction in the years 1700, 1800, 1900, 2100, 2200, and 2300.

For instance, these corrections cause 23 December 1903 to be the latest December solstice, and 20 December 2096 to be the earliest solstice—about 2.35 days of variation compared with the astronomical event.