Astronomy & Celestial Mechanics
the sky, computed
Concept

Gregorian calendar — where it appears

The civil calendar introduced in 1582, which omits three leap days every four centuries to give an average year of 365.2425 days. It was designed to keep the March equinox near a fixed date for the computation of Easter.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

How often Easter falls on each date, over the Gregorian computus's whole cycle. The fraction of years in which Gregorian Easter falls on each of its 35 possible dates, 22 March to 25 April, computed year by year over 5.7 million years — the length after which the computus repeats exactly, because the golden number, the weekday and the two century corrections only then return to the same combination. The distribution rises from 0.48 per cent on 22 March through a plateau near 3.3 per cent a date to a spike of 3.87 per cent on 19 April, then falls to 0.74 per cent on 25 April. The ramps at each end come from adding a Sunday to a full moon: the earliest dates need both the earliest full moon and the right weekday. The spike on 19 April has no astronomical meaning at all; it is made by a rule in the table that forbids the paschal full moon to fall on 19 April and moves it to the 18th, so the 18th is a full-moon date half as often again as its neighbours.

A full moon computed from the year number

The date of Easter is defined by the Moon and computed without looking at it — ten lines of integer arithmetic on the year number, a finite machine that repeats itself exactly every 5.7 million years. Its output has a spike on 19 April that no sky produces, a table that has kept pace with the real Moon for four centuries, and a Julian twin that is now four days behind it.

sky · Calendars Four tropical years, one for each season. How long the Earth takes to return to the same season, measured from each point of its orbit, minus the mean tropical year of 365.24219 days, in seconds, against the season point (the Sun's longitude). The perihelion drifts relative to the equinox, so between two returns of the same season the planet must cover slightly less than a full orbit in true anomaly, and that shortfall takes longest where the planet moves slowest. Measured from the March equinox the year is longer than the mean by 12 seconds; from the June solstice, 50 shorter; from the December solstice, 49 longer. The full range is ±51 seconds. The Gregorian calendar's average year, 365.2425 days (dashed), is 27 seconds longer than the mean and 15 seconds from the year counted from the March equinox, the one it was built to hold.

A year that depends on the season counting it

The tropical year is quoted to eight decimal places, and it is not one number. Counted from the June solstice it is fifty seconds shorter than counted from the December solstice, because the Earth's perihelion moves through the seasons and the planet covers the last of each year's shortfall at whatever speed it happens to be moving there. The Gregorian calendar was fitted to the year counted from the March equinox, which is why its average year is the length it is — and that year is itself drifting. On Mars the spread is fourteen minutes, and a calendar's leap rule can be more precise than the year it is meant to hold.

sky · Calendars

Named alongside it

The objects these essays reach for when they reach for this one.

Tropical yearClimatic precessionComputusContinued fractionEpactEquinoxGolden numberJulian calendarLeap-yearLength of dayLunisolar calendarMars

All concepts