Astronomy & Celestial Mechanics
the sky, computed
Concept

Julian calendar — where it appears

The calendar of 365 days with a leap day every fourth year, giving a mean year of 365.25 days. It gains on the seasons by three quarters of a day a century, which the Gregorian reform of 1582 corrected.

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 A star that walks through a calendar with no leap day. The day of the 365-day Egyptian civil year on which Sirius first rose in the dawn, seen from latitude 30°, against year, from 3000 BC to AD 501, counting from a coincidence of the rising with the civil New Year in AD 139. The civil year was a quarter of a day short of the star's, so the rising arrived one civil day later every four years and went once round the whole calendar in about 1458 years — the Sothic cycle. The star's own year was 365.2504 days, within a few minutes of the Julian year of 365¼.

A year kept by a star seen for one morning

For some seventy days each year Sirius is lost in the Sun's glare, and then one morning it rises just before dawn, for a few minutes, low in the east. The Egyptians kept a calendar of exactly 365 days, and against it that first morning slipped a day every four years, going round the whole calendar in about fourteen and a half centuries. The star's own year turned out to be the Julian year to within minutes — not because it had to be, but because two effects of precession cancel for Sirius seen from Egypt.

sky · Calendars

Named alongside it

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

Tropical yearCalendarComputusEpactGolden numberGregorian calendarHeliacal risingLunisolar calendarMetonic cyclePrecession of the equinoxesSidereal yearSirius

All concepts