The feast days

The feast dates follow the rule set given for this calendar, not any rabbinic or modern reckoning. Every day runs from sunset to sunset, so each feast begins at the sunset of the previous evening.

Two places are at work, and they are not the same one. The calendar is reckoned at Jerusalem, always: it is the sunset there that decides whether a new moon falls before or after a day boundary, and so which day carries which date. Moving the observer does not move a single date. What the observer sets is where you are standing — and that decides at what moment the day you have been told about actually opens and closes for you. The two sunset columns are computed for that place from Meeus chapters 12, 15, 22 and 25, and are shown on your own clock; for years outside the age of time zones they fall back to local mean solar time, and the line under the table says which of the two you are looking at.

Every month begins at the new moon. By rule 1, month I is the lunation that holds the first full moon after the March equinox — so that full moon lands on the 14th or 15th, at Passover, and the first day of month VII is a new moon as rule 7 requires. Pesach is the 14th, the Feast of Unleavened Bread runs from the 15th to the 21st, and the Day of Firstfruits is whichever of those days has its daylight half on a Sunday, so it always runs from sunset on Saturday to sunset on Sunday. The Feast of Weeks is 49 days later, again Saturday sunset to Sunday sunset. The Day of Trumpets, the Day of Atonement and Tabernacles fall on the 1st, the 10th, and the 15th to the 22nd of month VII.

Month I usually begins before the equinox: the rule asks that the month contain the first full moon after it, not that it start after it.

“New moon” here means the astronomical conjunction, the moment the Moon passes the Sun and is invisible. Counted from that instant, the full moon of month I falls on the 16th in 1860 of the 4001 years covered, the 15th in 1538, the 17th in 582 and the 14th in only 21 — that is, a day or two after Pesach on the 14th. A calendar that instead opens the month at the first visible crescent, one to two days after conjunction, moves the whole month later and brings that full moon back onto the 14th or 15th. Which of the two you mean changes every date on this page by a day or two.

In 64 of the 4001 years covered, the first full moon follows the March equinox by less than half a day; the page flags those, because a marginally different reading of “after the equinox” would move the entire year one lunation on.

How these dates are computed

Moon phases follow chapter 49 of Astronomical Algorithms: the mean phase from the lunation number k, then 25 periodic terms in the Sun's mean anomaly M, the Moon's mean anomaly M′ and its argument of latitude F, plus 14 planetary corrections. Equinoxes and solstices follow chapter 27 — table 27.A for years up to +1000, table 27.B after that, corrected by the 24 periodic terms of table 27.C.

The algorithms yield Dynamical Time. Times shown here are Universal Time, obtained by subtracting ΔT from the polynomial expressions of Espenak & Meeus, the standard extension of chapter 10 back to −500. ΔT grows from about a minute in 1900 to roughly 4¾ hours in 500 BCE, so it dominates every ancient date on this page.

Year numbering is astronomical: year 0 is 1 BCE, year −500 is 501 BCE. Before 15 October 1582 the Julian column is the date as it would actually have been written and the Gregorian column is proleptic; from that date on it is the other way round. The civil column is the darker one. The weekday is unbroken across the 1582 reform — it is derived from the Julian Day number itself.

Expect the moon phases to be good to about a minute for recent centuries and to a few minutes in antiquity; equinoxes and solstices to well under a minute after +1000 and within about a minute before it. The uncertainty in ΔT itself — tens of minutes at 500 BCE — is far larger than either.