Ecclesiastical new moon


An ecclesiastical new moon is the first day of a lunar month in an ecclesiastical lunar calendar. Such months have a whole number of days, 29 or 30, whereas true synodic months can vary from about 29.27 to 29.83 days in length. Medieval authors equated the ecclesiastical new moon with a new crescent moon, but it is not a phase of the true moon. If the ecclesiastical lunar calendar is accurate, the ecclesiastical new moon can be any day from the day of the astronomical new moon or dark moon to two days later. The ecclesiastical calendar valid for the Julian and Gregorian calendar are described in detail by Grotefend, Ginzel and in the Explanatory Supplement to The Astronomical Ephemeris.
The ecclesiastical new moon which falls on or next after March 8 is of special importance, since it is the paschal new moon that begins the paschal lunar month. The fourteenth day of the same lunar month is the first of the calendar year to occur on or next after March 21. This fourteenth day was called the paschal full moon by medieval computists. Easter is the following Sunday.
Calendar pages in medieval liturgical books indicated the ecclesiastical new moons by writing the Golden Number to the left of the day of the month on which the ecclesiastical new moon would occur in the year of that Golden Number. In some places the age of the moon was announced daily in the office of Prime at the reading of the martyrology.
When in the 13th century Roger Bacon complained about the discrepancy between the ecclesiastical moon and the observed lunar phases, he specifically mentioned the discrepancy involving the ecclesiastical new moon

Quilibet computista novit quod fallit primatio per tres dies vel quatuor his temporibus; et quilibet rusticus potest in coelo hunc errorem contemplari.

These complaints were finally addressed by the construction of the Gregorian calendar.
A check can be made on the difference between the astronomical new moon and the ecclesiastical new moon. The following table gives a comparison for 2010. All times are Greenwich Mean Time. Coordinated Universal Time is the same with a tolerance of 0.9 seconds either way.
New moon in 2010Ecclesiastical new moon, 2010
January 15 07hJanuary 17
February 14 03hFebruary 15
March 15 21hMarch 17
April 14 12hApril 15
May 14 01hMay 15
June 12 11hJune 13
July 11 20hJuly 13
August 10 03hAugust 11
September 8 10hSeptember 10
October 7 19hOctober 9
November 6 05hNovember 8
December 5 18hDecember 7

The long term accuracy of the Gregorian ecclesiastical lunar calendar is remarkable. It will be in error by one day in about 73 500 years while the error with respect to the tropical year will be one day in about 3320 years.
The following table gives the ecclesiastical new moon used for determining Easter for a range of years.
YearGregorian paschal new moonDays in paschal lunar month
2014April 129
2015March 2129
2016March 1029
2017March 2929
2018March 1829
2019April 530
2020March 2629
2021March 1529
2022April 329
2023March 2329
2024March 1229
2025March 3129
2026March 2029
2027March 929
2028March 2829
2029March 1729
2030April 430
2031March 2529
2032March 1429

Determining the age of the eccesiastical moon

In the liturgical books of the Catholic Church, the age of the moon is determined by using tabular methods.
For explicit calculations of the age of the ecclesiastical moon, a convenient formula has been derived by H. Fukś.
For a given day of the month and the year, define
the century number, the golden number, the epact and the day number, respectively as follows,
Then the age of the ecclesiastical moon on that day is given by
where
and
This formula reflects the age of the moon as given in tables of
Martyrologium Romanum
. On some years
with golden number 1 these tables give incorrect result in the fist cycle of January. Liturgical books stipulate that
in such cases the appropriate correction should be applied, and this is called
`"pronounced age of the moon", defined as
Even with the above correction, the formula is applicable till year 16399. Afterwards, another correction needs to be applied because further anomalies
may appear.
Fully corrected formula for the age of ecclesiastical moon, eliminating all known anomalies, has been proposed by H. Fukś as well:
Python implementation of all of these formulas is available.