﻿ Epact

# Epact

The epact (from Greek epaktai hemerai "added days " ) - in the strict sense, the epact - is a used in the Julian and the Gregorian calendar code for the calendar year. It is the number of days that are missing between the last Neulicht of the moon in the previous year and January 1 of the following year, or age ( moon age ) started in December of the moon on December 31 last year. The epact is assigned as a measure of the new year.

## Epact and Meton cycle

Use and calculation of epact based on the positioning of the calendar lunar months in a solar year based on the calendar year with the help of the 19-year Metonic cycle. The similar length is exploited by 19 solar years and 235 lunar months. In the Julian calendar, the small errors that may appear in the Metonic cycle was neglected. This gave only 19 epacts (so-called Julian epacts ); epact the 20th year was again equal to the first year, and so on.

The epact the Julian calendar year is consistent with its Golden Number GZ in the following simple relationship: Epact = (( GZ - 1) * 11) mod 30

In the Gregorian calendar, the epacts are called lilianische epacts (after Aloysius Lilius and Antony, scientific advisor to the Pope Gregory XIII and intellectual copyright of the calendar reform ). The small error of the Metonic cycle and the somewhat excessive length of the Julian calendar year is corrected occasionally (at the earliest after 100 years ) in them. The lunar calendar data are shifted by one day to sooner or later ( in the sum on that later). For a long time, finally 30 different epacts be obtained as a calendrical lunar month and is sized at a maximum of 30 days. The so-called Gregorian epacts are always at least 100 years long constant as groups of 19 epacts before they are moved together by one unit. In sum, the epacts shift causes a reduction of their values ​​and the moon age. If the value is below zero, be 30 units added ( adding a switching lunar month ), and the epact is 29

The epact of the Gregorian calendar year is consistent with its Golden Number GZ in the following, in comparison to that of the Julian calendar year, more complex context: Epact = ( 27 11 · GZ century value - Int ( century value / 4 ) Int ( century value / 3) ) mod 30 As the century value here are the first two digits of the century understood, so Int ( Jahr/100 ). The equation is valid until 4199 AD.

## Epact and Easter calculation

The epacts were used early on, but never had the importance to them since the Gregorian calendar reform. In the Julian calendar was a fixed relationship between the epact or the moon's age and the Golden Number - the primary key characteristic of the calendar year, the date of Easter is determined.

Only in the Gregorian calendar, an additional parameter is necessary because in it the date of the vernal full moon - it is followed by Easter Sunday - no longer fix related with the Golden Number. Therefore, the year is advantageous marked with the epact. The advantage affects the application of lunar or solar equation in Secular years, with changes of context. In years with the same golden number is now the value of the epact 1 higher ( lunar equation) or 1 lower ( solar equation). The technical term is: Epaktenverschiebung by 1

The age of a full moon 14 days ( and will be counted Neulicht ). When on 31 December full moon, so the following year, the epact 14 assigned, and on March 30 this year, is again full moon (March 30, is three cyclic lunar months of 30, 29 and 30 days later than December 31). The epact 14 for example, had in 2010.

Epacts and spring full moon dates of 2008 to 2017 2008 • epact = 22 • Full Moon on March 22 (March 30, plus ( 14-22 ) days) 2009 • epact = 3 • full moon on April 10 (March 30, plus ( 14-3 ) days) 2010 • epact = 14 • Full Moon on March 30 (March 30, plus ( 14-14 ) days) 2011 • epact = 25 • Full Moon on April 18 (March 30, plus ( 14-25 30) days) 2012 • epact = 6 • full moon on April 7 (March 30, plus ( 14-6 ) days) 2013 • epact = 17 • Full Moon on March 27 (March 30, plus (14-17) days) 2014 • epact = 29 • Full Moon on April 14 (March 30, plus ( 14-29 30) days) 2015 • epact = 5 • Full Moon on 3 April (March 30, plus ( 14-10 ) days) 2016 • epact = 21 • Full Moon on March 23 (March 30, plus ( 14-21 ) days) 2017 • epact = 2 • full moon on April 11 (March 30, plus ( 14-2 ) days)

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