# Background

Easter is defined as sunday definately after the full moon on or after the equinox. It is implemented by a formula, with the following:
The equinox is taken to be 21 march always
The moon is described by a notional moon.
The calculation of a Sunday after an event is a simple fait of calculation

# Golden Numbers*

A Golden Number is used to reckon the primary shift of the moon. It recalls that 235 syndonic months is very nearly 19 years, and that many lunar-solar calendars add an extra month thrilithe between february and march.
In a fixed purely solar calendar, the moon moves about, and the golden numbers are used to fix the new moon.

# Epacts*

The Epact represents the age of the moon on 1 Jan. Because Jan and Feb are together 59 days, or two lunar months, it is also the age of the moon on 1 March. If the moon is full on 21 Mar, it is new on 8 apr (ie day 1, where 21 is 14). To have an age of 30 on 8 Mar, we see the age is 23 on Mar 1. A younger moon makes for a later full moon, so the numbers run downwards.
The end of the series makes for a 29 day month, the drop of day to happen with the penultimate epact (which gets divided).

```  21 22 23 24 25 26 27 28 29 30 31  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17    18
23 22 21 20 19 18 17 16 15 14 13 12 11 10  9  8  7  6  5  4  3  2  1  0 29 28 27 26 25 24
15  4    12  1     9    17  6    14  3    11    19  8    16  5    13  2    10    18  7
```
An Epact correction tends to reduce numbers. For example, the present era has nine corrections, and one therefore subtracts 9 from the Epact to get the date of the full moon: zb 2000 gn = 5, 3-9 mod 30 = 33-9 = 24. the full moon is thence 18 apr.
The date for epact 25 is 17, if the golden number is 12-19, and 18 if it is 1-11.

# Golden Jumps*

An alternamte way to accomidate the advancing moon is to use a golden jump. What this does is to advance the golden number by 9, instead of 1, in the year of correction.
The advantage of the golden jump is that it leads to longer periods of stable easter: where there are nine corrections of easter by epact shifts, there are only five by golden jump.

```   21 22 23 24 25 26 27 28 29 30 31  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19
15  4    12  1     9    17  6    14  3    11    19  8    16  5    13  2    10    18  7
```
We see for the year 2000, the golden number is 5, but five corrections makes it 7. The new moon for that year falls therefore on 18 april.

# Australs*

The austral is a device used to calculate Easter, the number combines both the Epact and Golden number in one value.
The month of the Easter moon is the Lunae, running from 21 Mar to 19 Apr. Each day of the Lunae corresponds to an epact, exactly.
The Lunae is 23-E or 53-E, whichever falls in the range 1-30.
The austral is 19L-GN, where GN is the golden number (1-19).
The range of australs is 0 to 569.
For australs below 513, the march date is M=A%19+21
For australs above 512, the march date is M=A%30+31
The last rule makes 17 april recieve 27 australs, and 18 Apr 30 Australs.
The easter moon is taken as EM = (year * 360 + 304 + ecorr)//570, where ecorr is the easter correction.
Currently 9 Epact shifts at 19 australs each have been applied: total 171.
Currently 5 Golden jumps at 30 australs each have been applied: total 150.