Moon phase chart

Gold number	Date of incidence in March	Age of the Moon as of March 22( epakta)	Moon Circle	Date of spring full moon	Correct letter
1	23	0	17	April 5	About
2	12	XI	18	March 25
3	31	XXII	19	April 13
4	20	III	1	2April	A
b	9	XIV	2	March 22	b
6	28	XXV	3	April 10	have
7	17	VI	4	March 30	And
8	6	XVII	5	April 18	b
9	25	XXVIII	6	April 7	P
10	14	IX	7	March 27	F
11	3	XX	8	15 April	H
12	22	I	9	4 April	N
13	11	XII	10	March 24	G
14	30	XXIII	11	12 April	X
15	19	IV	12	1 April	K
16	8	XV	13	March 21	A
17	27	XXVI	14	9 April	E
18	16	VII	15	March 29	3
19	5	XVIII	16	April 17	u

Moon phase chart .According to the Greek writer Macrobius( 5th century AD), the Julian calendar was introduced so that the first day of the year of the new calendar( January 1, 45 BCE) coincided with the new moon. Undoubtedly, this was done with the intent - for the convenience of calculating the phases of the Moon, which( perhaps on the basis of the metonic cycle) were supposedly "painted" according to the numbers of the months of the calendar.

The question of the "combination" of the lunar calendar with the solar( Julian) became truly "in full growth" before the Christian theologians in the II century.n.when the Christian tradition of celebrating Easter began to take shape. After unsuccessful attempts to use octaetherid to calculate its date, they seem to have re-invented the 19-year cycle and, having assumed that every 19 years certain phases of the moon fall exactly on the same dates of the Julian calendar, a schedule of phases( "ages") of the Mooncalendar months of the cycle. In other words, a kind of "perpetual calendar" was built in which for each year of the 19-year cycle of the new moon( more precisely - neomenii) were compared with specific dates of the calendar months. This table has been used for many hundreds of years both for calculating Easter dates and for dating events, especially Western European historians. By the same principle, a table of dates for the new moon on the 20th century was compiled.

Let us consider in more detail how the "meton cycle" fits into the Julian calendar and how it is possible to compile a "perpetual calendar" of the phases of the moon. Since 19 calendar years = 19X365.25 = 6939.75 days, 235 synodic months - 6939.688 days, it was accepted that the cycle consists of 6940 days.

But 12 synodic months are 354.367 days, and the lunar calendar year is 354 days.

Therefore, if in the first year of the cycle the new moon( neomenia) had to be, say, on March 23, then a year later it would have to be 11 days earlier, ie on( March 11-11) on March 12, and by March 23 ageThe moon will be equal to 11 days. Months of the lunar calendar can have definite names. And that the beginning of one of them( let's call it conditionally "spring") does not go far from March 23, in the second year it is possible to make the insertion of the month in 30 days - to repeat one of the months again. As a result, the beginning of the year shifts relative to March 12: 1) back for 11 days, since the lunar year is shorter than the solar year, but at the same time 2) forward by 30 days, since one month was inserted. Therefore, the beginning of the year - the lack of a spring month - will be on( 12-11 + 30 =) 12 + 19 = March 31, that is, after the insertion, it moves 19 days ahead. The age of the moon by March 23 will be 22 days. Continuing these arguments further and making six additional insertions of the additional month in 30 days, and find the distribution of spring neomen.

In chronology, it was decided to calculate the "age" of the Moon on March 22, and when it was determined, the account included the original day. So, in the example above, in the second year of the cycle, March 12 was considered the first day, the 13th - the second, the 22nd-11th. Consequently, the age of the Moon on March 22 was equal to 11. The age of the Moon, defined on the system of such an "inclusive account" on March 22, was called the lunar epakta( the Greek word "epakta" means "surplus number").Recorded, as was customary, in Roman numerals, the age of the moon on March 22( lunar epakt) is also given in Table.

The ordinal number of the year in the 19-year lunar cycle was called the golden number. This number( numerus aureus), and to a greater extent, epakt, was widely used by Western European historians when dating events.

Looking ahead, we note that historically there were two ways of numbering the years in the 19-year lunar cycle. One of them is "Alexandrian", in which the account of the years was started from the coming to power of the Roman emperor Diocletian - from August 29, 284 AD.e., when the beginning of the Alexandrian( Egyptian stable) year coincided with the new moon. Just the serial number of the year in this cycle and received the name of the golden number. However, in Byzantium and Rus, the "Syriac", or "Byzantine"( also "Constantinople") 19-year cycle, in which the ordinal number of the year is called the lunar circle, was usually used. The use of this cycle began, apparently, in the middle of the III century.n.e. As a starting point, the lunar year was adopted, in which the new moon fell on September 24 - the day of the autumn equinox. This condition is met by 249 AD.E., since in it the conjunction took place on September 23 at 23 hours 2 minutes. As can be seen from the table, the golden number of the calendar year is greater than the corresponding lunar circle by 3.

TABLITSA.Nineteen-year cycle of spring new moons and full moons, lunar epos and serviceable letters

In Table.the dates of the spring full moon and the working letters are also given, which, when calculating Easter dates on fingers, indicated the date of "damage" to the moon.

Here, too, the dates of the neotenies occurring for every 19 years only for March are indicated. In fact, the phases of the moon were painted from year to year for all calendar months. This "perpetual calendar" is given both in two versions: for the XX century, and then the dates of the months are read according to the Gregorian calendar, and for the IV-VI centuries.n.e. .

"The Jump of the Moon". Three of the four consecutive 19-year cycles always include five leap years and only one - four leap years. The numbering of leap years, that is, their position relative to the first year of the cycle, turns out to be different in each subsequent 19th anniversary. Therefore, to paint the dates of the phases of the moon in the Julian calendar for all 19 years, it was convenient to accept that all the years of this cycle are simple. Under this condition, the cycle consists of 365 X 19 = 6935 days. As you can see, 4.75 days have been ejected from the real calendar cycle in 19 years. Obviously, as many of them-it is necessary to throw out and from the lunar cycle. For this it is assumed that the year of 12 lunar months contains

( 6 * 30 + 6 * 29 =) 354 days, year from 13 months( there are seven in a cycle) - 384 days. As a result, the duration of the lunar cycle is 354 * 12 + 384 * 7 = 6936 days.

Therefore, from the real lunar cycle in 235 synodic months, equal to 6939.69 days, during the compilation of the phase table of the Moon, 3.69 days were thrown out. And in order to bring the lunar calendar in line with the "shortened" already Julian, it is necessary to "throw out" one more day from the account of the days in the lunar cycle, that is, once in 19 years "move" the phase of the Moon back not by 11,but for 12 days, or, what is the same, forward not by 19, but by 18 days. This is exactly what was done at the transition from the last cycle to the first: in the 19th year the neocene cycle falls on March 5, and in the 1st cycle on March 5, March 5.Accordingly, the lunar epact, which usually increases by 11 or decreases by 19, decreases here by 18.

This shortening of one lunar month for one day in medieval Europe was called saltus Lunae, the "leap of the moon".It, as noted by the Dutch historian of astronomy A. Pannekoek, "throughout the Middle Ages. .. remained a wonder, since the man-imposed rule-the Moon" jumps "every 19 years-was regarded as a sacred fact of nature."

In fact, as we have seen, there is nothing mysterious about the "arithmetic" of this "eternal calendar"."Surplus" in the duration of the real lunar months is almost completely compensated by 366 days of leap years, although both in the "perpetual calendar" are not apparent. This, of course, sometimes leads to calculations for the displacements of the true phases of the moon within one day. After all, if, say, neomenia in a leap year occurred on February 29, then in the table it will be "dated" on March 1.But how difficult it is to predict the phase of the moon because of the unevenness of its motion. Therefore, we had to sacrifice accuracy for the sake of simplicity. And it turned out pretty good!

Circle of the Moon. In the example above, when recording the date of the christening of Rus, the chronicler also used such a calendar characteristic as the circle of the moon - the "Byzantine" count of the year in the 19-year lunar cycle. The circle of the moon is found in the annals and dating of documents quite often.

Circles of the Moon

However, the circle of the Moon L of a given year can also be established by a simple calculation. First of all, it is defined as the remainder of dividing by 19 numbers of year B from the "creation of the world": L = | B / 19 |

For example, in 1986 n.e.= 7494 AD from the "creation of the world."Dividing 7494 by 19, we find in the remainder 8. This is the circle of the Moon in 1986. We are also convinced that the chronicler in the above-mentioned example indicates the circle of the moon of 6496 AD "from Adam".

However, it is not necessary to move to the year of the era from the "creation of the world".The circle of the moon can also be found as the remainder of the division by the 19th day of the year and.e. R., reduced by 2:

L = |( B-2) / 19 |

So, in the case of the same 1986, we find after 1984( for 1984 = 2 =) 1984 for 19 the same remainder 8.

And here is how the moon phases were set for the randomly taken year using the moon circle. The intermediate element in such calculations was the base O - the age of the moon on March 1( inclusive account!).In the ancient Easter tables it is known as the Femelion. In the V century.n.e.the age of the Moon for the year with the circle of the Moon L = 1 was assumed to be 11( O1 = 11).But in connection with the inaccuracy of the metonic cycle, the numerical value of the base tripled from the fourteenth century. It is already assumed to be equal to O1 = 14. Like the epact, in each subsequent year the base is increased by 11, and seven times per cycle is reduced by 19.

To determine the base of any year, first find its circle of the Moon L. Next is the product( L-1) XII, add it to the base of the first year( O1 = 14) and the result is divided by 30. The remainder will be the basis of the given year,

However, to account for the "jump of the Moon" in the 17th, 18th and 19th lunar circlesthe bases are increased by one.

If you subtract the base number from 30, you can get the date of the new moon in March. Obviously, after this it is not difficult to "paint" the phases of the moon for all other months of the year.

In particular, for 1986 we have the circle of the Moon L = 8. After a simple calculation, we find the base of the year Os = 1.Consequently, the estimated new moon( neomenia) this year falls on March 1 st. Art.

The "perpetual calendar" is not eternal .From the above and beginning of this section comparing the duration of the 19 Julian calendar years and 235 synodic months it is clear that the first of these time intervals is slightly larger than the second. Therefore, in relation to the dates of the Julian calendar, the phases of the Moon fall behind by 0.06135( = 1 h 26 min) for every 19 years or for a whole day for 310 years. And if in one year the full moon took place, say, on March 22, that is, it came after the spring equinox, then in 310 years it already falls on March 21, 310 years on March 20, etc.

Consequently, the "eternal calendar" described above - the schedule of the phases of the moon by the numbers of the months of the Julian calendar - is not really "eternal", it must be periodically corrected. To do this, every 310 years, the specific phase of the moon must be shifted one day back, that is, to reduce the number of months per unit. We will see further that such a correction by the rules for calculating the date of Orthodox Easter was not provided. Therefore, the so-called spring "Easter" full moon actually in our time falls in each year for four to five days after the true astronomical full moon.