530 Pages

The Petin-Meton calendar or New World Calendar is a lunisolar calendar with 7- and 8-day weeks created by Mikhail Petin.

## History

The solar Gregorian calendar, which practically functions now as a World calendar is nevertheless perceived nowadays by the most of our planet population only as Western or Christian calendar.

### Week fallacy

The analysis of the history of creation of the Gregorian calendar and of its lacks shows the influence on it of certain subjects and phenomena. For example, one can assert that there is the following dependence:

the Bible - an industrial cycle (work, rest) - a calendar - nature (the Sun, the Moon, the Earth)

In recent times (IV century CE) Christian Church (the Bible) exerted its influence on the calendar: a mythical industrial cycle (7-day’s week) was introduced into the calendar, which is present in the calendar at the present time.

There observed in Nature the cycles connected with the seen movement of heavenly bodies (the Sun, the Moon, the Earth). These natural cycles are reflected in a calendar. They are a calendar basis and are used for counting of long time intervals. For example, the seen Sun movement defines the seasonal solar year in a calendar, the Moon movement [defines] - the month (lunation), the Earth rotation [defines] - the sutki (day + night). A mythical 7-day’s week is absent in Nature.

A calendar problem, in particular, lies in the fact that in the 313 year (IV century CE) the Roman Emperor Constantine has wrongly introduced a 7-day’s week into the solar (Julian) calendar when one had legalized Christian. Unfortunately, this mistake was not corrected in 1582 by Roman Pope Gregory XIII and by the author (reformer) Christother Clavius while making the Julian calendar reform.

The mistake of Emperor Constantine is in the inequality between the duration of a CALENDAR month and the average duration of the NATURAL lunar cycle (29,5305888531 sutki). Strictly speaking, the duration of one week should be equal to:

```                    29,5305888531 : 4 = 7,382... sutki.
```

Further, taking into account the idea, that in any calendar there can be only the integers (fractional numbers should be approximated to the nearest integers) it is necessary to consider, that:

```          I week = 7,38х1 =  7,38 =  7 sutki,        i.e. 7,
I+II week = 7,38х2 = 14,76 = 15 sutki,        i.e. 7+8,
I+II+III week = 7.38x3 = 22,14 = 22 sutki,        i.e. 7+8+7,
I+II+III+IV week = 7.38x4 = 29,52 = 30(or 29) sutki, i.e. 7+8+7+8(or 7).
```

Thus, the next conclusion follows: For conformity of the CALENDAR months to the NATURAL lunar cycles, the following conditions should be observed:

• the calendar months (lunations) should have structure
• 7+8+7+8 (30 sutki) and 7+8+7+7 (29 sutki), grouped in the Meton-cycles known from the ancient times (before the Julian and Gregorian calendars).

### Disadvantages of the Gregorian calendar

The Gregorian calendar is rather accurate and widespread but besides an erroneous 7-day’s week it has a number of lacks:

• the duration of months is different (from 28 up to 31 days),
• the months of different duration alternate randomly,
• the quarters of a year have different duration (from 90 to 92 days),
• the first half-year period is always shorter than the second one (three days - in an ordinary year and two days - in a leap year),
• the years and months begin with different week days,
• 10 - 11 weeks " are split ", i.e. one part of them belongs to one month, the other part belongs to the other month,
• the number of working days in different months of the same year is various (23-27 days at a six-day working week and 19-23 days at a five-day working week),
• the dates of months are not coordinated with week days as well as the with Moon phases,
• the calendar is not convenient for women (in a female calendar the periods of the women biorhythms are close to the periods of lunar cycles),
• a non-Christian part of the Earth’s population (5 billion persons from 6 billion of the total number of people on the Earth) criticizes the Gregorian calendar,
• the initial date in a calendar is only a myth, a legend, but not the fixed astronomical phenomenon.

How can all these lacks be eliminated?

### Requirements

A New World Сalendar should:

• be a double calendar, i.e. a solar (seasonal) and a lunar-solar one. Note. Such official STATE calendars (but with a 7-day’s week) exist now, for example, in Israel, UAE, etc.
• have structures of months: 7+8+7+8 (30 days) and 7+8+7+7 (29 days),
• have the initial date in a calendar as the astronomical phenomenon instead of myths, legends about the birthdays of prophets etc.,
• be precisely synchronized (an accuracy -/+ 1.5 day) in relation to natural solar and natural lunar cycles,
• be acceptable for any religion,
• etc.

For the last 200 years the calendar experts have created a lot of projects of calendars with a 7-day's week. But all of them are as though «the curve mirrors» which are not convenient to use.

The unique project of a calendar «with a flat mirror» (i.e. 7+8+7+8 and 7+8+7+7) is placed on the web pages linked below.

The new World Calendar has a number of advantages in comparison with the solar Gregorian or other calendars:

• it is not required to introduce the "special" dates. Dates 15 and 30 of the lunar months are the same usual integral days of the week, as all others,
• the duration of months is unified - 29 and 30 days,
• the structure of months - constant and easily remembered,
• the lengths of lunar years are reduced from six values up to three: 354, 355, 384 days,
• the quantity of working days in each month is constant (24 days at a 6-day working week and 20 days at a 5-day working week),
• the months, quarters of years and years begin and finish at the same days of a week,
• the dates of months and days of a week are synchronized with phases of the Moon (with the rotation of the Moon around the Earth), which allows to take into account the workers efficiency in productions connected with the biorhythms, arising under the influence of the Moon,
• the new calendar is more convenient for women, than the Gregorian Calendar,
• all calendar cycles:
• the sutki (day + night),
• the lunation (lunar month),
• the solar year,
• the Meton cycle (19 solar years),
• the Grand Meton cycle (6479 solar years) correspond to the natural rotation periods of heavenly bodies (the Sun, the Moon, the Earth) relative to each other,
• each Grand Meton cycle is attached to the precise heavenly time reference points of time (orientirs), i.e. the moments of the mutual position of the Sun, the Moon, the Earth when the Southern solstice, the solar eclipse, midday are simultaneously observed and when the solar eclipse will be repeated through the lunation period. Such next in turn combination of mutual positions of the mentioned above heavenly bodies had taken place on December 20, 1786 with the subsequent repeated solar eclipse on January 19, 1787.
• correction of discrepancy of lunar and solar years concerning the calendar structure and also between themselves is simple; it can be carried out by high precision compensating methods.

The New World PETIN-METON calendar is the answer to a question on a calendar reform which was raised in 1953 in the United Nations under the initiative of the India delegation which had offered "to ratify for whole of the world a new, uniform and constant calendar, astronomically coordinated with the movement of the Earth around the Sun which be more correct, scientifically reasonable and favourable, as compared with the Gregorian calendar". The account of lunar months and solar years in the new World PETIN-METON Calendar creates conditions for rapprochement of religious traditions of Christianity, Islam, Judaism, Buddhism etc., based on the most ancient observation of the seen movements of the Sun, the Moon, the Earth.

Being guided by the preservation of an invariance of each religious doctrine, and also principles of friendly mutual relation, one can hope, that spiritual academies of different countries will consider an opportunity of application of the new solar + lunar-solar calendar in their states as the World calendar.

Expansion of cultural, trading, technical, telecommunication connections between peoples (especially rapid development of the Internet-network in recent years) facilitates the calendar reform, which is of great international value.

## Definitions, terms and symbols

Natural cycles:

• natural solar sutki (day + night) - a time interval between two consecutive same culminations of the natural Sun centre at daily rotation of the Earth around its own axis. Owing to non-uniformity of the year's movement of the Earth on an orbit, and also non-perpendicular of Earth axis to a plane of its orbit the natural solar sutki duration are changeable within one year.
• natural tropical year = 365,242192 natural solar sutki - a time interval between two consecutive passages the centre of the natural Sun through the East equinox's point at annual movement of the Earth on an orbit.
• solar Meton cycle = 19 solar years = 6939,6017 sutki - the period of time, practically equal to the lunar Meton cycle, i.e. 235 lunar sinodic months (6939,6883 sutki),
• solar Grand Meton cycle = 341 solar Meton cycles = 6479 solar years = = 2 366 404,2 sutki - the period of time, after which the Earth and the Moon (on the Southern solstice day) come back to the initial position concerning the Sun,
• mean lunation (mean lunar sinodic month) = 29,5305888531 sutki - the mean value of the time interval between two consecutive identical phases of the Moon,
• lunar year = 12 (13) mean lunations - the time intervals according to Table-calendars (types МА, МВ, Мcorr)
• lunar Meton cycle = 235 mean lunations = 6939,6883 sutki - the period of time, practically equal to the solar Meton cycle, i.e. 19 solar years (6939,6017 sutki ),
• lunar Grand Meton cycle = (341 х 235 - 1) mean lunations = 2 366 404,2 sutki - the time interval, after which the Earth and the Moon (on the Southern solstice day) come back to the initial position concerning the Sun.
• 1 precession cycle = 25 796,178 solar years (tropical) is the period of movement the Earth axis on the cycle cone about stars (precession). In the World PETIN- METON Calendar the influence of precession is taken into account by means of the solar years (tropical).
• d, the drift of the lunar cycle relatively the solar cycle.
```  velocity of drift d = (6939,6883 - 6939,6017) sutki : 19 solar years
= 0,00456 sutki/year
= 0,0866 sutki/Meton cycle
```

## Calendar cycles

### solar calendar

• mean Sun - on the Earth's equator the fictitious point moving within the year in regular intervals with such speed, that it always passes through the Eastern equinox

point simultaneously with natural the Sun,

• mean solar sutki = 1 mean sutki (further: sutki) - a time interval between two consecutive same daily culminations of the mean Sun,
• calendar tropical year (further: tropical year) = 365,242192 sutki - a time interval between two consecutive passages of the centre of the mean Sun through the Eastern equinox point. Its duration slowly changes and equal to
365,24219879 - 0,0000000614 (Т - 1900) mean solar sutki, where: Т - the current year.
• Equation of time - a difference between the mean and natural solar sutki. The Equation of time continuously varies. Four times in the each year, namely: about April 16, June 14, September 1 and December 25 the Equation of time is equal to zero and achieves the greatest value (on absolute size) 4 times:
```         About February 12 - ....     + 14,3 minutes,
May 15 - ....     -  3,8 minutes,
July 27 - ....     +  6,4 minutes and
ember 4 - ....     - 16,4 minutes,
```
• solar month - a time interval determined, for example, by the Gregorian solar calendar,
• week = 7 (or 8) days - an industrial cycle, i.e. 5 (or 6) days of work and 2 (or 3) days for rest,
• weekdays can be named, for example, in the following way: Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday, Lunaday. Weekdays are synchronized with phases of the calendar mean Moon (see below - a lunar-solar calendar),
• DoM - day of month,
• DoW - day of week,
• solar year = 365 sutki,
• leap-year = 366 sutki,
• an intercalary day = 1 sutki,
• solar Meton cycle МА = 19 solar years = 6940 sutki
• solar Meton cycle МВ = МА - 1 sutki = 6939 sutki ,
• solar Grand Meton cycle GMet = 6479 solar years = 2 366 404 sutki. Note. In the World PETIN-METON Calendar the rules of the solar (seasonal) calendar correspond to the rules of the Gregorian Calendar.

### lunar-solar calendar

• sutki - the period of time equal to the mean solar sutki,
• lunation LA = 30 sutki - a time interval between two consecutive identical phases of the calendar mean Moon cycle (=29,5305888531 days), approximated to an integer to the greater side,
• lunation LB = 29 sutki - a time interval between two consecutive identical phases of the calendar mean Moon cycle, approximated to an integer to the smaller side,
• week = 7 (or 8) days - an industrial cycle, i.e. 5 (or 6) days of work and 2 (or 3) days for rest,
• weekdays can be named, for example, in the following way: Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday, Lunaday. Weekdays are synchronized with the phases of the calendar mean Moon, i.e:
• each lunation begins on Monday - the New Moon Day;
• Date 15 of each lunation is an additional day off (Lunaday) - the Full Moon Day;
• structure of the calendar lunations: 7+8+7+8 or 7+8+7+7 days,
• DoL - day of lunation,
• DoW - day of week,
• lunar year LYA = LA+LB+LA+LB+LA+LB+LA+LB+LA+LB+LA+LB = 354 sutki,
• lunar year LYB = LA+LB+LA+LB+LA+LB+LA+LB+LA+LB+LA+LA = 355 sutki,
• lunar year LYC = LYA + LA = 384 sutki,
• lunar Meton cycle МА = 235 lunations = 8 LYA + 4 LYB + 7 LYC = 6940 sutki,
• lunar Meton cycle МВ = 235 lunations = 9 LYA + 3 LYB + 7 LYC = 6939 sutki,
• correcting Meton cycle Мcorr = (235-1) lunations = 10 LYA+3 LYB+6 LYC = = 6909 sutki,
• base lunar cycle MetАВА = MA+MB+MA = 20 819 sutki,
• lunar Hipparh cycle HA = 5 MetАВА + MA = 111 035 sutki,
• lunar Hipparh cycle HВ = HA + MA + MetАВА = 138 794 sutki,
• lunar Petin cycle PA = 4 [5 (MA+MB+MA)+MA]+2MA+MB+MA = 471 899 sutki,
• lunar Grand Meton cycle GMet = 3 PA + Mcorr + 2 PA= 2 366 404 sutki.
• accuracy of a lunar-solar calendar (+/- 1,4 sutki) - the maximal time misalignment between the moment of the top culmination of the centre of the natural mean Moon and midday of any calendar Date on the chosen long time interval (for example, 380 380 years).

The alternation and the durations of the cycles of the World PETIN-METON calendar within the limits of an interval of time of 6479 solar years are:

• Меtоn-cycles
• 19-year Меton-cycle МА (6 940 sutki),
• 19-year Меton-cycle МВ (6 939 sutki),
• 19-year Меton-cycle Мcorr (6 909 sutki),
• a base Меton-cycle:
• 57-year Меton-cycle (20 819 sutki),
• Hipparch-cycles:
• 304-year Hipparch-cycle HA (111 035 sutki),
• 380-year Hipparch-cycle НВ (138 794 sutki),
• Petin-cycles:
• 1292-year Petin-cycle РА (471 899 sutki),
• 1311-year Petin-cycle РВ (478 808 sutki),
• Great Меton-cycle:
• 6479-year cycle GMet (2 366 404 sutki).

The beginning of nearest next the Great Меton-cycle (i.e. the GMet-2 ) is December 21, 1786 CE.

## Notation

Formats of the calendar date in the World PETIN-METON Calendar: for example, September 17, 2006 CE (Gregorian calendar)

### solar calendar

• date ! Gregorian year - for example: Date 271, year 2006 or
• Gregory date ! Gregory month ! Gregory year - for example: September 17, 2006 CE (Gregorian calendar)

### lunar-solar calendar

• date ! lunation ! Gregory year - for example: Date 21, lunation11, year 2006 or
• date ! lunation ! lunar year ! Meton-cycle ! Grand Meton-cycle - for example: Date 21, lunation 11, lunar year 11, Meton-cycle 12, GMet 2
Community content is available under CC-BY-SA unless otherwise noted.