PETIN M

PETIN M.I.

The World PETIN - METON calendar

Contents – http://NewWorldCalendar.narod.ru/index.htm

Examples I - IV. The passing from the World Petin-Meton calendar

(Gregorian part) to existing the Gregorian calendar.

The examples of calculation of the World Petin-Meton calendar (Gregorian part) - 102, 2004 AD etc

is considered below.

I. Example. The passing from the World Petin-Meton calendar (Gregorian part)

to existing the Gregorian calendar

1. 102 – 11 = 91 days , as date 102 > data 11, which is December, 31 in the preceding year.

Note. If date < 11, for example date of the World PETIN-METON calendar is 9, 2004 AD,

it’s necessary to make correction:

1A. 2004 years

- 1

-----------

2003 years , and then

2A. 9 – 11 + 365 =363 days, (see table 1 column Simple - http://Petin20Mikhail.narod.ru/index.htm )

3A. 363

–334 , where: 334 is mod M_i for [1+...+11] months (table 1).

_{-------------}

29 days, i.e. December 29.

4A. Finally, date 9, 2004 AD [the World Petin-Meton calendar (Gregorian part)] is December 29, 2003 AD (existing the Gregorian calendar).

Note. «LeapG» is a Gregorian leap year, i.e. +1 day.

«LeapM» is a Meton leap year, i.e. -1 day.

The rule of definition of simple solar years

at which the duration of each year is equal to 365 days, but years:

а) multiple of 4, are equal to 365+1 = 366 days, i.e. leapG years;

б) multiple of 100, are equal to 365 days;

в) multiple of 400, are equal to 365+1 = 366 days, i.e. leapG years;

г) multiple of 3200, are equal to 365 days;

д) multiple of 134 400, are equal to 365+1 = 366 days, i.e. leapG years.

2. As 2004 is a leapG year and 102 > 59, therefore

3. 92 – 91 = 1 April, here 91 is modM_gfor [1+2+3] months (table 1).

Finally, date 102, 2004 AD [the World Petin-Meton calendar (Gregorian part)] is April 1, 2004 AD,

LeapG year.

II. The definition of JD. Date 1 of April, 2004

4. 2004 year

– 1, i.e. the correction between BC/AD

---------

2003 year

5. 2003 : K₁ = 5,0075, where: K₁= 400 from the table 2 -( http://Petin20Mikhail.narod.ru/index.htm )

for interval of (>400) – 2800 years.

We take 5 instead of 5,0075

5 x K₁ = 5 x 400 = 2000 years

5 x K₂= 730 485 days, where: K₂ = 146 097 from the table 2

for interval of (>400) – 2800 years.

6. 2003 – 2000 =3 years

7. 3 : K₁ = 1 , where: K₁= 3 from the table 2

for interval of (>3) – 4 years.

1 x K₁ =3 years

1 x K₂ = 1095 days, where: K₂ = 1095 from the table 2

for interval of (>3) – 4 years.

8. For leapG year and the [1+2+3] months (before April, see table 1) modM_g = 91 days.

9. The sum of days:

730 485

1095

--------------------

731 671 days

10. Finally, JD for April 1, 2004

731 671

1 721 426 i.e. JD of January 01, 1 AD

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2 453 097 days i.e. April 1, 2004 it coincides with a result of the working algorithm for Forsythe’s

converter: http://home.austin.rr.com/rumblefische/calendars/cconverter.html

III. Return account

1. 2 453 097 days , i. e. JD of a solar date X (the sum)

- 1 721 426, i.e. JD of January 01, 1 AD ( the augend)

-------------

731 671 days ...(the addend) , i.e. interval (JD) between January 01, 1 AD and a solar date X.

2. 731 671 : K₂ =5, 0081, where: K₂ = 146 097 from the table 2 - ( http://Petin20Mikhail.narod.ru/index.htm )

for interval of 146 098 – 1 022 679 days.

We take 5 instead of 5,0081

5 x K₁ = 5 x 400 = 2000 years, where: K₁= 400 from table 2 for interval of 146 098 – 1 022 679 days.

5 x K₂= 730 485 days, where: K₂ = 146 097 from the table 2.

3. 731 671

- 730 485

----------------

1186 days – interval with leapG year (table 2), i.e. JD between January 01, 2001 AD and a solar date X.

4. 1186 : K₂ = 1,084, , where: K₂ = 1095 from the table 2

for interval of 1096 – 1 461 days.

We take 1 instead of 1,084 and

1 x K₁ = 1 x 3 = 3 years, where: K₁ = 3 from the table 2 for interval of 1096 – 1 461 days.

1 x K₂= 1095 days, where: K₂ = 1095 from the table 2.

5. 1186 days

- 1095

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91 days in the leapG year (the augend), i.e. JD between January 01, 2004 AD and a solar date X.

6. It is necessary to define a quantity of months and days between January 01, 2004 AD and a solar date X.

In leapG year a nearest mini modM_g (table 1) is 91 days, i.e. the [1+2+3] months and 00 days.

7. January 01, 2004 AD

+ 3 months 00

--------------------------------

April 01, 2004 AD

8 . The sum

1 i.e. . the correction between BC/AD

+ 2000 years

3 years

-------------------

2004 years , i.e. finally April 1, 2004 (existing Gregorian calendar)

IV. Example. The passing from existing the Gregorian calendar

to the World PETIN-METON calendar (Gregorian part).

It is necessary to make the following:

6A. After mentioned above point 5 Example III

92 days

+ 11 days

----------------

103 days

Notes: a) if the given result is equal to 71 in the leapG year – this is date 366 in the World PETIN-METON

calendar.

b) if the result is equal to < 71 in any year, point 7A mentioned below no required.

c) any result in the simple year doesn't require point 7A.

7A. As two conditions (leapG year and 103 > 71) are simultaneously

103 days

- 1 day i.e. leapG day

-----------------

102 days, i.e. finally 102, 2004 (Gregorian part of the World PETIN-METON calendar)

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Contents – http://NewWorldCalendar.narod.ru/index.htm