PETIN M.I.
PETIN - METON calendar
Contents - http://Petin1Mikhail.narod.ru/index.htm
Examples I - IV. The passing from the Petin-Meton calendar
(Gregorian part) to existing the Gregorian calendar.
The examples of calculation of the Petin-Meton calendar (Gregorian part) - 102, 2004 AD etc
is considered below.
I. Example. The passing from the 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 PETIN-METON calendar is 9, 2004 AD,
its necessary to make correction:
1A. 2004 years
1, i.e. the correction between BC/AD
-----------
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 Mi for [1+...+11] months (table 1).
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29 days, i.e. December 29.
4A. Finally, date 9, 2004 AD [the 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 modMg for [1+2+3] months (table 1).
Finally, date 102, 2004 AD [the 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) modMg = 91 days.
9. The sum of days:
730 485
1095
91
--------------------
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
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)
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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
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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 modMg (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 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 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 PETIN-METON calendar)
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