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,

itÆs necessary to make correction:

1A.            2004     years

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

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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)

Note½LeapG╗ is a Gregorian leap year, i.e. +1 day.

½LeapM╗ 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 modMfor [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

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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.

+    3 months  00

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8 .   The sum

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

+       2000 years

3 years

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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

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

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