PETIN M.I.

PETIN - METON calendar

   Contents - http://Petin1Mikhail.narod.ru/index.htm

            XI. Example. The control of the calculating

How does it calculate misalignments for:

- Day 1, Month 11, Year 2108  (5 October 2108 AD),

- Day 1, Month  2, Year 2198  (8 January 2198 AD) ?

Is it the number of days that the new moon

comes after 12:00 of the first day of the month?

Suppose, that the New Moon was on the Greenwich

meridian at noon (12.00) Day 01 Month 1, 1 AD, 1721436 JD

(or 11 January, 1 AD).

  This is an initial point of calculating.

   In the PETIN-METON Calendar:

  Meton cycle(Simple)= 6940 days = 235 lunations =

                     = 19 solar(lunar) years.

  Meton cycle(Leap) = 6939 days = 235 lunations =

                     = 19 solar(lunar) years.

  2xMeton cycle(Simple)+ Meton cycle(Leap)=

             = 6940+6940+6939 = 20819 days =

          = 705 lunations = 57 solar(lunar) years.

  5x[2xMeton cycle(Simple)+ Meton cycle(Leap)] + Meton cycle(Simple)=

       = 111035 days = 3760 lunations = 304 solar(lunar) years

See also Tables 1-6 and Examples IX-X

of Enclosure 3 - http://Petin46Mikhail.narod.ru/index.htm  .

Then

I.           Interval of time from Date 1 Month 1, 1 AD

   to Date 1 Month 11, 2108 AD equals:

2108-1=2107 lunar years and 10 lunar months.

Further:

2107 = 6x304 + 4x57 + 1x38 + 17 years, where:

6x304 years = 666210 days     or 22560 lunations

   4x 57       =  83276              2820

   1x 38(table 6)   =  13880               470

      17 (table 5) =   6172               209

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                 769538 days     or 26059 lunations

   It's necessary to add 10 lunar months = 5x(30+29)=295 days.

II.       Finally interval of time from Date 1 Month 1, 1 AD (1721436 JD)

   to Date 1 Month 11, 2108 AD equals:

769538+295=769833 days (or

26059+10=26069 lunations).

Further: 769833+1721436 = 2491269 JD

It is corresponds to the noon (12.00) 5 October 2108 AD

(Gregorian calendar).

If the period of the Moon revolution equals 29.530588 days,

then 29,530588x26069=769832,90 days.

In this case the misalignment equals:

769832,90 – 769833 = -0,10 days.

It is necessary to subtract this misalignment -0,10 days

from 12.00 5 October 2108 AD for defining the actual New Moon time,

which will be 09.34 5 October 2108 AD.

III.   Analogically for Date 1 Month 2, 2198 AD.

Interval of time from Date 1 Month 1, 1 AD to Date 1 Month 2,

2198 AD equals:

2198-1=2197 lunar years and 1 lunar month.

2197 = 7x304 + 1x57 + 12 years, where:

7x304 = 777245 days       or    26320 lunations

1x 57 =  20819                    705

   12 =   4341 (table 5)          147

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        802405 days       or    27172 lunations

 It's necessary to add 1 lunar month = 30 days (or 1 lunation).

Finally interval of time from Date 1 Month 1, 1 AD (1721436 JD)

to Date 1 Month 2, 2198 AD equals:

802405+30=802435 days (or

27172+1=27173 lunations).

Further: 802435+1721436 = 2523871 JD

It is corresponds to the noon (12.00) 8 January 2198 AD,

2523871 JD (Gregorian calendar).

 The period of the Moon revolution equals 29.530588 days,

then 29,530588x27173=802434,67 days.

In this case the misalignment equals:

802434,67 – 802435 = -0,34 days.

It is necessary to subtract this misalignment -0,34 days

from 12.00 8 January 2198 AD for defining the actual

New Moon time, which will be 03.44 8 January 2198 AD.

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