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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