PETIN M.I.
PETIN - METON calendar
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3. The results of calculations (Part 1).
3.1. The misalignment value dT concerning the beginning of a lunar calendar count - Date 1, Lunation 1-LA, Lunar year 1-LYB, Meton cycle 1-MA, Grand Meton cycle 1-GMet ( or December 21, 4694 BCE Gregorian calendar) is determined by the expression
dT = N x 29,5305885 – dDJD , day,
where:
N – the number of lunar cycles concerning the beginning of the lunar calendar count
before the chosen date, day,
dDJD – the number of days (Julian calendar) concerning the beginning of the lunar
calendar count before the chosen date, day.
3.2. The misalignment values dT at the end of each lunar month, lunar year (for initial Meton simple cycle or Meton leap cycle) are given in Tables 6B, 7 and 8 accordingly.
Table 6B.
The misalignments at the end of the month, days
1 month -0,4694115 -0,4694115 -0,4694115
2 +0,0611770 +0,0611770 +0,0611770
3 -0,4082345 -0,4082345 -0,4082345
4 +0,1223540 +0,1223540 +0,1223540
5 -0,3470575 -0,3470575 -0,3470575
6 +0,1835310 +0,1835310 +0,1835310
7 -0,2858805 -0,2858805 -0,2858805
8 +0,2447080 +0,2447080 +0,2447080
9 -0,2247035 -0,2247035 -0,2247035
10 +0,3058850 +0,3058850 +0,3058850
11 -0,1635265 -0,1635265 -0,1635265
12 +0,3670620 +0,3670620 -0,6329380
13 -0,1023495 -- --
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384 days 354 days 355 days
Table 7. Meton simple cycle
SimpleM (Meton lunar years)
¹¹ Misalignment Duration of
year on the end lunar year
of lunar year
0 0.0000000 - - 355
SimpleM1 -0.6329380 354 - -
Etc. 2 -0.2658754 - 384 -
3 -0.3682243 354 - -
4 -0.0011617 - - 355
5 -0.6340997 354 - -
6 -0.2670371 - 384 -
7 -0.3693860 354 - -
8 -0.0023234 - - 355
9 -0.6352614 354 - -
10 -0.2681988 - 384 -
11 -0.3705477 354 - -
12 -0.0034851 - - 355
13 -0.6364231 354 - -
14 -0.2693605 - 384 -
15 -0.3717094 354 - -
16 -0.0046468 - 384 -
17 -0.1069857 - 384 -
18 -0.2093446 - 384 -
SimpleM19 -0.3116935 - - -
Table 8. Meton leap cycle
LeapM (Meton lunar years)
¹¹ Misalignment Duration of
year on the end lunar year
of lunar year
0 0.0000000 - - 355 -1 (leap)
LeapM1 +0.3670626 354 - -
SimpleM2 +0.7341253 - 384 -
Etc. 3 +0.6317763 354 - -
4 +0.9988389 - - 355
5 +0.3659009 354 - -
6 +0.7329635 - 384 -
7 +0.6306146 354 - -
8 +0.9976772 - - 355
9 +0.3647392 354 - -
10 +0.7318019 - 384 -
11 +0.6294529 354 - -
12 +0.9965155 - - 355
13 +0.3635775 354 - -
14 +0.7306401 - 384 -
15 +0.6282912 354 - -
16 +0.9953538 - 384 -
17 +0.8930049 - 384 -
18 +0.7906560 - 384 -
SimpleM19 +0.6883071 - - -
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