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Re: Ariadne's thread
Posted:
Nov 20, 2011 6:51 AM
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Milo Gardner informed me about a 405-lunation
period in the Maya calendar. Further periods were
13 and 20 days, combined in the Tzolkin of 260
days. How long are 405 lunations? 15 and 17
lunations counted in the 30 29 30 29 30 29 30 ...
mode are 443 and 502 days respectively.
17 15 17 15 17 lunations yield 502 945 1447
1890 2392 days for 17 32 49 64 81 lunations
respectively. One lunation is 29 days 12 hours
44 minutes 2.9 seconds (modern average from
1989 AD). 81 lunations are 2391.977... or
practically 2392 days, mistake less than half
a minute per lunation, or five hours in a lifetime.
5 periods of 81 lunations are 405 lunations,
11959.8885... or practically 11960 days,
920 periods of 13 days or 596 periods of
20 days or 46 Tzolkin, periods of 260 days.
The Tzolkin and the rounded year of 365 days
were combined in the Calendar Round of 94900
days. An actual year is a little longer than 365
days, 365.24219879 days, called a tropical year.
Is there a reasonable way to combine the Tzolkin
with the tropical year? Let us find out. 10 Tzolkin
are a little more than 7 tropical years, while
7 Tzolkin are slightly less than 5 years:
10/7 (plus 7/5) 17/12 24/17 31/22 38/27
45/32 52/37 59/42
59 Tzolkin are 15340 days. 42 tropical years
are 15340.172... days or practically 15340 days.
73 Tzolkin = 18980 days = 52 rounded years
59 Tzolkin = 15340 days or 42 tropical years
46 Tzolkin = 11960 days or 405 lunations
I don't know whether a period of 59 Tzolkin
or 42 tropical years played a role in the Maya
calendar, but the numbers make sense.
The idea of the Maya calendar may have been
a solid structure provided by the 260-day count,
while the astronomical cycles were 'hung' into
the calendar whose weight was carried by gods
('burdened with bundles of time').
The synodic Venus year lasts 583.92 days,
the synodic Mars year 779.936 days. The Maya
counted 584 days for the Venus year, and may
have counted 780 days for the Mars year. Two
Calendar Rounds are 18980 days or 325 rounded
Venus years, while 3 Tzolkin are one rounded
Mars year.
Next time: a strange period of 819 days
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