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Re: Lunisolar Cycle Multiples of Short Lunar Cycle

by Irv Bromberg :: Rate this Message:

On 2009 May 15, at 14:22 , ELITE 3000 wrote:

But which cycles are the most accurate in terms of lunation period and mean year compared to the mean solar year (365.242 189 67 days (365 d 5 h 48 min 45 s))

Irv replies:

That is 365+31/128 days, which doesn't approximate any equinox or solstice -- why do you care about it?

That average also keeps getting shorter due to tidal slowing of the Earth rotation rate, whereas in the present era the mean northward equinoctial year and the mean north solstitial year are nearly constant, and will remain that way for the next 4-5 millennia and 11-12 millennia, respectively, enabling good approximation with simple fixed arithmetic leap cycles.

Check out the various solar year lengths that are evaluated for drift relative to each of the equinoxes and solstices in my "Solar_Calendar_Drift" spreadsheet at:

http://individual.utoronto.ca/kalendis/leap/Solar_Calendar_Drift.xls

You can replace any of the entries with your own to see how they look, just follow the format of the other entries.

ELITE continued: and the mean lunation period (29.530589 days (29 d 12 h 44 min 2.9 s)) (correct me if I have the mean solar year/syndonic month slightly off)?

Irv replies: That mean lunation period is a tad long for today. The mean synodic month is getting progressively shorter. If one insists on using a fixed lunation period for a lunar calendar or a lunisolar calendar, then it is better to choose a period that is intentionally too short by about 1/2 second, so that its era of best accuracy will endure longer. Check out the various lunation periods that are evaluated for drift in my "Lunar_Calendar_Drift" spreadsheet at:

http://individual.utoronto.ca/kalendis/lunar/Lunar_Calendar_Drift.xls

In this case you will find that there is a very broad and comprehensive range of lunation periods represented by the many cycles evaluated in the spreadsheet. Those that are not represented, however, are the very long lunisolar cycles that are the topic of this thread, so again, feel free to replace any of the entries with your own to see how they look, just follow the format of the other entries.

-- Irv Bromberg, Toronto, Canada

<http://www.sym454.org/leap/>

<http://www.sym454.org/lunar/>

<http://www.sym454.org/seasons/>

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