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Re: Unhindered option RE: Cycles of interest RE: Lunisolar Cycle Multiples of Short Lunar Cycle

by Irv Bromberg :: Rate this Message:

On 2009 May 19, at 14:10 , Brij Bhushan Vij wrote:
For my calculations I use the value 29.53058881 days (29d 12h 44m 2s.873184). Mean values as shown by me: MeanLunation =29.5305893733 (29^d12^m44^m2^s.92) is close enough to be practical, UNLESS there is a better value achievable, sir.

On 2009 May 19, at 15:31 , Irv Bromberg wrote:

I looked into this further and found that improving on the accuracy is very method dependent, so I have to say that that lunation period is about as accurate as one can use. I was just suggesting that it is not ideal to use an accurate lunation period for a lunar calendar intended to be used today and into the future, because the astronomical mean lunation period is getting progressively shorter. Instead, I suggest intentionally using a slightly shorter lunation period, which will allow the lunar approximation to serve with better accuracy for a longer duration until correction is necessary.

I had suggested a shorter mean month somewhere in the range of 2.0 to 2.5 seconds in excess of 29d 12h 44m. Compare with the Gregorian Easter computus which is about 2.7 seconds in excess, or the even shorter mean month used for the Dee Easter computus which is less than 2.4 seconds in excess, or the shorter still mean month used for the modern Hindu lunisolar calendar (Arya) of less than 2.3 seconds in excess. These shorter cycles will endure further into the future, provided that they are set up to be a bit late in the present era, then in the future they will drift earlier until they are accurate, and later they will drift late again (when the astronomical mean synodic month gets shorter than the cycle mean month). These cycles are shown in my lunar calendar drift spreadsheet at:

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

Irv adds, using Hindu mean month fractions from "Calendrical Calculations: Third Edition" by Dershowitz and Reingold:

(I hope I got the the following right, because I don't know much about the Hindu calendars. Any corrections would be appreciated!)

The Hindu synodic month used for the old Hindu calendar before 1100 AD, as documented around the 4th century in the Surya Siddhanta as 29 + 7087771 / 13358334 days = 29 days 12h 44m 2.8s, was about 1/2 second too short for the era when Hindus started to use that calendar, but is actually almost perfect for the present era.

Using the Lunar Calendar Drift spreadsheet cited above, with an epoch of 400 AD, the Surya mean month affords a mean lunar drift of <8 hours from 2400 BC to 6200 AD.

By contrast, the Arya lunar month, used as the mean synodic month for the modern Hindu calendar since 1000 AD, is 1577917500 / 53433336 days = 29 days 12h 44m 2 + 597062 / 2226389 seconds, or about 4/5 second too short for the era when Hindus started to use that calendar, and still about 1/2 second too short for the present era.

Using the Lunar Calendar Drift spreadsheet cited above, with an epoch of 1000 AD, the Arya mean month affords a mean lunar drift of <8 hours from 1000 BC to 8300 AD.

Anyone who is designing a fixed cycle lunar calendar for use today and for as long as possible into the future would be well advised to follow the Hindu examples, by choosing a mean lunation period that is intentionally slightly too short, to maximize the duration that the calendar will serve with reasonable accuracy, because the astronomical mean synodic month is getting progressively shorter in terms of the mean solar days that calendars need.

I arbitrarily picked the mean lunar drift limit of <8 hours. Anybody can view the charts in the spreadsheet after updating them for any desired epoch and choose whatever cutoff limit is desired.

-- Irv Bromberg, Toronto, Canada

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

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

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