[Avodah] Molad Alert: Friday night

[Micha Berger]

On Fri, Mar 04, 2011 at 10:14:23AM -0500, Zev Sero wrote:
>> IIRC, the real Molad is a good deal different from the one we announce.

> Of course it is.  The real length of a month is different every time.
> What we use is the average length, rounded to the nearest chelek.

Actually, today's average is longer than the molad. The molad was
known since at least Galus Bavel, although I believe it dates back to
Maamad Har Sinai. But at that time it was longer than the average lunar
month. Then the tides pull back on the moon, the moon slows down, its
orbit shrinks and the month is getting shorter at a rate of something
like 3 sec each century. More precisely, the usual formula (a 2nd order
approximation) is given by LE Doggett as:
    S = 29.5305888531 + 0.00000021621 * T - 3.64E-10 * T^2
where all time is given in days, and T is days since 1/1/2000. (I pulled
it from the web, obviously.)

Hipparchus found the average over 345 years. Given that the first year
had an "astronomical molad) of a little over 3 seconds longer than the
year he took that measurement, his average should have been off by 1-1/2
sec. But it wasn't. Instead of getting 3024169 hours in 4267 lunations,
he should have gotten around 3024189 hours (4267 months * 16.5 sec/month
+ 3024169). How was he 19-1/2 hours off, which shifts the average by
16.8 second (15.3 from the erroneous number he should have gotten)?

Meanwhile, the month is still shrinking, so that when we get to the 4th
or 5th cent CE the molad was within a cheileq of a lunar month. Just
around when we finalized the calendar algorithm currently in use -- give
or take a single issue of dechiyah that waited for R' Saadia Gaon's day.

In the mid-4th century, the currently announced molad would have been
accurate for mid-way between the Nile and the Euphrates. (Not Alexandria,
the leading edge, as I wrote before, but the mid-point.)

But the tides are still there and the month is still getting shorter
-- and we're still using the same molad. At this point, the molad is
something like 108 chalaqim off. Alternatively, we could keep the molad
correct and say the "timezone" is sliding east. Not sure why we would
want to, but enough web sites and books do this excercise. So, we could
say that we now compute the molad accurately for Kandahar, Afghanistan.

>> There is also the Molad according to the RAMBAM and at least one
>> other person.

> This is definitely not true.  The Rambam has the same molad as everyone
> else.  If there's someone who has a different one, I'd like to know
> who it is, and what possible basis they might have.

I think RYL was remembering a machloqes about notation. The Rambam used a
Moslem-style clock, where the day starts at 6pm. Therefore, he would have
us announce the molad using numbers that start 6 hours earlier than we do.
Some molad, as RZS notes there is only the one, but different way of
describing it.

:-)BBii!
-Micha

-- 
Micha Berger                 Life is complex.
micha at aishdas.org                Decisions are complex.
http://www.aishdas.org               The Torah is complex.
Fax: (270) 514-1507                                - R' Binyamin Hecht