[Avodah] Where is the Molad announced for?

[Micha Berger]

On Wed, Dec 23, 2020 at 05:22:10PM +0200, David Cohen via Avodah wrote:
> I don't think that they *first* picked an exact meridian and *then* set the
> molad to exactly correspond to the moment of the mean conjunction expressed
> in the mean solar time of that meridian.  Note that the molad is expressed
> to the precision of a chelek, and mean solar time changes by one chelek for
> every 50 "seconds of longitude."  At the latitude of Jerusalem, that's
> about 1.3 km.  You'd have to explain why they chose exactly the meridian
> that they did, and not 2 km to the west or 2 km to the east, which would
> result in the molad being one chelek earlier or later.

We aren't talking one cheileq, though.

I'm going to step WAY back and start from alef. That means that I will
be talking down to many people as I start, and hopefully fewer and fewer
as I continue.



There are two rounding issues with the molad, because we use the word
"molad" to mean two things:

1- The halachic estimate of the average *duration* between two new moons.
IOW, 29 days, 12 hours, 44 min 1 cheileq.

2- The time of a particular new moon. Like when the Chazan announces,
"The molad will be at ...."

About issue #1, the interval of the molad:

The time between new moons is not a constant. The average time between
new moons is also not a constant, it drifts down the centuries. (And even
more weirdly so since we are measuring it using days and parts of a day,
which also changes length compared to seconds on an atomic clock over
the centuries.)

So there is an error between the estimate halakhah decided was "good enough"
and the exact value. In fact, since the interval between new moons is an
irrational number of days, there is no way to express it as an exact number.
Like pi or the square root of 2, for which halakhah also has sanctioned
estimates -- 3 and 1-2/5, respectively.

But this error in estimation, at any point since Adam to well past the
year 7,000 is to the order of chalaqim, and really is within the room
of saying Chazal estimated.

About issue #2, the time of the molad:

The effects of the error in #1 are cumulative, adding up 12 or 13 times
per year, year after year, century after century. Here the difference
between the announced molad and the time the new moon would be on
average is to the order of minutes.

How many minutes? Well, that depends which clock we're using to announce
it in. We are definitely using standard hours, not solar ones. And we
are definitely using local time rather than standard time, since the
molad calculations predates trains and the invention of time zones
(as R/Prof Levine pointed out). But which local time?

The obvious assumption is Yerushalayim local time. But in that case,
the error in the *time* of the molad would be
2 hours 42 sec: nowadays
22 min, 25 sec: when our calendar was established
15 min, 27 sec: at its minimum, 10 years before the first Chanukah (164bce)

So our choices, as I see it, is:

1- Explain it is okay for the time of the molad to be 15-22 min off in the
   days of chazal, and stick to the common belief that the time is
   Y-m local.

I replied to Prof Levine forwarding the OU's claim that it is indeed
Y-m standard time. I wrote to say I found this implausible. 15-22 min
off is not a small error.

To the extent that I cannot believe that's what the Rambam means either.
And was looking for how that implication of the Rambam's words isn't a
valid inferance.

2- Use for the meridian where the local clock is 15 min 22 sec later,
   so the minimum error (164bce) is zero. That's 4 deg 7 min east of
   Yerushalayim, which is about 1/3 of the way to Bavel.

3- Use the meridian where the local clock is 22 min 25 sec later, so
   that the error between astronomy and the *time* of the halachic
   molad was zeros at the end of Chazal's day. 

I was advocating for the third option, because it is a convergance of
three issues:
    a- the meridian where time is 22 min 25 sec later than Y-m arguably
       runs in the middle between di be'ar'a deYisrael di beBavel.
    b- this eliminates the error in the *time* of the molad is the era
       when our calendar was set up, and
    c- it is also the era when the *interval* between molads ("molad"
       definition #1) was correct to the average time between astronomical
       real new moons was within a cheileq. (And it includes the time
       when it was 0.)

You can object to my support of #3 by saying that the precision of the
interval is no big deal without touching my objection to the common
assumption of Y-m standard.

Tir'u baTov!
-Micha

-- 
Micha Berger                 Our greatest fear is not that we're inadequate,
http://www.aishdas.org/asp   Our greatest fear is that we're powerful
Author: Widen Your Tent      beyond measure
- https://amzn.to/2JRxnDF                      - Anonymous