# How accurate is the Molad?

To the best of my knowledge the Molad is every 29.5 days + 793 Chalakim. Is there any information showing if the current Molad calculation is accurate scientifically? If it is off by how much is it off? How far off culmitavely are we now from the actual timing of the new moon?

• One important thing to keep in mind is that the actual duration between successive new moons varies from month to month, so the fixed molad is an average value that differs from the actual value each month by a varying amount. Any difference between the official molad and the actual average is on top of that variation. – Isaac Moses Sep 24 '14 at 14:38
• @IsaacMoses Such variations would not be expected by people with a geocentric solar system where everything moves in perfect circles. – Double AA Sep 24 '14 at 19:43
• @DoubleAA nor even a heliocentric solar system where everything moves in perfect circles. – msh210 Sep 29 '14 at 19:39
• @msh210 I suppose but very few people (if any?) have ever believed such a thing. – Double AA Sep 29 '14 at 19:42
• @DoubleAA, really? Ask anyone on the street who's never taken any college-level math or physics courses, and who hasn't taken high-school physics within the past few years. I bet a good fraction of such people believe in a heliocentric solar system where everything moves in perfect circles. – msh210 Dec 29 '16 at 17:16

I would recommend having a look at this site. The maths is much too complicated for me, but the upshot is that our molad is two hours later than the molad when the calendar was formulated, and is getting progressively later every year. The author includes a chart (and good luck to you if you can read it) that indicates the relationship between the actual lunar conjunction and the molad.

The same author (Dr Irv Bromberg) has written a number of online articles that concern the Hebrew calendar, some easier to understand than others. He has also advanced various proposals for calendrical reform, which he refers to as the rectified Hebrew calendar. It's definitely worth a look.

• The system has auto-awarded the bounty. My carelessness in not paying closer attention to the time limit, but, it accomplished what I would have done, anyway. I will try to read one of your sources, at least, B"N, in a few days. Thanks for the good contribution & Happy Chanukah. – DanF Dec 30 '16 at 17:52
• The molad is averaging 6 hours after the conjunction. We aren't trying to get the time of no moon, but 6 hours later, when it's first visible to the naked eye again. – Micha Berger Aug 21 '17 at 23:20

Just because the "error" in the molad moment seems small doesn't mean that it is insignificant. The approximately +2h delay relative to the mean lunar conjunction moment currently causes the provisional date of Rosh HaShanah (before the application of the postponement rules) to land on the "wrong" date (one day later) in 2/24 = 1/12 of years.

• The math reasoning seems correct. Your answer would be a bit stronger if you can back it up with showing what has actually happened to the date, over time. – DanF Dec 28 '16 at 22:27
• Welcome to the site. Consider reading this short Beginners' Guide to the site. While I am big fan of Einstein, he was wrong about quantum mechanics, and about the expanding universe :) – mevaqesh Dec 29 '16 at 7:11

I am glad you asked this question, esp. just before Rosh Hashanna! I have been wondering about the same thing.

It states:

In the present era the median length of the lunar cycle is about 29 days 12 hours and 30 minutes, the MSM is slightly more than 29 days 12 hours and 44 minutes, the shortest lunations are about 29 days 6 hours and 30 minutes, and the longest are about 29 days and 20 hours. Thus the length of the synodic month varies over a range spanning about 13 hours and 30 minutes! These variations were greater in the past and will diminish in the future:

The longest lunar cycles occur when Moon is moving slowest (near apogee) and Earth is moving fastest (near perihelion). The shortest lunar cycles occur when Moon is moving fastest (near perigee) and Earth is moving slowest (near aphelion). The declining mean Earth orbital eccentricity tends to reduce the range of lunar cycle variations. The average lunar cycle (mean synodic month) has miniscule long-term change compared to short-term periodic variations.

The article is quite technical, and I wasn't able to understand much of it. But, the summary, above, mentioning aphelion and perihelion, makes sense, if you understand the basic concept that gravity causes an object to accelerate as the gravitational force increases. Thus, when the moon is closest to the Earth, it will have a faster orbit.

There are other web sources that may explain this concept simpler. B"N, I will edit my answer after Yom Tov. Again, great question!

• Both that link and Wikipedia conclude that due to tidal transfer of angular momentum, the accumulated change is about 2 hours on average, but the variation in the lunar cycle means that this corresponds to ranging from 12 hours early to 16 hours late. – Henry Sep 24 '14 at 22:26

This article explains how far things have drifted over time:

http://yourjerusalem.org/2010/02/jewish-calendar-is-slowly-drifting-off-track/

To summarize it, there are two calendars in use (lunar and solar), and both are not quite 100% perfect. Of the two, the lunar calendar is a lot more accurate (it is off by about 1/7th of a "chelek", very reasonable to simply round it down), and the molad has moved "off" by only about three hours (backwards - the month is a little longer) since the calendar was first instituted 1650 years ago.

• Two hours. The molad seems three hours off from Y-m, but it could only have drifted 2 hours since R' Hillel II's day. I think this means that we're really announcing the time of the molad as per a meridian that runs between Eretz Yisrael and Bavel, somewhere around the middle of the Jewish settlement of the time. Not Jerusalem Time. – Micha Berger Aug 21 '17 at 23:14
• Getting rid of the rounding, the difference is quite small. Rather than saying we're almost 3 hours off J-m Time (GMT +2:21), we are somewhat over 2 hours off Ur Kasdim (?) Time (GMT +2:44). – Micha Berger Aug 21 '17 at 23:16