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Conventional wisdom has it that about 1600 years ago, the latter Hillel utilized his Sanhedrin to sanctify the Hebrew calendar as we know it today until the year 6000. (Presumably by that point we'll have something else.)

If I understand correctly, Hillel's calendar was based on the astonomy of the time, and as such over the course of its ~1800 year run, it will have unintentionally lagged several days behind the solar calendar.

Has anyone worked on what a new calendar would look like? Could it maintain the notable features of the current one (e.g. Purim never on shabbos) and yet still get the updated formula for solar leap years right?

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    We already have a guide for the new calendar. It involves witnesses, courts, moons etc.
    – Double AA ♦
    Commented Dec 26, 2012 at 17:06
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    @DoubleAA, all fine and good, but when it was handled by courts month-to-month, they still used their knowledge of astronomy to determine whether to make it a leap year, as well as what range of events were acceptable as plausible testimony. I'm still trying to understand how that would work.
    – Shalom
    Commented Dec 26, 2012 at 17:20
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    This question presupposes that Chazal had an incorrect or incomplete understanding of astronomy. On what do you base that assumption?
    – yoel
    Commented Dec 26, 2012 at 17:42
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    @yoel On looking outside with a stopwatch in three months and noticing that the day where sunrise to sunset is exactly the same length of time as sunset to sunrise is March 20 not a few days later. Try it one time and tell me what you find. (Not to mention sending satellites to planets such as Uranus or Neptune.)
    – Double AA ♦
    Commented Dec 26, 2012 at 18:33
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    @yoel Also it does not presuppose that. It only presupposes that they didn't use a perfect understanding in making this calendar. Perhaps they had a better understanding but didn't use it because it was too complicated. (Can you imagine Tosfot writing out Maxwell's equations in language like this judaism.stackexchange.com/questions/22870/…? Oy Gevalt.)
    – Double AA ♦
    Commented Dec 26, 2012 at 18:35

2 Answers 2

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Amazing what you can see when you look.

Irv Bromberg at the University of Toronto discusses an adjustment. Currently there are 13 months in 7 years out of every 19; the new formula would involve 130 leap years out of every 353.

As he clarifies, witnesses only determined when exactly the new month would start; the Sanhedrin could decide whether to make it a leap year.

As far as the problem with the existing system:

... the average moment of the northward equinox ... drift[s] progressively earlier in the Hebrew calendar year, at a rate that is currently about one day earlier per 220 years. Until today the average equinox has drifted about 6 days earlier than the start of Nisan, in Jerusalem.

He observes that if we continued the current system for another 4000 years, we would actually get Passover not in the springtime anymore, violating a key design requirement. (My comment -- fortunately Hillel said "eh this will get us by for 1600 years and then we'll see how it's going"; so we won't be forced to hit that point.)

See Wikipedia for more.

Just for consideration, the average length of a solar year, in days:

  • As measured by scientists today: 365.2424
  • As used by the Gregorian calendar by most of today's world: 365.2425
  • As the Hebrew calendar has been doing for 1500+ years: 365.2468
  • As used by the Julian calendar in Europe until 500 years ago: 365.25

So Hillel's approximation was good for its time, and had an expiration date that allowed enough time to develop an alternative, (?), but not long enough that it would fail its design requirements. Not too shabby.

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  • The adjustment is an interesting albeit radical idea, but it could not possibly be implemented without unanimous agreement of virtually all subgroups in Judaism. And the chance of that ever happening is close to nil.
    – Dave
    Commented Dec 27, 2012 at 14:45
  • @Dave, the current system will still work okay for the next 227 years. At that point ... we'll figure it out.
    – Shalom
    Commented Dec 27, 2012 at 15:14
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    What happens in 227 years? Won't it take about 4,000 years for Pesach to become a critical issue?
    – Dave
    Commented Dec 27, 2012 at 17:48
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    @Dave, my understanding is that Hillel and his Sanhedrin only sanctified the months until the year 6000. At that point we'll need a Sanhedrin to do it.
    – Shalom
    Commented Dec 27, 2012 at 20:08
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    @Dave The classic (joke) reason: they got tired of saying "Mekudash! Mekudash!" so many times.
    – Double AA ♦
    Commented Feb 22, 2013 at 7:57
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When we have another Sanhedrin, we can fix it. It won't be a fixed calendar then, according to the Rambam; we would return to the original system of witnesses for the new moon, and deciding on the leap year depending on the seasonal weather. They could use modern astronomy for checking the witnesses. The only reason they needed Hillel the Nasi's calculations was that it yielded a system that was both accurate enough and simple enough.

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