Tuesday, November 18, 2008

Molad - Moon's Race against Earth

From articles written for the Yated Neeman (USA) by Avraham Broide
(Jerusalem based translator and journalist. phone: 02-5856133; email: broide2@netvision.net.il


The moon is an erratic traveler, sometimes zipping through its monthly circuit at high speed, and sometimes gliding along at a more leisurely pace. Because of this, the difference between a long month and a short month is sometimes as long as thirteen and a half hours.

Why does the moon speed and slow down with such maddening irregularity?

Let us explore what the Molad, or "New Moon."

About every 29.5 days, the moon begins a new month at the Molad, soon after it passes directly between the earth and the sun. Sometimes, the moon blocks the sun's light from earth during this maneuver and we experience a solar eclipse. Why does the moon take varying times to run this monthly race?

The answer is based on the difference between circles and ellipses. If the moon and earth traveled in perfectly circular orbits, Molads would always arrive with (almost) perfect regularity, since objects traveling in circular orbits never alter their speed.

However, since the moon and earth have elliptical orbits, and objects move in elliptical orbits vary their speeds, the earth and moon constantly slow down and speed up depending on their place in orbit.

Illustration: The earth moves slowest when it is furthest from the sun on the left, and speeds up as it moves nearer the sun towards the right.  

This is why the moon has irregular molads!

If the moon is moving slowly towards the end of the month and the earth is moving faster, the moon takes longer to catch up with the sun-moon-earth axis and you have a longer month. The opposite happens when the moon is moving fast and the earth is moving slowly. In such a circumstance, the moon catches up with the sun faster and you have a shorter month.

Illustration: In this example, the moon is near earth and moving faster, while the earth is far from the sun and moving slower.

Some time after the Churban, Hillel II created the modern calendar which avoids the irregular-month problem by using the average month-length mentioned by Raban Gamliel (Rosh Hashana 25a): "So I received from the house of the father of my father; the renewal of the moon is not less than 29 and a 1/2 days, 2/3 of an hour, and 73 parts (1/18th of a minute)."

With this average molad, it is very easy to calculate the average molad of any month of the past or future.

However, incredibly accurate as Raban Gamliel's average month-length may be, it is gradually becoming less precise due the "stretching of time."

What is the "stretching of time?" Not some obtruse, Einsteinian concept, but simply the gradual lengthening of the day due to the moon's constant tugging on the world's oceans. Friction caused by the tides' flow and ebb is slowing down the world's spin, lengthening the days by about 0.00175 seconds per year, and due to this our modern days are about 1.75 seconds longer than the days of a thousand years ago.

Since Raban Gamliel's average month-length is tailored for the shorter days of the past, the lengthening days have gradually pushed Chazal's molad so far backwards that unlike the time of Hillel II when it was accurate to milliseconds, it is now off by about 0.6 of a second per month. These small differences have added up and nowadays, on average, the average molad calculation runs about two hours late!

This does not matter, since the Chazon Ish lays down a general rule in connection with a similar issue that Chazal's measurements do not have to absolutely coincide with reality. Also, using a chelek (1/18 of a minute) as his smallest unit, Raban Gamliel could in any case not have expressed the molad average with more accuracy.


We mentioned that the Molad calculation began ticking from the time of Ma'asei Bereishis. If so, what is the meaning of Hashem's command in Egypt (Shemos 12:2), This month shall be for you the first of months?

In his fascinating discussion of this verse, the Ramban not only explains this point, but also resolves a triple contradiction.

First, he explains that This month shall be for you the first of months is saying that just as it is a mitzvah to constantly remember Shabbos by calling the days rishon b'Shabbos and sheni b'Shabbos, so it is a mitzvah to start the counting of the months from Nissan, in order to remember the redemption from Egypt.

But how can one say that the count begins in Nissan? The year begins with Rosh Hashana in Tishrei as it says (Shemos 34:22), And the festival of ingathering [Sukkos] at the changing (tekufas) of the year? The Ramban answers that although we call Nissan the first month and Iyar the seventh month, this does not mean that they are the first or seventh months of the year, but that they are the first or seventh month since our redemption.

The Ramban now raises another difficulty. How why do call the months by the names Nissan, Iyar, etc? Isn't this a violition of the Torah's command to name them Rishon and Sheni after Yetzi'as Mitzrayim?

To answer this question, he cites the Yerushalmi (Rosh Hashana 1:2) that states, "The names of the months came with them from Bavel." In other words, the Jews innovated a new month innovation system after returning from the second galus. Why? In order to fulfill the verse (Yirmeyahu 16:14,15), It will no longer be said, as Hashem lives who raised bnei Yisroel from the land of Egypt, but, as Hashem lives who raised bnei Yisroel and who took bnei Yisroel from the land of the north [Bavel].

"We reverted to called the months the names they are called in Bavel to be a reminder that we were there and that Hashem, may He be blessed, raised us from there," the Ramban concludes. "Because these names, Nissan, Iyar, and the rest, are Persian names, and are only mentioned in the sefarim of the prophets who were in Bavel (Zechariah 1:7, Ezra 6:15, Nechemiah 1:1) and in Megillas Esther (3:7). ...And until today, the nations in the lands of Persia and Madai, so they call them Nissan and Tishrei and all of them, like us. And so we make remembrance, with [these] months, of the second redemption, as we had made until now of the first [redemption]."

Actually, the people in Bavel pronounced them a little differently, for example, Simanu instead of Sivan, Du'uzu instead of Tamuz,  and Arakhsamma instead of Marcheshvan. Also, they counted Shevat before Teveis. But our version is close enough to eternally remind us of our redemption from the land of Nevuchadnezer and Haman.


In light of the Ramban's statement that the Hebrew month-names and their numerical symbols serve such important functions, how can we use non-Jewish month names such as January and February, that remind us neither of Yetzias Mitzrayim, nor of our escape from Bavel?

One intriguing answer is that, in the Torah view, non-Jewish months are not months at all as their timing is purely arbitary and has nothing to do with the Molad. In fact, the earliest Roman calendar created in about 3008/753 BCE by the mythic first king of Rome, Romulus, did not even have twelve months, but only ten! This early ten month system helps explain a surprising incongruity connected with these month's names.

Most of the first four months are named after false gods, raising a sha'alah how we are permitted to use them. Martis was the god of war, Aprilis probably refers to hog raising, Maius was an Italian god, and Junius was yet another god.

By the time he reached the fifth month, Romulus' imagination seems to have ran dry as labeled the remaining six months as 5th, 6th, 7th, 8th, 9th, and 10th, or, in Latin, Quintilis, Sextilis, September, October, November, and December.

Since this ten month year had a miniscule length of only 304 days, far less than the solar year of 365 days, in about 3061/700 BCE, the Romans tacked two more months to the year, Januarius and Februarius, stretching it to 355 days.

Centuries later, Julius Caesar, made the names of the last six months a joke when he shifted the beginning of the year from March to January, so that the names September, October, etc., no longer make any sense. Also, Quintilis was renamed Julius after Julius Caesar, and Sextilis was later renamed Augustus after Augustus Caesar, bringing the month's name to their present form. 

All this makes it obvious that the secular months have nothing to do with our lunar year. They are not months in the Torah meaning of the word, and thus one can argue that using them does not constitute a substitute for the names of the Hebrew months.

Of course, it is no big mitzvah to use them either.

(Sources: Duncan David Ewing, "The Calendar," 1999, Fourth Estate, London. Source of molad information: Dr. Bromberg Irv of University of Toronto, Canada, "Moon and the Molad of the Hebrew Calendar." )  


  1. I find the statement curious:

    "Also, using a chelek (1/18 of a minute) as his smallest unit, Raban Gamliel could in any case not have expressed the molad average with more accuracy."

    The Bavli and the Yerushalmi both quote a baraita which gives units of time far smaller than the chelek. It can be found in the first perek of Yerushalmi Brachot.

  2. Gedaliah, Please cite the location of the Yerushalmi in Berachos and I will investigate whether it is possible to resolve your question.

    Avraham Broide.

  3. Avraham,

    Daf 5a in Brachot. Make sure you see it with the accompanying note of the GR"A for a corrected nusach. Also the length of a rega is mentioned in Bavli Brachot 7a and Avodah Zarah 4a.


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