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The establishing of Rosh Chodesh, the New Moon, did not originally depend on the sighting of the moon, but completely on astronomical calculations. "What?!  But I thought ORIGINALLY the new moon had to be witnessed?" you probably said to yourself as you read this.

Consider this - during the forty years that the Benei Yisrael  were in the desert, they were covered by the pillar of cloud by day and the pillar of fire by night, making it impossible for them to make any astronomical sightings.  Since both the sun and moon were invisible to them, it would have been impossible for them to construct a calendar based on actual observation.  This is clear evidence that calculation was the original means of determining the calendar.  Witnesses were not used.  This situation existed for 1100 years, from the time of Moshe until the time of Antignos of Socho in 3548 (213 b.c.e).

Following is further evidence...

Shemot 12:2 "This month shall be for you the beginning of months..."

It is significant that at this juncture G-d did not instruct Moshe and Aharon to relay the content of this message to the Benei Yisrael.  Surely the word לָכֶם "lachem" (for you), implied that the fixing of the new moon was a commandment applicable to each and every Jew!  Failure of G-d to issue the customary instruction: "say to all the Benei Yisrael, etc.," therefore indicated that the determining of the new moon was something reserved for the elders of the people, a court of experts, and was not something incumbent on the individual Jew.  This is why these instructions were address to both Moshe and Aharon in their capacity as the experts at the time.  The word lachem, in this instance means: "to the likes of you, to trained experts."

If proof were needed that we base our calendar on astronomical calculations rather than the sighting of the moon, consider the fact that during the wanderings of the Benei Yisrael in the Wilderness for 40 years when their encampment was totally enveloped by the Ananei HaKavod, G-d's "Clouds of Glory", neither the people nor their leaders were able to sight the moon.  They did not even see the sun by day either but depended totally on the pillar of cloud or fire to light the way for them.  This is confirmed by Nechemya 9:19 "You in Your abundant compassion did not abandon them in the Wilderness.  The pillar of cloud did not depart from them to lead them on the way by day, nor the pillar of fire by night to give them light in the way where to go."

How would the the Benei Yisrael have been able to fix the date of the new moon unless they had based themselves on their astronomical calculations?  Clearly, the principal method of determining the new moon is based on calculations.  We have an old-standing tradition that 5 of the 12 months of the year always have 30 days whereas 5 other months always have 29 days.  the remaining 2 months fluctuate between 29 and 30 days respectively.  In some years both of these months have 30 days.  In some years both have 29 days, and in some years one of them has 29 days whereas the other month has 30 days.  The two months which are subject to these variations are Cheshvan and Kislev.

We have another tradition that the first day of Tishrei is New Year's day (Rosh HaShanah), and that according to a ruling handed down by Moshe from Sinai each "month" (lunar orbit) consists of 29 days, 12 hours and 793 parts (chelakim - the hour is divided into 1080 equal parts - therefore the lunar month is 29 days, 12 hours, 44 minutes and 3 seconds). (Rosh HaShanah 25)  All this is based on Divrei HaYamim Alef (1 Chronicles) 12:33 "Of the benei Yissachar, men who knew how to interpret the signs of the times to determining how Yisrael should act; their chiefs were two hundred, and all their kinsmen followed them."  No other matter requires as much knowledge and insight as determining the times of the calendar, the dates of the festivals based on comparison with the seasons determined by the solar calendar.

Of course, if the new moon has been sighted everybody knows that a new month has begun, etc.  It is easy then to calculate the tenth of the month to determine Yom Kippur and the 15th of the month to determine the first day of Sukkot, etc.  The Sages needed to know what calculations are required in order to inform the people ahead of time what to expect and in order to check whether sightings of the new moon which had been claimed were in fact possible according to their charts.  It is this aspect which the verse from Divrei HaYamim Alef dealing with the benei Yissachar deals with.

Note that during the time of David and Yonatan calculations formed the basis of the determination of the new moon as David said to Yonatan (Shmuel Alef 10:5) "Tomorrow, on the new moon I will sit beside the king..."  If the new moon had been determined merely by sighting, how did David know it would be observed on the morrow?  Perhaps there would not be a sighting of the new moon by then?  It is clear then that the date was determined by calculation if sightings failed to confirm these calculations.  In fact, from that episode in Shmuel Alef (Samuel 1) it is clear that already at that time the Sages arranged for two consecutive days of the new moon being observed seeing that we read in verses 24-27 of the same chapter, "The new moon came and the king sat down to partake of the meal...but David's place remained vacant.. That day however Shaul said nothing... But on the day after the new moon, the second day, David's place was vacant again..."  It is clearly impossible to say that the day described as "the second day" refers to another new moon the following month and that this is why they called it "hachodesh hasheni" (the new moon, the second day).

Shaul asked Yonatan (v27) "why did not the son of Yishai come to the meal yesterday or the day before?"  The story goes on, "Yonatan rose from his seat angrily and he did not eat on the second day of the new moon."  Clearly the date of the new moon was determined by means of calculations.  This system was in effect for 1100 years from the time of Moshe until the time of Antignos from Socho who, together with Shimon HaTzadik, was the leader of the Jewish people around the time Ezra and his colleagues came to Eretz Yisrael from Babylon.  (Moshe died in 2488 after the creation of Adam whereas Antignos lived around 3460 years after the creation of Adam.)  Two of Antignos' students, Tzadok and Beissus, were the ones who misunderstood their teacher's meaning when he exhorted his students not to serve G-d like servants who serves a human master for the sake of reward, feeling entitled to it.  Antignos urged his students to relate to the service of G-d as does a servant who volunteers to serve his master out of love and not out of a desire for reward.  These two students thought that there was no system of reward and punishment in Judaism as a result of which they forsook the path of Torah.  A by-product of their heresy was that they raised questions against the system of determining the time of the new moon, claiming that the principal mitzvah in observing the commandment of sanctifying the new moon was the sighting of it not the calculations on paper.  Such a new thesis forced leading rabbis of that time to respond and to prove to these heretics that their calculations were accurate and more reliable than sightings so that Rabban Gamliel came out publicly saying not to be too concerned about whether actual sighting had taken place.  He claimed to have had a tradition from his grandfather that the month (lunar orbit) is never shorter than 29 days 12 hours and 793 parts.  These words of Rabban Gamliel prove that he did not base his calendar on sightings but on astronomical calculations.

We have an explicit Mishnah (Rosh HaShanah 25) which states that "if both the elders of the court and the entire nation had clearly seen the new moon but it became night while the elders examined witnesses who testified to the sighting of the new before the elders were able to pronounce the new moon on the day just concluded, they would declare the month to have had 30 days."  This proves that the elders did not rely principally on the sighting.  Had they done so, how could they have added another day to the month seeing not only the witnesses but they themselves had sighted the new moon on the previous night?  Clearly, if they decided to make that month one of thirty days in spite of the sighting, they must have based themselves on their calculations.

There is even more compelling evidence...

The Mishnah at the end of the second chapter in Rosh HaShanah records that two witnesses appeared claiming to have sighted the new moon at its appropriate time, i.e. the night between the 29th and the 30th of the month.  They also claimed that on the following night, i.e. the night of the 31st, the moon had not appeared in the sky.  Rabban Gamliel accepted their testimony.  If Rabban Gamliel and his colleagues had been basing their declarations of the new moon only on sightings, how could he have accepted such testimony which contradicts all we know about the behavior of the moon?  Surely, the fact that the moon did not appear on the following night meant that the witnesses had lied in the first place!  Clearly, Rabban Gamliel relied on his calculations in the first instance and when these proved that the new moon had been due to appear when it did he accepted the visual evidence that it had indeed been sighted on the appropriate night.

As to the statement of the Sages (folio 24) that Rabban Gamliel had a reproduction of the sky on the wall of his study which he employed to instruct laymen, the meaning is that he wanted to convince the supporters of Tzadok and Beissus of his absolute competence in astronomical matters from month to month.  He wanted to show them beforehand in which manner and at what angle sightings of the moon after the end of the present month would occur.  When these students noticed that Rabban Gamliel had correctly predicted where and when in the sky sightings of the new moon would occur, he mananged to discredit Tzadok and Beissus who had tried to undermine the authority of the Jewish Supreme Court.  As a result, the allegations against the calendar calculations of the leading elders of the Jewish people ceased.  Nonetheless, the practice of encouraging people to come forward as witnesses to new-moon sightings continued but primarily as a reminder of an established custom, not as something of halachic necessity.

It is unanimously agreed that the authority to determine calendar adjustments is vested in the hands of the Jewish Supreme Court or its equivalent as something handed down from the time of Moshe, provided such court is composed of the most knowledgeable and G-d-fearing people of their generation.  This is the law which G-d commanded to Moshe in our verse here.  The words הַחֹדֶשׁ הַזֶּה לָכֶם (hachodesh hazeh lachem - This month shall be to you), may therefore be translated as "you have authority to delegate the adjustments which may have to be made to this month."

Thus far the commentary of Rabbeinu Chananel.

The authority delegated by G-d to the Rabbinical authorities is of such fundamental significance that we read in Sanhedrin 42 that if the Jewish people had not been granted the opportunity to perform any other commandment except to recite the benediction over the new moon once a month and to the thereby welcome the eternal presence of the Shechinah, this would be deemed sufficient for them.  They base this on the wording הַחֹדֶשׁ הַזֶּה (hachodesh hazeh - this month) here and זֶה אֵלִי וְאַנְוֵהוּ (zeh Eli ve'anvehu - this is my G-d and I will exalt Him) in Shemot 15:2.  What this Midrash is trying to tell us is that the verse here is an explanation of the peculiarly worded text of the benediction recited when blessing the new moon.  It is an allusion to the Jewish people as a spiritual concept, so called as it is a crown, sanctified and the exclusive property of the people of Yisrael, who are referred to in Yeshayahu 46:3 as "transported by G-d on His arms ever since their inception" (in the house of Lavan).  Seeing that he who utters this benediction finds himself in the presence of the Shechinah, he must recite it while standing (not while seated).  This ensures that he is conscious of the necessary awe when in the Presence of G-d.

Reciting the benediction over the new moon is equivalent to testifying to the fact that G-d created the universe and all that is in it.  This is the principal pillar of our religious faith.  Seeing the moon renews itself month after month makes it easy to understand that G-d created one universe after another.  Some unidentified Sages have said that the black color we observe on part of the moon serves as a reminder of the Benei Yisrael who are in exile and who count their months based on the lunar orbits.  Concerning this phenomenon Shlomo said in Shir HaShirim 6:10 "beautiful as the moon, brilliant as the sun."  G-d granted beauty to the moon and brilliance to the sun.  The reason is that the moon resembles woman's lower physiognomy in that it is activated by the male.  The moon similarly receives its input from the sun.  This is also the meaning of the statement in Ketubot 59 "woman exists for the sake of beauty" (rather than for the performance of menial labor).  Speaking of the sun, however, Shlomo used the term בָּרָה (barah), as it is clear, distinct.  See that Shlomo used different adjectives in describing moon and sun it is clear that the moon lacks brilliance.  You need not be surprised at the choice of metaphors by Shlomo as the Shechinah which accompanies the Jewish people in their exile and which reflects the strength of the moon is also feeling the pain of the Jewish people in their troubles.  We know this from Yeshayahu 63:9, "In all their troubles He was troubled."


The Seven Cycles

There are seven astronomical bodies, and each has its particular cycle.  This is their order:

1. First sphere, closest to the earth, is the Yareach (Moon).  It shines with reflected light.
2. Second sphere is called Mercury.  In Hebrew it is called Kochav, which literally means "star."  Some say this is because it rules over the destiny of the stars.
3. Third sphere is called Nogah (Venus).
4. Fourth sphere is the Shemesh (sun), which makes a complete cycle every year.
5. Fifth sphere is called Maadim (Mars).
6. Sixth sphere is called Tzedek (Jupiter).
7. Seventh sphere is called Shabatai (Saturn).

- Bachya; MeAm Lo'ez