Sunday, September 26, 2010

How the calendar might look with a Sanhedrin

It is an interesting exercise to attempt to compare what the Sanhedrin might announce to the calculated calendar that we use

While the molad is announced in terms of Jerusalem Solar Time, the tables below are shown in terms of Israeli clock time, based of the time zone (UTC +2). This allows the announced molad to be compared to the actual astronomical conjunction. The announced molad is based on the average calculated lunar cycle.

For the actual conjunction, sunset, and moonset times, I used the time charts at Time and Date along with a guess at visibility based on .6 of the time between sunset and moonset.
I assumed the Sanhedrin magically came into existence in time to declare Cheshvan because I did not want to deal with Rosh Hashannah of this year.

I also took the calculated Molad (Solar Time in Yerushalayim) and converted it to the Israeli Time Zone (UTC + 2) Clock Time as explained by Torah Tidbits in Yerushalayim. For example, the 5770 table gives the time as the Rambam declares it, as we currently announce it, and accordint to Israeli Clock Time. Thus, the time being shown is clock time rather than the actual announced time. This difference is based on the fact that noon in Solar Time (as used in the announced molad) is approximately 11:40 AM by the clock.

The point is to show what the effects would be with the various possibilities as the year progresses. I left out Rosh Hashanna because it seems that when you get a "two day" situation, Rosh Hashanna becomes Tishrei 1 and 2 rather than Elul 30 and Tishrei 1. The reason being that the entire idea of two days is based on the waiting for the declaration and the way korbanos are handled. Since Rosh Hashanna starts as soon as the declaration is made and everywhere in the country treats it as two days mishum safek, it is possible that the way we handle the same situation with every other month would be different. In any case, the entire set of comments was to show how the differences would propagate through the year.

Calculated Molad chart for the year 5770
Month Date Israel Time Rosh Chodesh
Cheshvan
Sunday, October 18, 2009
11:10 PM IST
Sun/Mon Oct 18/19
Kislev
Tuesday, November 17, 2009
11:54 AM IST
Tue/Wed Nov 17/18
Teves
Thursday, December 17, 2009
12:39 AM IST
Fri, Dec 18
Shvat
Friday, January 15, 2010
1:23 PM IST
Sha Jan 16
Adar
Sunday, February 14, 2010
2:07 PM IST
Sun/Mon Feb 14/15
Nisan
Monday, March 15, 2010
2:51 PM IST
Tue, Mar 16
Iyar
Wednesday, April 14, 2010
4:35 AM IDT
Wed/Thu Apr 14/15
Sivan
Thursday, May 13, 2010
5:19 PM IDT
Fri May 14, 2010
Tamuz
Saturday, June 12, 2010
6:03 AM IDT
Sha/Sun Jun 12/13
Av
Sunday, July 11, 2010
6:47 PM IDT
Mon, Jul 12
Elul
Tuesday, August 10, 2010
7:31 AM IDT
Tue/Wed Aug 10/11

This table shows the actual (astronomical) time of the new moon (conjunction) in Israel Time. This can be gotten from a number of tables, such as the Naval Observatory time showed in the previous posting.

Astronomical Conjunction chart for 5770
Month
Date
Israel Time
Cheshvan
Sunday, October 18, 2009
7:33 AM IST
Kislev
Monday, November 16, 2009
9:14 PM IST
Teves
Wed, December 16, 2009
12:39 AM IST
Shvat
Friday, January 15, 2010
1:23 PM IST
Adar
Sunday, February 14, 2010
2:07 PM IST
Nisan
Monday, March 15, 2010
2:51 PM IST
Iyar
Wednesday, April 14, 2010
4:35 AM IDT
Sivan
Friday, May 14, 2010
5:19 PM IDT
Tamuz
Saturday, June 12, 2010
6:03 AM IDT
Av
Sunday, July 11, 2010
6:47 PM IDT
Elul
Tuesday, August 10, 2010
7:31 AM IDT


Calculated Average Molad chart for the year 5771
Month Day Molad Israel Clock Time Rosh Chodesh
Cheshvan
30 Tishri 5771
Fri 8 Oct 2010
08:20:02 AM
7:59 AM IST
Fri/Sha 
Oct 8/9
Kislev
30 Cheshvan 5771
Sat 6 Nov 2010
09:04:03 PM
8:43 PM IST
Sun/Mon
Nov 7/8
Teves
29 Kislev 5771
Mon 6 Dec 2010
09:48:04 AM
9:27 AM IST
Tue/Wed
Dec 7/8
Shvat
29 Teves 5771
Tue 4 Jan 2011
10:32:05 PM
10:11 PM IST
Thu
Jan 6
Adar I
29 Shevat 5771
Thu Feb 3 2011
11:16:06 AM
10:55 AM IST
Fri/Sha
Feb 4/5
Adar II
28 Adar A 5771
Fri March 4 2011
12:00:07 AM
11:39 PM IST
Sun/Mon
Mar 6/7
Nisan
28 Adar B 5771
Sun April 3 2011
12:44:08 PM
1:23 AM IDT
Tue
Apr 5
Iyar
29 Nisan 5771
Mon May 3 2011
01:28:09 AM
2:08 AM IDT
Wed/Thu
May 4/5
Sivan
28 Iyar 5771
Wed June 1 2011
02:12:10 PM
2:52 PM IDT
Fri
June 3
Tamuz
29 Sivan 5771
Fri July 1 2011
02:56:11 AM
3:36 AM IDT
Sha/Sun
July 2/3
Av
28 Tamuz 5771
Sat July 30 2011
03:40:12 PM
4:20 PM IDT
Mon
Aug 1
Elul
29 Av 5771
Mon Aug 29 2011
04:24:13 AM
5:04 AM IDT
Tue/Wed
Aug 30/31

The best time to see the crescent Moon, according to my research ("Observing the new Moon" R. E. Hoffman, Monthly Notes Roy. Astron. Soc., 340, 1039-1051 (2003).), is 0.6 of the time between Sunset and Moonset. The first crescent Moon appears between 15 and 55 hours after the true conjunction.
He has published predictions of possible first sightings of the new moon at
You can download my predictions for the next year at http://chem.ch.huji.ac.il/nmr/foo/handouts/5771e.pdf, and for last year at http://chem.ch.huji.ac.il/nmr/foo/handouts/5770e.pdf
Some of these estimates show that the moon would definitely not be visible to the naked eye at that time.
I should point that that as Dr. Hoffman says
 I do not publish calendars based on sightings because we are commanded to use our calculated calendar until a recognized Sanhedrin rules otherwise. If you do publish such a calendar, it is more than likely that a few individuals will follow it in contradiction to the halakhah.
Rosh Hashanna of 5772 will be Thu/Fri Sept 29/30

The actual conjunction and the possible “first visibility” list is shown below.

Note that the first visibility range is delayed because the first date is October 8, 5:16 PM – 5:26 PM. This is probably too short a time to actually see the moon. The following month, the first moonrise is at 4:45 PM which is less than ten hours. If the moon is seen on or before day 29 of the month, then the Sanhedrin would be able to declare the next day Rosh Chodesh and the previous month would be a 29 day month. Otherwise, the previous day would be a two day Rosh Chodesh by default. This occurs for Chesvan and Kislev. Note that Teves has two possibilities. If witnesses see the moon at the first available date (Dec 6), then Dec 7 would be the only day of Rosh Chodesh, unlike the calculated calendar which has two days. This would make the fast of Asara B'Teves occur one day earlier, Thursday, December 16, instead of Friday, December 17. This would also affect the declaration of the month of Shvat. Since it is the middle of the rainy season, it is very probable that the witnesses would miss the first sighting of the moon, forcing Teves to have tw days of Rosh Chodesh, just like the calculated calendar.

If Teves only had one day of Rosh Chodesh (December 7), then January 5 would be day number 30 of that month. This would force Shvat to have a two day Rosh Chodesh and would bring it back in sync with the calculated calendar.

Adar II now has two possibilities again because of the end of the rainy season. It is also possible that it would be missed because of the early time within the rang that the visibility occurs (19 hours 18 minutes). If it were visible, the Sanhedrin might deliberately not hold court because it would force Purim to occur on Shabbos. This affects Nisan, just as Teves did Shvat.

Note that Daylight Savings Time in Israel starts April 2. Thus, All time from April on are in Daylight Savings Time.

Nisan now has three possibilities because of the tw possibilities of Adar II. If Adar II had only one day Rosh Chodesh, then Nisan is forced to have two days Rosh Chodesh and comes back into sync with the calculated calendar. This is the same situation as if Adar II had two days Rosh Chodesh and the witnesses saw the moon in time for Nisan to have one day Rosh Chodesh. It is probable that they would see it as the moon would be 26 hours old. If they do not see it, Nisan has two days Rosh Chodesh and Pesach becomes Wednesday April 20 instead of Tuesday April 19. This is a significant effect and shows why we need the calendar to be precise. This also shows the reason for two days of Yom Tov in Chutz La'Aretz.

Iyar can now be either a one day or two day Rosh Chodesh depending on what had happened with Nisan (assuming that the witnesses do see the moon at the designated time. If they miss the moon, it would of course be forced to be a two day Rosh Chodesh.

Because Shavuos is defined as being counted from Pesach, the date would have been defined by what happened to Nisan.

Had Iyar had a single day of Rosh Chodesh, June 2 would have been the thirtieth day of the month forcing two days of Rosh Chodesh whether the moon was seen or not. If there had been two days of Rosh Chodesh, it would have again depended on whether or not the moon had been seen. This would set up three possibilities.

This sets up three possibilities for Sivan, but the first of Sivan woul occur on either June 3 or 4. This leads to Tamuz having one or two days Rosh Chodesh, but in either case, the first of the month is July 3. This brings it back in sync with the calculated calendar.

Av can now have one or two days Rosh Chodesh, meaning that Tisha B'Av can be on August 9 or 10.

While the moon on the day of the conjunction of Elul (Aug 29) may be visible, the time interval is only two minutes so it would probably be too close to the sun. If we assume that the second interval is seen, then the first of Elul is on the same day in either case. This allows Rosh Hashana to start as expected by the calculated calendar. On the other hand, if that day is not seen, Elul starts even later and causes a problem with Rosh Hashana because Elul 29 is pushed forward to September 29.

The Conjunction for Rosh Hashana 5772 is September 27 at 2:09 Am, with a possible visibility at 6:45 PM on September 28 (40 h 36 m moon age). This is Elul 29 according to the analysis above, which would make Rosh Hashanna occur on September 29 and 30. This is the same as determined by the calculated calendar.

Conjunction chart for the year 5771
Month Conjunction Visibility Range “best Time”
(.6 of way)
Rosh Chodesh
Cheshvan
Thu, Oct 7, 2010 
8:44 PM IST
Oct 9 5:14 – 6:10 PM
5:47 PM
45 h 3 m
Fri/Sha 
Oct 8/9
Kislev
Sat, Nov 6, 2010 
6:52 AM IST
Nov 7 4:45 – 5:36 PM
5:15 PM
34 h 23 m
Sun/Mon
Nov 7/8
Teves
Sun, Dec 5, 2010 
7:36 PM IST
Dec 6 4:35 – 5:14 PM
4:58 PM
21 h 22 m
Tue
Dec 7
Teves
Sun, Dec 5, 2010 
7:36 PM IST
Dec 7 4:35 – 6:16 PM
5:35 PM
46 h 50 m
Tue/Wed
Dec 7/8
Shvat
Tue, Jan 4, 2011 
11:03 AM IST
Jan 4 4:48 – 5:00 PM
4:55 PM
5 h 52 m
Too early to see 
Shvat
Tue, Jan 4, 2011 
11:03 AM IST
Jan 5 4:49 – 5:59 PM
5:31 PM
30 h 28 m
Wed/Thu
Jan 5/6
Shvat
Tue, Jan 4, 2011 
11:03 AM IST
Jan 5 4:49 – 5:59 PM
5:31 PM
30 h 28 m
Thu
Jan 6
Adar I
Thu, Feb 3, 2011 
4:31 AM IST
Feb 3 5:15 – 5:45 PM
5:33 PM
13 h 2 m
Too early to see
Adar I
Thu, Feb 3, 2011 
4:31 AM IST
Feb 4 5:16 – 6:39 PM
6:15 PM
13 h 44 m
Fri/Sha
Feb 4/5
Adar II
Fri, Mar 4, 2011 
10:46 PM IST
Mar 5 5:40 – 6:20 PM
6:04
19 h 18 m
Sun
Mar 6
Adar II
Fri, Mar 4, 2011 
10:46 PM IST
Mar 6 5:40 – 7:13
6:35 PM
43 h 49 m
Sun/Mon
Mar 6/7
Nisan
Sun, Apr 3, 2011 
5:32 PM IDT
April 4 7:00 – 7:57 PM
7:34 PM
26 h 2 m
Mon/Tue
Apr 4/5
Nisan
Sun, Apr 3, 2011 
5:32 PM IDT
April 4 7:00 – 7:57 PM
7:34 PM
26 h 2 m
Tue
Apr 5
Nisan
Sun, Apr 3, 2011 
5:32 PM IDT
April 5 7:01 – 8:52 PM
7:37 PM
50 hours 5 m
Tue/Wed
Apr 5/6
Iyar
Tue, May 3, 2011
9:51 AM IDT
May 3 7:20 – 7:42 PM
7:33 PM
9 h 42 m
Too early to see
Iyar
Tue, May 3, 2011
9:51 AM IDT
May 4 7:21 – 8:39
8:07 PM
34 h 16 m
Wed/Thu
May 4/5
Iyar
Tue, May 3, 2011
9:51 AM IDT
May 4 7:21 – 8:39
8:07 PM
34 h 16 m
Wed
May 4
Sivan
Thu, Jun 2, 2011
12:03 AM IDT
Jun 2 7:40 – 8:21 PM
8:04 PM
20 h 1 m
Thu/Fri
June 2/3
Sivan
Thu, Jun 2, 2011
12:03 AM IDT
Jun 2 7:40 – 8:21 PM
8:04 PM
20 h 1 m
Fri
June 3
Sivan
Thu, Jun 2, 2011
12:03 AM IDT
Jun 3 7:40 – 9:12 PM
8:35 PM
44 h 32 m
Fri/Sha
June 3/4
Tamuz
Fri, Jul 1, 2011
11:54 AM IDT
July 2 7:49 – 8:39
8:19 PM
32 h 25 m
Sha/Sun
July 2/3
Tamuz
Fri, Jul 1, 2011
11:54 AM IDT
July 2 7:49 – 8:39
8:19 PM
32 h 25 m
Sun
July 3
Av
Sat, Jul 30, 2011
9:40 PM IDT
July 31 7:37 – 7:55 PM
7:47 PM
22h 7 m
Mon
Aug 1
Av
Sat, Jul 30, 2011
9:40 PM IDT
Aug 1 7:36 – 8:32 PM
8:09 PM
46 h 29 m
Mon/Tue
Aug 1/2
Elul
Mon, Aug 29, 2011
6:04 AM
Aug 30 7:06 – 7:42
7:27 PM
37 h 23 m
Tue/Wed
Aug 30/31
Elul
Mon, Aug 29, 2011
6:04 AM
Aug 30 7:06 – 7:42
7:27 PM
37 h 23 m
Wed
Aug 31


Thursday, September 16, 2010

How a Sanhedrin might not change the printed calendar this year

 The time and date calendar can be used to estimate if the eidim can see the moon after the astronomical molad and allow us to guess if the Sanhedrin would declare the new month on the same or a different day than calculated by our fixed calendar.

For example, the astronomical molad for Cheshvan is 8:44 PM October 7. The moon times for October 8 are 6:12 AM rising and 5:26 PM setting. The noon % illumination is .8% at 11:52. The sunrise and sunset times are 5:37 and 5:16. Thus, it would probably not be visible at moonrise.  The noon illumination on October 9 is 4.1 % at 12:49.  I would therefore guess that the visibility during this time would be about 1%. This may be visible during the ten minutes after sunset and before moonset (about 17 hours after the astronomical molad). This would mean that Beis Din could not declare the chodesh until October 9 (since they must do so during the day). This would mean that the declared month would match the calculated month and Tishrei would have 30 days as the printed calendars show.

Kislev has the astronomical new moon at 6:52 AM on November 6, which seems to imply that eidus between moonset and sunset on November 6 might be possible however moonset and sunset are both 4:45 PM so it would probably be drowned out.  If it was visible, Cheshavan would be a 29 day month, while if not (as is most probable) it would be a 30 day month as shown in the printed calendar

This seems to show that for at least Cheshvan and Kislev, the Sanhedrin would most probably declare the chodesh to be the same as our calculated calendar.  It might be interesting to estimate what might happen during the rest of the months of the year and see what would have to be done to ensure that next Rosh Hashannah did not come out on one of the "forbidden" dates.

There are sites that calculate the percent visibility of the moon for a specific date and time. For example, the U.S. Naval observatory says

Although the date and time of each New Moon can be computed exactly (see, for example, Phases of the Moon in Data Services), the visibility of the lunar crescent as a function of the Moon's "age" - the time counted from New Moon - depends upon many factors and cannot be predicted with certainty. In the first two days after New Moon, the young crescent Moon appears very low in the western sky after sunset, and must be viewed through bright twilight. It sets shortly after sunset. The sighting of the lunar crescent within one day of New Moon is usually difficult. The crescent at this time is quite thin, has a low surface brightness, and can easily be lost in the twilight. Generally, the lunar crescent will become visible to suitably-located, experienced observers with good sky conditions about one day after New Moon. However, the time that the crescent actually becomes visible varies quite a bit from one month to another. The record for an early sighting of a lunar crescent, with a telescope, is 12.1 hours after New Moon; for naked-eye sightings, the record is 15.5 hours from New Moon. These are exceptional observations and crescent sightings this early in the lunar month should not be expected as the norm.
Obviously, the visibility of the young lunar crescent depends on sky conditions and the location, experience, and preparation of the observer. Generally, low latitude and high altitude observers who know exactly where and when to look will be favored. For observers at mid-northern latitudes, months near the spring equinox are also favored, because the ecliptic makes a relatively steep angle to the western horizon at sunset during these months (tending to make the Moon's altitude greater).

I would guess that they must have had some occurrance that managed to make it within 15.5 hours (in perfect conditions) in order to set the record. I saw that they did not say when the record was set. Phil Chernofsky has told me that the Israel New Moon Society uses a figure of 18 - 20 hours after the conjuction (astronomical molad) for the earliest possible visibility. I think that if we use the 18 hour figure to get the % of illumination we could calculate. Given that 29.5 days is 708 hours, 18 - 20 hours is approximately 5% - 6% illuminated. We can then use the illumination table to estimate if the moon would be seen around moonset on a particular day. This assumes that the eidim would see the moon between sunset and moonset only. Thus, I would add 18 hours to the conjunction and go to the next sunset time for that estimate.

The Naval observatory calculator generates a table for the year showing the percent illuminated for each day at midnight or noon in Universal Time or one of the U.S. timezones. This would be 7 hours earlier than the time shown for Yerushalayim. The South African Astronomical Observatory has a table of predictions showing where the moon would be visible as well as when it is first visible in South Africa. Another calculator is found at the fishing site http://www.noreast.com/moon/ This calculates the % illuminates at a set hour for a given day. It appears that this is also Eastern Time. Because the Muslims still use "eidus" as the start of their months, they have developed algorithms and maps showing where the moon would be visible.

A set of predictions and maps can be seen at HM Nautical Almanac Office This shows the best time to see the previous new moon for the location requested at the standard time for the first three days of the new moon. It also gives an estimate of the ease of the sighting. For example, September 8 shows the best tim at 5:48 PM with a classification of F. September 9 is 6:04 PM with a classification of C, September 10 is 6:20 PM with a classification of A. The following month is shown with a set of three maps showing the area of the world which can see the moon, but it is more difficult to read. There is no data other than those two months.

There is a Java Applet which gives the location, moon age,  and illumination for specific times at specific locations. Yerushalayim is not listed but the latitude (32.083333 N) and longitude (34.8 E) can be entered explicitly. Use the time about halfway (4/9) between sunset and moonset for the estimate being used.


Month          Best time      Pct      Age

Cheshvan     Oct 8, 1721   1.7%   1d 02h 33m  
Kislev          Nov 7, 1651   3.5%   1d 15h 55m





Cheshvan

Monday, September 13, 2010

Why four out of five years (5771 - 5775) start on Thursday - Friday

The Jewish year has three possibilities for the number of days in a regular or leap year. The reason is that the lunar month is approximately 29.5 (twenty nine and a half) days long. If this was exact, then just alternating 29 and 30 day months would be correct. However, the exact average cycle is 29 days 12 hours 793 "parts" in length. A "part" is one in 1080 of an hour. The 793 "parts" converts to 44 minutes and 1 "part" as can be seen by looking at a chart of the molad announcements for the year. As a result, there are almost 15 minutes more than 29.5 days. This is handled by having the months of Cheshvan and Kislev be either 29 or 30 days and having the three possibilities of 29 and 29, 29 and 30, or 30 and 30. This calculation actually differs from the astronomical new moon as the year progresses. It is calculated by the total number of days in a lunar year and dividing by twelve. As a result, the actual molad can vary from the calculated value by as much as 10 hours.

Rosh Hashannah (first day) can never occur on Sunday, Wednesday, or Friday so that Yom Kippur cannot occur on Friday or Sunday and Hoshannah Rabbah can never occur on Shabbos.

Judaism 101 gives an interesting mnemonic for determining the leap years in the cycle using a piano keyboard
Keyboard 
illustrating pattern of leap years
As can be seen the leap years are years 3, 6, 8, 11, 14, 17, and 19 (0).

This means that the pattern for these 5 years are L R R L R

A more detailed explanation is here

This makes the regular year have 353, 354, and 355 days ("adding 3, 4, or 5 days to the day of the week of Rosh Hashannah), while leap years have 383, 384, and 385 days ("adding" 5, 6, and 0). The Jewish year uses a 19 year cycle and the leap years can be shown by taking the year number as modulus 19. This year (5771) is year 14 of the cycle (year 19 of the cycle has modulus 0). The five years involved are thus 14, 15, 16, 17, 18 Year "17" is the next leap year. This year (a leap year) both Cheshvan and Kislev are 30 days so that next Rosh Hashannah (5772) will be also be on Thursday and Friday. The following year will have Cheshvan 29 days and Kislev 30 days (30 Kislev 5772 is 26 December 2011). This brings the following Rosh Hashannah (5773) to Monday and Tuesday. .

5773 will have 29 days in Cheshvan and Kislev which brings Rosh Hashannah back to Thursday again (from the modulus calculation above.) for 5774.

5774 is year 17 of the 19 year cycle and is again a leap year and again will have both Cheshvan and Kislev set to 30 days. This means that the following (regular) year of 5775 will again start on Thursday.

Since 5775 is not a leap year, Rosh Hashannah of 5776 will occur on Monday and since it is again a leap year (modulus number 0) with both Cheshvan and Kislev 30 days, the following year (5777) is again on Monday.

Larry Nussbaum pointed out by email the following five years starting with 5776 are L R R L R as well with the leap year again being "full" (both Cheshvan and Kislev having 30 days) This means that four out of those five years start on Monday, with the "off year" being Thursday. The last year of this pattern (5780) is year number 4 of the cycle, so 5781 (year 5), which starts on Shabbos,  is also regular and 5782 starts on Tuesday. 

This double pattern is quite rare. This appears to be to only such pattern (2 sets of 4 out of 5 back to back) in the past 247 years. In 5760 - 5764 we had 4  of 5 years with RH on Shabbos. There is no short cycle (like 19 or 28 years) when it comes to days of the week for yom tovim. The only cycle is a 247 year cycle (and that's not 100% guaranteed). Mr. Nussbaum also pointed out that the Tur has a 247 year calendar.

I saw this on the Mail Jewish mailing list, from Richard Fiedler

Mail.Jewish Mailing List
Volume 59 Number 26
Produced: Tue, 14 Sep 2010 01:15:16 EDT
From: Richard Fiedler
Date: Mon, Sep 13,2010 at 10:01 PM
Subject: Dates of Rosh HaShanah

Rosh HaShanah 2013 has another extremely unusual aspect. The Old Moon will be visible on Wednesday Morning Sept 4, 2013 and we will welcome in Rosh HaShanah Wednesday Night.

The Molad of Tishrei 2013 will be Yom Chamishi (Thursday), 16 hours 830 parts. This is under the window of the Molad Zaqen rule (18 hours causes a deferral of Rosh HaShanah) that normally prevents as Old Moon from being seen Erev Rosh HaShanah.

If you will join me in Jerusalem that week I will be on Mount Scopus at 5:10 AM when the Moon will rise. The Sun will rise at 6:16 AM. We will be seeing the cause of the Gemora of Rabban Gamliel and Rabbi Yehoshua (120 CE).

The reason for this is rooted in a very exceptional lunar orbit which is taking a path below the African Continent. Here is a link to the R H van Gent chart of Lunar Visibility for that date. https://files.me.com/richardfiedler/tfsa4d


The above comment shows the "old moon" being visible the day before Rosh Hashanah by the fixed calendar. I realized as a result of a comment that I received that the Sanhedrin is based on eidus, which means that the eidim had to have seen the new moon. IIRC this is a minimum of six hours after the actual astronomic molad, which oscillates around the average announced molad. Actually, a member of the Israel New Moon Society has told me that the new moon would not be visible to the naked eye until it is at least 18 -20 hours old. The question would be when the actual astronomic "new moon" would be. I looked up on the internet and  went to a planetary body calendar website to get these values. Note that the current rule is that Daylight time in Israel ends the Sunday morning before Yom Kippur. As a result, DST ends September 8. The times shown below are therefore in Daylight Savings Time.

Moonrise and moonset in Jerusalem (DST)

Date             Moonrise    Moonset
Sep 4, 2013  5:10 AM      6:09 PM
Sep 5, 2013   6:06 AM      6:43 PM


Meridian Passing

                     Sep 4                    Sep 5      
Time:           11:42 A.M.          12:27 P.M.
Altitude:       65.6°                    61.4°
Distance:     396,157 km          392,621 km.
Illuminated: 1.5%                    0.1%

Phase: New at 2:37 P.M. Sep 5

I also checked and sunrise is 6:16 and 6:17 A.M. and sunset is 6:59 P.M. and 6:58 PM on those days. This seems to imply that IF the six hour time is correct, then the new moon would probably not be visible until 8:43 P.M. which is well after moonset. Note that the .1% illumination is at the meridian (which is "drowned out" by the noon sun) If the two hours before the new moon are linear to the 4 hours after the new moon, then the illumination would be no more than .2% and the six hours would be about .3% The previous days meridian shows 4.8% illumination which would make the moonrise illumination about 2.5%, with the sun still below the horizon. This may indeed allow it to be seen. In the case of the new moon, since the moon sets 15 minutes earlier than the sun, it would seem to be very difficult to see it. The illumination at the meridian for the day after the new moon (approximately 22 hours) is 1.0%.  If the 18 hour estimate mentioned earlier is correct, this implies that the old moon would indeed have been visible.

When the Sanhedrin is reestablished, there will be a set of 30 day months until Rosh Chodesh gets co-ordinated with the eidus and astronomical molad rather than the fixed average molad that we announce now. As a result the Sanhedrin would have had to be established a number of months before this so that Rosh Hashannah could be on Shabbos (September 7) while Elul remained 29 days.