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


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