Jewish Calendar Tutorial Worksheet 2 (515BC Todays Sequence)

YEAR BEING CALCULATED: 515 B.C. TODAY'S SEQUENCE

PART II: CALCULATION OF THE DAY OF THE MONTH FOR THE MOLAD IN THE ROMAN CALENDAR
COMMENT: POINTS 1 - 4 CAN BE COPIED OVER FROM THE FIRST
CALCULATION FOR THIS PARTICULAR YEAR.

1.
STARTING DATE YEAR: 3761 B.C.
STARTING DATE MOLAD OF TISHRI: OCTOBER 7 or SEPTEMBER 37
STARTING DATE EXACT TIME: D2 H5 P204

2.
YEAR BEING CALCULATED: 515 B.C.

3.
THE DIFFERENCE IN YEARS:3246 YEARS

4.
CONVERTING THIS DIFFERENCE INTO THE NUMBER OF 19-YR CYCLES
PLUS REMAINING COMMON YEARS AND LEAP YEARS:
170 cycles plus a remainder of 16 years
The remainder of 16 years = 11 Common Years + 5 Leap Year

5.
WE ARE NOW GOING TO CALCULATE THE DIFFERENCE BETWEEN THE JEWISH CALENDAR AND THE ROMAN JULIAN CALENDAR. THIS CALCULATION COULD NOT POSSIBLY HAVE BEEN PERFORMED BEFORE THE JULIAN CALENDAR CAME INTO EXISTENCE.
COMMENT: For calculation purposes we again turn all periods of time into Parts.

A.PER CYCLE EVERY JEWISH 19-YR CYCLE IS SHORTER THAN 19 JULIAN YEARS BY 1H 485P. SO WE MULTIPLY THIS BY THE NUMBER OF CYCLES INVOLVED: 1H 485P = 1,565P
THUS: 1565 x 170 = 266,050P

B.THE AVERAGE COMMON YEAR IS SHORTER THAN THE AVERAGE JULIAN YEAR BY 10D 21H 204P. SO WE MULTIPLY THIS BY THE NUMBER OF COMMON YEARS INVOLVED: 10D 21H 204P = 282,084P
THUS: 282,084 x 11 = 3,102,924P

C.THE AVERAGE LEAP YEAR IS LONGER THAN THE AVERAGE JULIAN YEAR BY 18D 15H 589P. SO WE MULTIPLY THIS BY THE NUMBER OF LEAP YEARS INVOLVED: 18D 15H 589P = 483,349P
THUS: 483,349 x 5 = 2,416,745P

6.
NOW DO THE FOLLOWING CALCULATION:
(AMOUNT FOR LEAP YEARS) - (AMOUNT FOR CYCLES + AMOUNT FOR COMMON YEARS)

IF THE ANSWER IS A NEGATIVE VALUE, THEN IT MUST BE SUBTRACTED FROM THE STARTING DATE MOLAD VALUE, THUS MAKING THE MOLAD EARLIER. AND IF THE ANSWER IS A POSITIVE VALUE THEN IT MUST BE ADDED TO THE STARTING DATE MOLAD VALUE, THUS MAKING THE MOLAD LATER.
THUS:
(2,416,745P) - (266,050P + 3,102,924P)
= 2,416,745 - 3,368,974 = -952,229P

7.
THIS TOTAL WE NOW CONVERT BACK INTO DAYS, HOURS, PARTS.
-952,229 / 1080 = -(881 HOURS plus 749P)
-881 / 24 = -(36 DAYS plus 17H)
THUS THE TOTAL IS: -(36 DAYS plus 17 HOURS plus 749 PARTS)

8.
NOW WE ADD ADJUSTMENTS FOR DATES THAT ARE LATER THAN 1582 A.D. AND FOR NON-ROMAN LEAP YEARS AS FOLLOWS:
AFTER 1582 = ADD 10 DAYS
AFTER 1700 = ADD 1 DAY
AFTER 1800 = ADD 1 DAY
AFTER 1900 = ADD 1 DAY
AFTER 2100 = ADD 1 DAY, etc.
CORRECTION FOR YEARS AFTER A ROMAN LEAP YEAR ARE THUS:
6H or 12H or 18H FOR 1 or 2 or 3 YEARS AFTER A ROMAN LEAP YEAR.
TOTAL ADJUSTMENT TO ADD FOR THIS YEAR = 12 HOURS

[Comment: 517 B.C. was a Julian Calendar leap year (as there is no year Zero) and so 515 B.C. requires a 12-hour adjustment.]

9.
NOW WE ADD THE TOTAL FOR THESE TOTAL ADJUSTMENTS TO THE PREVIOUS TOTAL:
 -(36D 17H 749P) + 12H = -(36D plus 5H plus 749P)

10.
IF THIS FINAL FIGURE IS A POSITIVE VALUE, THEN WE ADD IT TO THE STARTING DATE. IF THIS FINAL FIGURE IS A NEGATIVE VALUE, THEN WE SUBTRACT IT FROM THE STARTING DATE.

COMMENT: IF THIS IS A NEGATIVE VALUE GREATER THAN "6D 5H 205P", THEN WE USE SEPTEMBER 37 AS THE STARTING DATE, OTHERWISE WE USE OCTOBER 7 AS THE STARTING DATE. THIS MAKES CALCULATIONS EASIER WITHOUT ACTUALLY CHANGING ANYTHING.

11.
THUS: STARTING DATE +/- THIS FINAL TOTAL = THE DAY OF THE MONTH FOR THE MOLAD OF TISHRI. THUS:
THUS: SEPT 37 H5 P204 - (36D 5H 749P)
= SEPT 37 H5 P204 - 749P = SEPT 37 H4 P535
= SEPT 37 H4 P535 - 5H = SEPT 36 H23 P535
= SEPT 36 H23 P535 - 36D = AUGUST 31 H23 P535

12.
WE NOW COMPARE THE HOURS AND PARTS FROM THIS RESULT WITH THE HOURS AND PARTS IN THE DAY OF THE WEEK CALCULATION. THUS:
EXACT TIME FOR DAY OF WEEK CALCULATION = H23 P535
EXACT TIME FOR DAY OF MONTH CALCULATION = H23 P535
IF THESE TWO RESULTS ARE 100% IDENTICAL, THEN OUR CALCULATIONS ARE CORRECT. IF THEY ARE NOT 100% IDENTICAL, THEN WE MUST LOOK FOR WHERE WE MADE AN ERROR.

13.
OUR ASSESSMENT: THE RESULTS ARE 100% IDENTICAL!

14.
CONCLUSION: WE NOW HAVE THE PROOF THAT WE HAVE CALCULATED
THE MOLAD OF TISHRI CORRECTLY! OUR RESULT IS:
FOR 515 B.C. THE MOLAD OF TISHRI WAS WEDNESDAY, AUGUST 31
AT H23 P535, THIS BEING 5:29:43 p.m.

 

THIS CONCLUDES THE ACTUAL MOLAD CALCULATIONS. NOW THE MOLAD MUST STILL BE EVALUATED AGAINST THE 4 POSTPONEMENT RULES.

HOWEVER:

AS A MATTER OF INTEREST, WE ARE NOW READY TO COMPARE THIS MOLAD WITH THE REAL NEW MOON CONJUNCTION (expressed in LOCAL JERUSALEM TIME), AS DETERMINED BY MODERN ASTRONOMERS. FOR THIS PURPOSE WE USE THE TIME EXPRESSED IN MINUTES AND SECONDS, RATHER THAN EXPRESSED IN PARTS (i.e. HALAKIM).

MOLAD OF TISHRI FOR 515 B.C.: AUGUST 31 at 5:29:43 p.m.
REAL NEW MOON CONJUNCTION: AUGUST 31 at 2:52 a.m.

EVALUATION OF THE JEWISH MOLAD: IS IT TOO EARLY? IS IT BASICALLY CORRECT? IS IT TOO LATE?

ASSESSMENT:THE MOLAD IS OVER 14 HOURS AFTER THE REAL NEW MOON CONJUNCTION! IT IS OVER 14 HOURS LATE, THOUGH IT IS STILL BARELY ON THE SAME DAY (sunset to sunset reckoning) AS THE ACTUAL NEW MOON CONJUNCTION.

HOWEVER, THE DATE OF AUGUST 31 IS STILL MISLEADING! THAT IS A JULIAN CALENDAR DATE. BUT IN THE GREGORIAN CALENDAR (WHERE THE AUTUMN EQUINOX IS ON SEPTEMBER 23) THIS DATE IS REALLY AUGUST 25! AND THAT IS 29 DAYS BEFORE THE END OF SUMMER!

HAVING MADE THIS OBJECTIVE ASSESSMENT ABOUT THE MOLAD'S RELATIONSHIP TO THE REAL NEW MOON CONJUNCTION AND TO ITS TIME OF YEAR, WE ARE NOW READY TO LOOK AT WHETHER THE JEWISH CALENDAR FOR THIS MOLAD APPLIES ANY POSTPONEMENTS OR NOT.

We have now completed ALL the calculations that are required for determining the Molad of Tishri. We have also compared this Molad of Tishri to the real astronomical new moon conjunction of the Seventh Month. What remains to be done is the easy part: examining the Molad of Tishri against all 4 of the postponement rules, and thereafter determining all the dates for the Feasts and the Holy Days for the year.

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