Verify Mosaic Calendar via Easter date from Julian Day Numbers In summary, the straight forward Jubilee count of 50 years and Septennial counts of Sabbath years, (7-7's), and the independent 7 day week were the only requirements to keep the 3 appointed yearly feasts dictated under Mosaic law. The Sabbatical years need not be same as Jubilee Years. There are no contradictions between the Mosaic Law prescribing the 7 year intervals for Year of Release, and the 50 year intervals for the Law of Return. Reading what some have written about the Mosaic calendar, namely that Jubilee and Sabbath year counts are contradictory, begged to review that assertion. To look at this question, the Julian Day Number method to find Easter was applied to the matter. This results in a self correcting lunar solar year calendar. The count of 50th year Jubilee and Septennial counts of Sabbath years were instituted only after the Exodus, around 1450BC. As the Gregorian calendar is off by only about 1 day in 3500Years, intuitively the Easter calculation should be reasonably accurate. The Catholic Easter is based on finding a Paschal or 1st Full Moon on or after the Spring or Vernal Equinox. This corresponds to the Spring new moon, first full moon on or after March 21. Since Spring Equinox is relatively constant, the Catholic date and Julian Day Easter were used. On rare occasions, Astronomical Easter will not correspond with Catholic or Gregorian date Easter. However for simple evaluation, the Catholic Epact method was used, as adapted to Julian Day number method. These formula are given from a prior work, and as an appendix at end of this topic. It was found that a pattern of 49 year plus one, (1), Jubilee year are perfectly compatible with Mosaic Holy day calendar without complicated intercalation rules. This is because the spring equinox is very regular. It was previously shown that observational Equinoxes could be found by Egyptian methods learnt by Moses, as well as simple day counts from a prior observation. A Day count of 365 or 366 days is simple and possibly necessary under poor weather conditions. "And Moses was learned in all the wisdom of the Egyptians, and was mighty in words and in deeds."
OP Armstrong
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January2019 ‌.
Review of JD# Lunar Conjunction Dates to NASA Tables for “Easter Year” start Dates
Verify Mosaic Calendar via Easter date from Julian Day Numbers Year-Gregorian
Lun.Conj. by Easter Epact
NASA conjuction
otis-a.com
Rabbinical date
Observation date
-1462Apr13g
1187168.37
1187168.06
1187168.06
30Nisan
28Nisan
-974Apr12g
1365415.07
1365415.07
1365415.07
01Iyyar
28Nisan
-567Apr15g
1514072.11
1514072.11
1514072.32
29Nisan
28Nisan
-497Apr23
1539645.61
1539645.37
1539645.57
29Nisan
28Nisan
-457Apl11g
1554233.73
1554233.65
1554233.65
29Nisan
28Adar
26AD.Mar05
1730620.03
1730620.31
1730620.43
29Adar
28Adar
30AD.Mar21
1732096.56
1732096.24
1732096.24
01Nisan
28Adar
2019mar06
2458549.32
2458549.17
2458549.18
30Adar-1
28Adar
2451609.63
2451609.72
2451609.72
29Adar-1
28Adar
Y2k.Mar06 avg Error
0.08+\- 0.20
JD# eliminates Leap Year accounting, as this is performed by Calendar Converter routines
The Mosaic Spring New moon was calculated as Paschal Full moon, less 14 days. The validity of these new moons were confirmed by John Walker's web pages; Lunar Perigee and Apogee Calculator & Calendar Converter. Additionally spot checks of Walker by more complex methods proved the method validity within the selected date ranges 1450BC to 2019AD. The gap between Catholic Easter Year and Hebrew Year is caused by variances in start criteria. Easter only requires the start be at full moon, at or after Vernal Equinox. The Jewish new year often requires a first new moon after the VE. Further differences in Jewish new year arise as to whether it is a calculated new moon or a calculated visible new moon. Since the visible moon happens one or two days after conjunction, there can be difference twixt these dates. These difference are highlighted by the above Table. Basis of Method: The Nicene Council, 325AD, established Easter as the: 1)First Sunday, 2)After the 1st Full Moon, 3)On or After the Vernal Equinox. Here are used parts 2&3 of the Epact method. Also the Mosaic LuniSolar New year is taken to start 14 days prior to the Paschal Full Moon. While not absolutely in accordance with a Rabbinical New Year, it agrees with the method set out by Church Authorities in 325AD and upheld ever since. The validity of this method to set a 'moveable holiday' is commonly agreed. It is likely, on average, this method is close what was practiced by Hebrew priests from Moses time all way up to the captivity & destruction of Solomon Temple. The sighted moon and barley harvest intercalation cannot be simply reproduced. First a determination of spring equinox is a relatively straight forward observation, given ideal weather. The spring equinox could also be counted, given the regularity of earth orbit, 365.2422 days, or mostly on March 21, Gregorian. Second, sighted moon depends upon a more precise knowledge of weather conditions and lunar orbital variations. This also is fairly regular at 29.5306 days. The time between lunar conjunction and full moon is taken to average 14 days. OP Armstrong
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January2019 ….
Verify Mosaic Calendar via Easter date from Julian Day Numbers This method makes no effort to correspond to the Rabbinical calendar, as holy days were added either after or during the captivity period, and uses a molad which falls after Vernal Equinox, along with several other rules. All together, the method given here showed that a lunisolar year could be used to observe both seven year and 50 year cycles, without any conflict to the three primary holy days of Moses; Passover, Pentecost, Day of Atonement. Appendix, JD, Julian Day number routine to find start of New SoliLunar Year: F1. (A): Year number expressed as Astronomical Year, ... -3, -2, -1, 0, 1, 2, 3... etc, The years -1465 unto -1401, -1600 and -1252, & -1465 to 2019 were reviewed by calculation. F2. (B) Epact Lunation# {Julian Day # of Paschal Epact} [1+MOD((365.242454*(-4006-A)),29.5306))] & if>=30, then subtract 30 F3. JD# Jan1 (C) {Julian Day # of January 1st} 257898.52-365.242454*(-4006-A) F4. D=(B-1)+C
{Julian Day # of Paschal January New Moon}
F5. E=74.02+D
{Julian Day # of Paschal March Full Moon}
F6. F=257978.00-365.242454*(-4006-A) {Julian Day # of Catholic Equinox}* F7. G=IF(E>=F,E,E+29.531) {Julian Day # of Accepted Paschal Full Moon} F8. H=G-14 {Julian Day # of Paschal New Moon, or start of a new LuniSolar year} The Paschal new moon is the basis from which all declared Sabbaths, Free Week Sabbaths, and Feast/Fast days may be determined. F9. Auxiliary, if desired, determine week day by (7-INT(MOD((1.5+JD#),7))) one is Sunday and 7 is Saturday, etc. *F10 {Astronomical Equinox (over range,-4000 to 3000 +/-0.07d 98%) is: (2457102.448+(Yr-2015)*365.2422)+ ((-0.0005947871)*((Yr-2015)/1000)^4+(-0.00392591)*((Yr-2015)/1000)^3+(0.013808751)*((Yr-2015)/ 1000)^2+(0.1590901)*((Yr-2015)/1000)) see also texts on mathematical astronomy, most of whom neglect effect of tidal friction on earth rotation. Source here included tidal friction effect.}
The more precise astronomical Easter calculations returns a result that considers tidal friction. This method used the Computus structure applied to Julian day calendar, to avoid accounting for leap year days. The effect of leap years are a natural result when converting from Julian Day numbers to any calendar system. If desired to use something approaching observational astronomy, then the Paschal New moon could be replaced by “first ‘observational’ new moon on or after equinox” by inserting, F11, “IF(PNM.jd#<Equinox, PNM+29.5, PNM.jd#). Several methods, beyond this scope, have been proposed to find ‘observational’ new moon. But the conclusion remains unchanged: the OP Armstrong
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January2019 ….
Verify Mosaic Calendar via Easter date from Julian Day Numbers Mosaic system based on Vernal Equinox is sufficient to define the Passover, Pentecost(50th day), & Day of Atonement (15th day of 7th Lunar month). The Babylonian (Rabbinical) Hebrew calendar added more Holy Days and starts with a 7th month molad. A lunation, average moon, ranges between plus or minus a half (1/2) day of the lunar conjunction. The lunation counts per year were found to follow a pattern of 13,12, 13,12,12, 13,12,12, 13,12, 13... This was a natural result of using the Epact LuniSolar Year. This moon count per year was plotted in the following graph. For the period between -1600 and -458, the average day count was 365.2432. This was arrived at by subtracting the start Julian day of pseudo Paschal new moon less end Julian day of pseudo Paschal new moon, divided by elapsed years. This compares favorably to 1)Gregorian year of 365.2425 days 2)Rabbinical calendar of 365.2468, 3)the mean solar year 365.2422 days This method has a seasonal drift of 1day every 1270 year vs one day every 234 year for Rabbinical calendar. Thus it is suitable for era between Exodus and start 70 year judgement (about 1,000 years), without alteration. It is easily justified that at end of Solomon Temple era, the Mosaic calendar was dropped in favor of a Babylonian era calendar. * F12) Exact Jd# of January 1 for any Year, (Yr), greater than -4006: (2−(INT((Yr−1)÷100))+(INT((INT((Yr−1)÷100))÷4)))+(INT(365.25×(Yr+4715)))+(INT(30.6001×14))−1523.5 * F13) Exact Jd# of Mar21 (Paschal Equinox) for any Year, (Yr), greater than -4006: (No true Equinox +\-0.5d) (2−(INT((Yr)÷100))+(INT((INT((Yr)÷100))÷4)))+(INT(365.25×(Yr+4716)))+(INT(30.6001×4))−1503.5 * Linear Estimate of Equinox: (365.2422653×Yr+1721139.2179) range -4000 to 2200 98% are 0.04+/-0.05day * AA J.Meeus Ch26T26A&B cubic form on negative years is inaccurate in negative years.
As shown, today’s Rabbinical Calendar is an adaptation of the Babylonian Calendar. For all names correspond either to Babylonian or Syrian names and no names correspond to preExile names. The Mosaic era calendar seem lost to posterity. But perhaps the Mosaic Calendar proposed here, are a close variant of the calendar used in the era of Solomon’s Temple? With the exception that years were relegated to a particular event or a king’s reign. The Easter computus rules may offer a basis for a proleptic Mosaic calendar date that can be determined, relative to a Gregorian Calendar, for days of Passover, Pentecost, & Atonement.
OP Armstrong
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January2019 ….
Verify Mosaic Calendar via Easter date from Julian Day Numbers
A comparison of calendar month names shows the preBabylonian or Mosaic era Calendar were not preserved into the Post/Babylonian era. This comes from fact that “Law of Return”, or the 50th year, was not required. For the Samaria tribes were exiled and lost. It also likely that after 70 years exile all land records were lost for non exiled tribes. Only the 7th year release law was preserved in the post Babylon Exile Era, Neh10:31. The Mosaic era calendar used month numbers with a few names, Abib, Zif, Ethanim, & Bul. None of the Mosaic era names were used in Post/Babylon era as a new Babylon calendar was implemented.
One the other hand, almost all names of Rabbinical calendar can be found in either Syrian or Babylonian records. *F14) PNM.jd# = (IF((74.02+((IF((1+MOD((365.2422×(−4006−Y)),29.5306))>30,((1+MOD((365.2422×(−4006−Y)),29.5306))−30), (1+MOD((365.2422×(−4006−Y)),29.5306))))−1+(257898.52−365.2422×(−4006−Y))))>(365.24227×Y+1721139.2179),(74.02+ ((IF((1+MOD((365.2422×(−4006−Y)),29.5306))>30,((1+MOD((365.2422×(−4006−Y)),29.5306))−30),(1+MOD((365.2422×(−4006−Y)), 29.5306))))−1+(257898.52−365.2422×(−4006−Y)))),(74.02+((IF((1+MOD((365.2422×(−4006−Y)),29.5306))>30, ((1+MOD((365.2422×(−4006−Y)),29.5306))−30),(1+MOD((365.2422×(−4006−Y)),29.5306))))−1+(257898.52−365.2422×(−4006−Y)))) +29.5))−14
This formula, *F14, contains one input: Y. Where Y is the Astronomical Year (AY) of interest. This single formula may be copied into a spreadsheet adjacent to a row or column containing the value of Y (i.e. ‘B2’). It will return a Paschal New Moon, such that the full moon (14th day from Lunar Conjunction) will occur on or after the Vernal (Spring) equinox, with a certainty of 0.4 +/- 0.3 days, over a range from present Year to -3999AY(4,000BC). PNM means the Lunar Conjunction as defined above. From this date an entire Mosaic Era Calendar, (Passover, Pentecost, 7th Month High Holidays, Sabbatical & Jubilee Years) are known. The JD# may be changed to Gregorian Calendar dates by many Calendar routines. Tested over 7k civil years with year
OP Armstrong
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January2019 ….
Verify Mosaic Calendar via Easter date from Julian Day Numbers
of 365.2422 (instead of 365.242454) the composite time lost was 1.8day, compared to Gregorian Calendar
gain of 2.1d. One such web page to convert JD# to Gregorian date is: (http://otis-a.com/) Reference The first day of 7th month is 177 days after first day of year. Pentecost is 68 days after 1Abib, by Catholic exclusive counting, pg77. Many variants exist, based upon sect, 64D, 65D, 75D. “Anciently (Maimonides) the form of the year was wholly in-artificial: for it was not settled by any astronomical rules nor calculations, but was made up of lunar months set out by the phasis (moon appearance) … None had fewer than 29 days, so the new moon was never before the night following the 29th day; and, if they then saw it, the next day was the 1st day of the following month. Neither were any months more than 30 days, so they never looked for the new moon after the night following the 30th day; but then, if not seen, they concluded, the appearance was obstructed by clouds, and the next day was the first of the following month” The above formula follows the 19 year cycle, with 12 years of 12 lunar months and 7 years of 13 lunar months. Irrespective of leap years, under the Mosaic holiday cannon, all 3 Holy (1st, 3rd, 7th) months fall before the 11th month. If necessary to find a length of a specific year, find 1Abib of both the year and the following year, should the difference exceed 365d, then the year of question was a leap year. For an astronomical calendar, one could find 1Abib as INT(JD#pnm+1.75). This is a reasonable evening start to the new month with a visible crescent. If needed, add 0.09787 Julian days to convert from Universal Time to the Jerusalem Mean Solar Time. Dr.Irv considers visibility criteria to be “onerous and controversial”, & “optimistic even for ideal observing conditions.” Where-as conjunction & Equinox dates, as used above, are verifiable from many reliable sources: NASA, USNRO, otis-a.com, etc, over a large range of dates.
OP Armstrong
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January2019 ….