Hebrew Calendar Science and Myths
The Rosh Hashannah Drift

by Remy Landau
=================================

The Hebrew calendar moves more slowly in time than does the Gregorian calendar. As a result, the earliest possible start day for Rosh Hashannah is moving later and later into the Gregorian year.

The average Hebrew year length is 365.246822... days

The average Gregorian year length is 365.2425 days

Hence, the Hebrew calendar is drifting through the Gregorian calendar at an average rate of about 1 day in every 231.374 years.

Since the average Gregorian month is (365.2425/12) days long and the Hebrew calendar moves an extra day into the month about once every 231.374 years, each Gregorian day can host a Rosh Hashannah for an average period of some 7,042.226... years.

Also, since the Hebrew year continues to move around the Gregorian year, after an average of some 365.2425*231.374 = 84,507 years, the initially viewed Gregorian date will have returned to once again host the start of Rosh Hashannah.

Fixing the calendar rules over some 158,000 years it is possible to calculate the effect of the Rosh Hashannah drift for some 3 occurrences of each of the days in the Gregorian calendar, including the leap day of February 29.

The tabulation shows the first time a Gregorian date hosts a Rosh Hashannah, the last time it can do so within a particular cycle of years and the next time the Gregorian date can resume its hosting.

When Rosh Hashannah advances to a new day in the Gregorian calendar, it always does so in the 9th year of the 19 year cycle.

To determine the latest Gregorian date on which Rosh Hashannah can begin for some time interval Y and Y1, find the period in the column showing the first occurrences of the Gregorian dates. The first date in that period is the latest possible date for Rosh Hashannah during that time period.

For example, the period between 1900g and 2100g falls between the years 1815g and 2214g. Hence the latest possible Gregorian date for Rosh Hashannah is October 5.

To determine the earliest Gregorian date on which Rosh Hashannah can begin for some time interval Y and Y1, find the period in the column showing the last occurrences of the Gregorian dates. The first date past Y in that period is the earliest possible date for Rosh Hashannah during that time period.

For example, the period between 1900g and 2100g falls between the years 1766g and 2206g. Hence the earliest possible Gregorian date for Rosh Hashannah is September 5.

There exist some exceptions to the method since the table below shows that the various occurrences of the Gregorian dates do not necessarily all follow a progressively ascending year order.

October 4 never made it as a latest possible date because it first hosted Rosh Hashannah in 1834g, which was after October 5 first did that in 1815g.

The maximum separation between two advancing Rosh Hashannah dates appears to be 399 years for the first 3 Gregorian year cycles. That separation appears to have first taken place between the first occurences of September 28, -85g and September 29, 314g.

The table below identifies the maximum separations of 399 years with a single *, and the non-sequential year changes with a double **.

The tabulation begins with Monday August 11, -3744g (17H) because this was the earliest Gregorian date recorded for Rosh Hashannah since year 1H.

The Rosh Hashannah Drift
August 11 TO October 31
DATEFirst OccurenceLast OccurrenceNext Occurence
`Aug 11`
`**Mon     17H  -3744g`
`**Mon     17H  -3744g`
`**Sat  77491H  73731g`
`Aug 12`
`  Thu     36H  -3725g`
`  Sat    245H  -3516g`
`  Sat  77738H  73978g`
`Aug 13`
`**Sat     25H  -3736g`
`  Sat    397H  -3364g`
`  Thu  77871H  74111g`
`Aug 14`
`**Thu      6H  -3755g`
`  Mon    758H  -3003g`
`  Mon  78099H  74339g`
`Aug 15`
`  Mon     14H  -3747g`
`  Mon   1005H  -2756g`
`  Thu  78365H  74605g`
`Aug 16`
`  Mon     41H  -3720g`
`  Tue   1157H  -2604g`
`  Sat  78479H  74719g`
`Aug 17`
`**Sat     22H  -3739g`
`  Sat   1385H  -2376g`
`  Thu  78859H  75099g`
`Aug 18`
`**Thu      3H  -3758g`
`  Tue   1556H  -2205g`
`  Mon  79087H  75327g`
`Aug 19`
`  Mon     11H  -3750g`
`  Thu   1917H  -1844g`
`  Mon  79334H  75574g`
`Aug 20`
`  Mon     38H  -3723g`
`  Tue   2050H  -1711g`
`  Mon  79581H  75821g`
`Aug 21`
`**Sat     19H  -3742g`
`  Tue   2297H  -1464g`
`  Thu  79847H  76087g`
`Aug 22`
`  Sat     46H  -3715g`
`  Thu   2658H  -1103g`
`  Thu  79999H  76239g`
`Aug 23`
`**Mon      8H  -3753g`
`  Thu   2753H  -1008g`
`  Mon  80075H  76315g`
`Aug 24`
`**Sat      5H  -3756g`
`  Tue   3038H   -723g`
` *Mon  80474H  76714g`
`Aug 25`
`  Tue     24H  -3737g`
`  Thu   3152H   -609g`
`  Sat  80854H  77094g`
`Aug 26`
`**Thu     13H  -3748g`
`  Sat   3513H   -248g`
`**Thu  80835H  77075g`
`Aug 27`
`  Mon     21H  -3740g`
`  Thu   3646H   -115g`
`  Mon  81215H  77455g`
`Aug 28`
`**Sat      2H  -3759g`
`  Thu   3893H    132g`
`  Mon  81462H  77702g`
`Aug 29`
`  Sat     29H  -3732g`
`  Sat   4254H    493g`
`  Sat  81595H  77835g`
`Aug 30`
`**Thu     10H  -3751g`
`  Tue   4425H    664g`
` *Sat  81994H  78234g`
`Aug 31`
`  Mon     18H  -3743g`
`  Thu   4634H    873g`
`**Thu  81975H  78215g`
DATEFirst OccurenceLast OccurrenceNext Occurence
`Sep  1`
`  Mon     45H  -3716g`
`  Sat   4748H    987g`
` *Thu  82374H  78614g`
`Sep  2`
`**Sat     26H  -3735g`
`  Mon   5109H   1348g`
`  Thu  82469H  78709g`
`Sep  3`
`**Thu      7H  -3754g`
`  Tue   5413H   1652g`
`  Sat  82830H  79070g`
`Sep  4`
`  Mon     15H  -3746g`
`  Thu   5527H   1766g`
`  Thu  82963H  79203g`
`Sep  5`
`**Tue      4H  -3757g`
`  Mon   5850H   2089g`
`  Mon  83191H  79431g`
`Sep  6`
`  Sat     12H  -3749g`
`  Thu   6021H   2260g`
` *Mon  83590H  79830g`
`Sep  7`
`**Mon      1H  -3760g`
`  Tue   6249H   2488g`
`  Mon  83685H  79925g`
`Sep  8`
`  Thu     20H  -3741g`
`  Sat   6629H   2868g`
`  Thu  83951H  80191g`
`Sep  9`
`**Sat      9H  -3752g`
`  Tue   6648H   2887g`
`  Thu  84103H  80343g`
`Sep 10`
`  Mon    123H  -3638g`
`  Thu   7009H   3248g`
`  Thu  84445H  80685g`
`Sep 11`
`**Mon     66H  -3695g`
`  Tue   7142H   3381g`
`  Thu  84692H  80932g`
`Sep 12`
`  Thu    332H  -3429g`
`  Tue   7389H   3628g`
`  Sat  84863H  81103g`
`Sep 13`
`  Thu    484H  -3277g`
`  Sat   7617H   3856g`
`  Thu  85091H  81331g`
`Sep 14`
`  Thu    826H  -2935g`
`  Thu   7845H   4084g`
`  Mon  85319H  81559g`
`Sep 15`
`  Sat   1092H  -2669g`
`  Mon   8225H   4464g`
`  Mon  85566H  81806g`
`Sep 16`
`  Sat   1339H  -2422g`
`  Sat   8358H   4597g`
`  Sat  85699H  81939g`
`Sep 17`
`  Thu   1472H  -2289g`
`  Sat   8605H   4844g`
`  Mon  86060H  82300g`
`Sep 18`
`  Mon   1700H  -2061g`
`  Thu   8738H   4977g`
`  Thu  86079H  82319g`
`Sep 19`
`  Thu   1966H  -1795g`
`  Tue   9023H   5262g`
` *Thu  86478H  82718g`
`Sep 20`
`  Sat   2080H  -1681g`
`  Mon   9213H   5452g`
`  Sat  86687H  82927g`
`Sep 21`
`  Thu   2460H  -1301g`
`  Tue   9517H   5756g`
`  Sat  86934H  83174g`
`Sep 22`
`  Mon   2688H  -1073g`
`  Thu   9631H   5870g`
`  Thu  87067H  83307g`
`Sep 23`
`  Mon   2935H   -826g`
`  Mon   9954H   6193g`
`  Mon  87295H  83535g`
`Sep 24`
`  Sat   3068H   -693g`
`  Tue  10258H   6497g`
`  Thu  87561H  83801g`
`Sep 25`
`  Thu   3448H   -313g`
`  Tue  10353H   6592g`
` *Thu  87960H  84200g`
`Sep 26`
`  Thu   3600H   -161g`
`  Sat  10733H   6972g`
`  Thu  88055H  84295g`
`Sep 27`
`  Mon   3676H    -85g`
`  Tue  10752H   6991g`
`  Thu  88302H  84542g`
`Sep 28`
` *Mon   4075H    314g`
`  Thu  11113H   7352g`
`  Thu  88549H  84789g`
`Sep 29`
`  Sat   4455H    694g`
`  Tue  11246H   7485g`
`  Sat  88815H  85055g`
`Sep 30`
`**Thu   4436H    675g`
`  Tue  11493H   7732g`
`  Sat  89062H  85302g`
DATEFirst OccurenceLast OccurrenceNext Occurence
`Oct  1`
`  Thu   4683H    922g`
`  Thu  11854H   8093g`
`  Thu  89195H  85435g`
`Oct  2`
`  Mon   5063H   1302g`
`  Thu  11949H   8188g`
`  Mon  89575H  85815g`
`Oct  3`
`  Sat   5196H   1435g`
`  Mon  12329H   8568g`
`  Mon  89670H  85910g`
`Oct  4`
` *Sat   5595H   1834g`
`  Tue  12633H   8872g`
`  Sat  90050H  86290g`
`Oct  5`
`**Thu   5576H   1815g`
`  Sat  12709H   8948g`
`  Thu  90183H  86423g`
`Oct  6`
` *Thu   5975H   2214g`
`  Thu  12842H   9081g`
`  Mon  90411H  86651g`
`Oct  7`
`  Thu   6070H   2309g`
` *Thu  13241H   9480g`
`  Thu  90677H  86917g`
`Oct  8`
`  Sat   6431H   2670g`
`  Sat  13450H   9689g`
`  Sat  90791H  87031g`
`Oct  9`
`  Thu   6564H   2803g`
`  Tue  13621H   9860g`
` *Sat  91190H  87430g`
`Oct 10`
`  Mon   6792H   3031g`
`  Thu  13830H  10069g`
`**Thu  91171H  87411g`
`Oct 11`
` *Mon   7191H   3430g`
` *Thu  14229H  10468g`
` *Thu  91570H  87810g`
`Oct 12`
`  Mon   7286H   3525g`
`  Sat  14343H  10582g`
`  Thu  91665H  87905g`
`Oct 13`
`  Thu   7552H   3791g`
`  Tue  14609H  10848g`
` *Thu  92064H  88304g`
`Oct 14`
`  Thu   7704H   3943g`
`  Sat  14837H  11076g`
`  Thu  92159H  88399g`
`Oct 15`
`  Mon   8027H   4266g`
`  Mon  15046H  11285g`
`  Thu  92463H  88703g`
`Oct 16`
`  Thu   8293H   4532g`
` *Mon  15445H  11684g`
`  Mon  92786H  89026g`
`Oct 17`
`  Sat   8464H   4703g`
`**Sat  15426H  11665g`
`  Sat  92919H  89159g`
`Oct 18`
`  Thu   8540H   4779g`
` *Sat  15825H  12064g`
`  Sat  93166H  89406g`
`Oct 19`
`  Mon   8920H   5159g`
`  Thu  15958H  12197g`
`  Thu  93299H  89539g`
`Oct 20`
`  Mon   9167H   5406g`
`  Tue  16243H  12482g`
`  Sat  93660H  89900g`
`Oct 21`
`  Sat   9300H   5539g`
`  Mon  16433H  12672g`
`  Sat  93907H  90147g`
`Oct 22`
`  Mon   9661H   5900g`
`  Tue  16737H  12976g`
`  Sat  94154H  90394g`
`Oct 23`
`  Thu   9680H   5919g`
`  Thu  16851H  13090g`
`  Thu  94287H  90527g`
`Oct 24`
` *Thu  10079H   6318g`
`  Thu  17098H  13337g`
`  Mon  94515H  90755g`
`Oct 25`
`  Sat  10288H   6527g`
`  Mon  17421H  13660g`
`  Mon  94762H  91002g`
`Oct 26`
`  Sat  10535H   6774g`
`  Sat  17554H  13793g`
` *Mon  95161H  91401g`
`Oct 27`
`  Thu  10668H   6907g`
` *Sat  17953H  14192g`
`  Sat  95294H  91534g`
`Oct 28`
`  Mon  10896H   7135g`
`**Thu  17934H  14173g`
`**Thu  95275H  91515g`
`Oct 29`
`  Thu  11162H   7401g`
` *Thu  18333H  14572g`
` *Thu  95674H  91914g`
`Oct 30`
` *Thu  11561H   7800g`
`  Sat  18447H  14686g`
`  Thu  96016H  92256g`
`Oct 31`
`  Thu  11656H   7895g`
`  Tue  18713H  14952g`
`  Sat  96282H  92522g`

```First  Paged 10 Aug 1997