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

To continue the table click here.
To return to the top click here.
For other Additional Notes click here.
To continue the reading click here.

I'd love to hear from you. Please send your thoughts to:

Remy Landau

First  Paged 10 Aug 1997
Next Revised 19 Oct 1997