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.
| August 11 TO October 31 | |||
|---|---|---|---|
| DATE | First Occurence | Last Occurrence | Next 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 | DATE | First Occurence | Last Occurrence | Next 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 | DATE | First Occurence | Last Occurrence | Next 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 Next Revised 19 Oct 1997