Sepp Rothwangl said:
> The Catholics choose 21st of March as eternal „calendrical“ > vernal equinox That's what they may have said at the Council of Nicaea, but the modern definition is: Easter is the first Sunday after the first full moon which occurs at or after the vernal equinox. Daniel Otero said: > I suspect that Easter is indeed calculated as defined by Nicaea, but > that the actual sun is not used in these calculations. Instead, they > use a “mean” sun of sorts that is assumed to satisfy certain > highly regular motions that are not quite the same as those of the > real sun. There are two ways to calculate the dates and times of the equinoxes and solstices, using either the "mean sun" or the "true sun". See https://www.hermetic.ch/eqsol/eqsol.htm Regards, Peter 
Dear Daniel and Other Calendar People
Easter is calculated by an arithmetic rule in which the vernal equal is taken to occur on 21 March every year. Details are given in https://en.wikipedia.org/wiki/Computus When the Julian calendar was reformed by replacing it with the Gregorian calendar. Not only was 21 March placed closer to the vernal equinox, but also the 19year cycle used in reckoning the full moon was corrected. The full moon reckoned for the Julian calendar is about 4 days late and sometimes results in the Orthodox Easter occurring one week later than the Western Easter and this will happen in both 2019 and 2020. Karl Friday Alpha March 2019 Original message From : [hidden email] Date : 08/03/2019  14:44 (GMT) To : [hidden email] Subject : Date of Easter Sepp Rothwangl said: > The Catholics choose 21st of March as eternal „calendrical“ > vernal equinox That's what they may have said at the Council of Nicaea, but the modern definition is: Easter is the first Sunday after the first full moon which occurs at or after the vernal equinox. Daniel Otero said: > I suspect that Easter is indeed calculated as defined by Nicaea, but > that the actual sun is not used in these calculations. Instead, they > use a “mean” sun of sorts that is assumed to satisfy certain > highly regular motions that are not quite the same as those of the > real sun. There are two ways to calculate the dates and times of the equinoxes and solstices, using either the "mean sun" or the "true sun". See https://www.hermetic.ch/eqsol/eqsol.htm Regards, Peter 
In reply to this post by Peter Meyer
Karl said:
> Easter is calculated by an arithmetic rule in which the vernal [equinox] > is taken to occur on 21 March every year. Details are given in > https://en.wikipedia.org/wiki/Computus So does it ever happen that the date of (Western) Easter is NOT the first Sunday at or after the exact moment of the first full moon (actually, dark moon) which occurs at or after the exact moment of the (northern) vernal equinox? (Exact moments of full moon and vernal equinox expressed as date and time UTC.) Regards, Peter 
This occurs every now and then  this year, for instance.
The last previous occasion was in 1981, the next one (after 2019) will be in 2038. For a more complete list see http://www.staff.science.uu.nl/~gent0113/easter/easter_text3a.htm rvg Original Message From: East Carolina University Calendar discussion List <[hidden email]> On Behalf Of Peter Meyer Sent: Fri 08 March 2019 16:20 To: [hidden email] Subject: Re: Date of Easter Karl said: > Easter is calculated by an arithmetic rule in which the vernal > [equinox] is taken to occur on 21 March every year. Details are given > in https://en.wikipedia.org/wiki/Computus So does it ever happen that the date of (Western) Easter is NOT the first Sunday at or after the exact moment of the first full moon (actually, dark moon) which occurs at or after the exact moment of the (northern) vernal equinox? (Exact moments of full moon and vernal equinox expressed as date and time UTC.) Regards, Peter 
Dear Rob and Calendar People
All three examples have golden number 6. Indeed every such year between 1900 and 2100 except 1905 & 2000 appears on the list of years where arithmetic Easter is different from astronomical. There are also examples with other golden numbers, but none between 1981 and 2038. Karl Saturday Alpha March 2019 (Easter Sunday Gamma April in 2019) Original message From : [hidden email] Date : 08/03/2019  15:37 (GMT) To : [hidden email] Subject : Re: Date of Easter This occurs every now and then  this year, for instance. The last previous occasion was in 1981, the next one (after 2019) will be in 2038. For a more complete list see http://www.staff.science.uu.nl/~gent0113/easter/easter_text3a.htm rvg Original Message From: East Carolina University Calendar discussion List <[hidden email]> On Behalf Of Peter Meyer Sent: Fri 08 March 2019 16:20 To: [hidden email] Subject: Re: Date of Easter Karl said: > Easter is calculated by an arithmetic rule in which the vernal > [equinox] is taken to occur on 21 March every year. Details are given > in https://en.wikipedia.org/wiki/Computus So does it ever happen that the date of (Western) Easter is NOT the first Sunday at or after the exact moment of the first full moon (actually, dark moon) which occurs at or after the exact moment of the (northern) vernal equinox? (Exact moments of full moon and vernal equinox expressed as date and time UTC.) Regards, Peter 
In reply to this post by Peter Meyer
Dear Karl et al Is the problem with the leap year rule or with the table of epacts? Could the exceptional cases be minimized with a different leap year rule or lunar calculation? Walter Ziobro On Saturday, March 9, 2019 K PALMEN <[hidden email]> wrote: Dear Rob and Calendar People
All three examples have golden number 6. Indeed every such year between 1900 and 2100 except 1905 & 2000 appears on the list of years where arithmetic Easter is different from astronomical. There are also examples with other golden numbers, but none between 1981 and 2038. Karl Saturday Alpha March 2019 (Easter Sunday Gamma April in 2019) Original message From : [hidden email] Date : 08/03/2019  15:37 (GMT) To : [hidden email] Subject : Re: Date of Easter This occurs every now and then  this year, for instance. The last previous occasion was in 1981, the next one (after 2019) will be in 2038. For a more complete list see http://www.staff.science.uu.nl/~gent0113/easter/easter_text3a.htm rvg Original Message From: East Carolina University Calendar discussion List <[hidden email]> On Behalf Of Peter Meyer Sent: Fri 08 March 2019 16:20 To: [hidden email] Subject: Re: Date of Easter Karl said: > Easter is calculated by an arithmetic rule in which the vernal > [equinox] is taken to occur on 21 March every year. Details are given > in https://en.wikipedia.org/wiki/Computus So does it ever happen that the date of (Western) Easter is NOT the first Sunday at or after the exact moment of the first full moon (actually, dark moon) which occurs at or after the exact moment of the (northern) vernal equinox? (Exact moments of full moon and vernal equinox expressed as date and time UTC.) Regards, Peter 
Dear Walter and Calendar People
It is possible to reduce the number of years that the arithmetic Easter differs from the astronomical Easter, by changing the Arithmetic rule, but not eliminate them completely. In general, this would make arithmetic rule more complicated. A Newtonian method in which the full moons are reckoned by a calendar similar to my yerm calendar should produce fewer differing years. Karl Sunday Alpha March 2019
Original message 
In reply to this post by k.palmen@btinternet.com
Hi Karl,
Maybe related to the fact that, between 1700 and 2199, Easter full moons with golden number 6 always fall on the latest possible date (18 April). http://www.staff.science.uu.nl/~gent0113/publications/perpetual_calendar.pdf rvg Original Message From: East Carolina University Calendar discussion List <[hidden email]> On Behalf Of K PALMEN Sent: Sat 09 March 2019 17:50 To: [hidden email] Subject: Re: Date of Easter Dear Rob and Calendar People All three examples have golden number 6. Indeed every such year between 1900 and 2100 except 1905 & 2000 appears on the list of years where arithmetic Easter is different from astronomical. There are also examples with other golden numbers, but none between 1981 and 2038. Karl Saturday Alpha March 2019 (Easter Sunday Gamma April in 2019) Original message From : [hidden email] Date : 08/03/2019  15:37 (GMT) To : [hidden email] Subject : Re: Date of Easter This occurs every now and then  this year, for instance. The last previous occasion was in 1981, the next one (after 2019) will be in 2038. For a more complete list see http://www.staff.science.uu.nl/~gent0113/easter/easter_text3a.htm rvg Original Message From: East Carolina University Calendar discussion List <[hidden email]> On Behalf Of Peter Meyer Sent: Fri 08 March 2019 16:20 To: [hidden email] Subject: Re: Date of Easter Karl said: > Easter is calculated by an arithmetic rule in which the vernal > [equinox] is taken to occur on 21 March every year. Details are given > in https://en.wikipedia.org/wiki/Computus So does it ever happen that the date of (Western) Easter is NOT the first Sunday at or after the exact moment of the first full moon (actually, dark moon) which occurs at or after the exact moment of the (northern) vernal equinox? (Exact moments of full moon and vernal equinox expressed as date and time UTC.) Regards, Peter 
In reply to this post by Walter J Ziobro
Dear Walter and Calendar People
I think the following leap year rule and epacts would deliver a small improvement. Use a 77year cycle of 19 leap years with leap years 4 years apart within (like an extended 33year cycle). Then epacts that follow the 19year cycle like in the Julian calendar would give a good result. For the solar calendar to be accurate, some of its leap days need dropping. For each of these, one does a solar equation correction to the epacts. If these dropped leap days were to occur once every three 77year cycles, one would get the mean year of the 33year cycle (365.2424242424... days). Karl Monday Beta March 2019 Original message 
In reply to this post by Peter Meyer
Dear Karl et al Walter Ziobro On Monday, March 11, 2019 K PALMEN <[hidden email]> wrote: Dear Walter and Calendar People I think the following leap year rule and epacts would deliver a small improvement. Use a 77year cycle of 19 leap years with leap years 4 years apart within (like an extended 33year cycle). Then epacts that follow the 19year cycle like in the Julian calendar would give a good result. For the solar calendar to be accurate, some of its leap days need dropping. For each of these, one does a solar equation correction to the epacts. If these dropped leap days were to occur once every three 77year cycles, one would get the mean year of the 33year cycle (365.2424242424... days). Karl Monday Beta March 2019 Original message 
Walter, Karl sirs:
>Interesting. 3 x 77 = 231 years = 7 33 >years. It seems 231year cycle is important factor to consider. This can also be 11*21=231, perhaps may be interesting for epact count. 231 years have 84371/7=12053 weeks. Thanks & regards,
Brij B. VIJ
Monday, 2019 March 11H09:21 (decimal)
Sent from my iPhone

In reply to this post by Walter J Ziobro
Dear Walter & Calendar People
Yes. Three 77year cycles have 3x19=57 leap days one of which is dropped to leave 56 and seven 33year cycles have 7x8=56 leap days. Work remaining for this calendar is to find an epoch and epoch epact that best fits the astronomical calendar. Karl Monday Beta March 2019
Original message 
Karl, Walter, list sirs:
>Work remaining for this calendar is to find >an epoch and epoch epact that best fits >the astronomical calendar.
Epact calculations, in respect to current discussion may be useful for 77year ‘epact consideration’ when used along 3cycles as {20+(19,19,19)+{20+(19,19,19)+{20+(19,19, & 19}}=231years ie.3cycles of 77years. Please note; From my earlier demonstrated calculations: {Tithi=1 335/326919 day}= 1.001024718661197 d x 6932.5 tithi =6939.603862118751 days =19.0000061811592 Years! I link, this to Harappa 19year (now called & known as Metonic) cycle. It is my opinion, there cannot be better distribution achieved for epact observation.
In this above calculation, I show my Harappa Tithi, while my Tithi for 896year cycle 1+338/326919 day exactly fitting with 326257 days. Both Tithi values can be used independently as either/or situation, where need arises. Regards,
ExFltLt Brij Bhushan VIJ (Retd.)
Tuesday, 2019 March 12H05:91(decimal)
Sent from my iPhone

In reply to this post by k.palmen@btinternet.com
Dear Calendar People
I thought of a provisional epoch and epoch epact for this calendar. The epoch is the same as for proleptic Gregorian and DeeCecil calendars and the epact of year 1 (Golden number 2) is 20, so 19year cycles initially start with epact 9. Also I decided the dropped leap day will occur in the middle of the 231year cycle on the 29th of the 57 leap years that would otherwise occur, which is the 117th year of the 231year cycle and the 40th year of the second 77year cycle of the 231year cycle. This ensures that the mean year start is exactly the same as for the DeeCecil calendar. Also years 309 to 347 are aligned with the Julian Calendar and each 19year cycle starts with an epact of 8 (reduced from 9 by one dropped leap day in year 117), which puts the Paschal full moon on April 5 and so for these years 309347 the Easters are exactly the same as for the Julian calendar. Work still needs to be done to see how this compares with astronomical Easters today and it can be adjusted to improve the fit with astronomical Easters. Karl Thursday Beta March 2019 Original message 
Sirs:
I have been discussing my 19year Harappa Tithi Calendar for quite some time.
This format is based on Gregorian calendar with 13th removed from Every month to suit my Tithi calendar format using Tithi=1+335/ 326919 day (or even 1+338/326819 day ) having SQUARE fit in my 896year Cycle. The two Tithi units can comfortably be used in both (19years or 896/years) cycles. The
denominator is so chosen as to have No. of Tithi in 11082 moons, in 327257 days  the number of days in my 896years=46751 weeks having Mean Year=365.2421875days.
You are aware of my improved Mean Lunation value as:
Regards,
Flt Lt Brij Bhushan VIJ (Retd.), IAF
FRIDAY, 2019 March 15H23:38 (decimal)
Sent from my iPhone

In reply to this post by Gent, R.H. van (Rob)
Dear Robert and Calendar People
This suggests that if the epacts were 1 less (28 instead of 29 for years of golden number 1), then these Easter full moons would occur a month earlier. This could correct 1924, 1943, 1962, 2019, 2038, 2057, 2076 & 2095, but not 1981 which would then be a month out rather than a week out and also 1905 & 2000, which are correct. I've been thinking about my 77year cycle calendar as described in an earlier note. I thought a good initial epact would be 20 (for year 1 golden number 2), but now think 18 would be better this gives epact 7 to years of golden number 1 from AD 1 to 116. For years 1965 to 2195, this becomes 28 also from 2003 to 2079 half the years are 1 day earlier than Gregorian and half match the Gregorian (for March & April) and so for (almost) half the years reducing the epact by 1, and changing to this calendar, would make no difference to the Easter full moon DAY. More work would need to be done in checking other years particularly those that have the Easter full moon in or near a weekend. Karl Saturday Beta March 2019 Original message From : [hidden email] Date : 10/03/2019  13:28 (GMT) To : [hidden email] Subject : Re: Date of Easter Hi Karl, Maybe related to the fact that, between 1700 and 2199, Easter full moons with golden number 6 always fall on the latest possible date (18 April). http://www.staff.science.uu.nl/~gent0113/publications/perpetual_calendar.pdf rvg Original Message From: East Carolina University Calendar discussion List <[hidden email]> On Behalf Of K PALMEN Sent: Sat 09 March 2019 17:50 To: [hidden email] Subject: Re: Date of Easter Dear Rob and Calendar People All three examples have golden number 6. Indeed every such year between 1900 and 2100 except 1905 & 2000 appears on the list of years where arithmetic Easter is different from astronomical. There are also examples with other golden numbers, but none between 1981 and 2038. Karl Saturday Alpha March 2019 (Easter Sunday Gamma April in 2019) Original message From : [hidden email] Date : 08/03/2019  15:37 (GMT) To : [hidden email] Subject : Re: Date of Easter This occurs every now and then  this year, for instance. The last previous occasion was in 1981, the next one (after 2019) will be in 2038. For a more complete list see http://www.staff.science.uu.nl/~gent0113/easter/easter_text3a.htm rvg Original Message From: East Carolina University Calendar discussion List <[hidden email]> On Behalf Of Peter Meyer Sent: Fri 08 March 2019 16:20 To: [hidden email] Subject: Re: Date of Easter Karl said: > Easter is calculated by an arithmetic rule in which the vernal > [equinox] is taken to occur on 21 March every year. Details are given > in https://en.wikipedia.org/wiki/Computus So does it ever happen that the date of (Western) Easter is NOT the first Sunday at or after the exact moment of the first full moon (actually, dark moon) which occurs at or after the exact moment of the (northern) vernal equinox? (Exact moments of full moon and vernal equinox expressed as date and time UTC.) Regards, Peter 
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