Astronomical Easter Comparison & Calculation by OP Armstrong 9.5/15

Table-A Calculation Formula for Astronomical Easter Calculation, Gregorian Year JD# MethodA B C D E F G H I J

YR pEpact JD#1Jan JD#JanNM JD#PFM1 JD#Eqnx JD#PFM WkDy JD# Easter D#ck-4000 24.3 260090.45 260113.8 260187.8 260170.2 260187.8 7 260188.8 12019 6.0 2458484.8 2458489.8 2458563.8 2458563.4 2458563.8 5 2458566.8 1

Yr pEPCT JD#Jan1.3 (B-1)+C 74.02+D F.3 or F.7 IF(E>=F,E,E+29.5) f.6(G) IF(H=1,G+7,8-INT(H)+G) f.6(i)

The above Table-A is a tabulation of calculation steps for finding Astronomical date of Easter. The example calculations use formula-2 of Table-B to determine moment of January New Moon for selected year, expressed as astronomical Julian Day number, JD#. Alternatively one could use any number of resources to arrive at a value for column B. Just be sure to express the moment as an Astronomical formatted Julian Day Number, JD#. Julian calendar or Gregorian calendar dates may be verified by the day of week. The numbers in column F, JD#.Equinox, are for equinox moment by formula 4 of Table B. The month number and day-of-month may be determined in a spreadsheet by adding two more columns and using formula 8 and 9,Table B, given that Year, Yr, is stated as input in column-A. Alternatively, the Easter JD# may be converted back to Gregorian Date by several free programs. This routine was compared by 70 dates. If using JMT in place of GMT (UT), then add an offset of 0.098 days to step “I” and “J”.A check was made against the WCC Easter dates table for years 2025 to 2001. Against that Table this method using formula 2 and 4 reproduced their result. Other checked instances returned results that matched either the Catholic Easter dates or alternative astronomical calculation results. However the data of Ovidiu Vaduvescu did not confirm the astronomical values set forth in the WCC document nor results of this calculation. If Equinox and PFM dates are closer than one (1) day, verification by a more precise routine is advised. NEXT N3 1

Astronomical Easter Comparison & Calculation by OP Armstrong 9.5/15

Name (Nu) TABLE-B Excel Astronomical Name Formula: Yr-year; JD#-Julian Day

pEpact.Cassidy.f1 29.09-MOD(MOD(Yr,19)*11-INT((Yr-1502.57-12*MOD(Yr,19))/228),29.983)

pEpact.Cassidy.0.f1b 29.5-MOD(MOD(Yr,19)*11-INT((Yr-1584-12*MOD(Yr,19))/228),30)

pEpact.Lunation#.f2 IF((1+MOD((365.242454*(-4006-Yr)),29.5306))>=30,((1+MOD((365.242454*(-4006-Yr)),29.5306))-30),(1+MOD((365.242454*(-4006-Yr)),29.5306)))

JD# Jan1.f3 257898.52-365.242454*(-4006-Yr)

JD# Equinox.f41st Page

(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))

March 1st Moon.f5 JD#.Jan1 + pEpact + 59

Day of Week.f6 (1+INT(MOD((1.5+JD#),7))) one is Sunday and 7 is Saturday, etc

JD#21March.f7 257978.00-365.242454*(-4006-Yr)

Day of Month.f8 1+INT(MOD(((INT(MOD(((INT(JD#+0.5)+(-

37+INT(0.5+0.75*INT((INT(JD#+0.5)-4479.5)/36524.25))))-59.25),365.25)))+0.5),30.6))

Month Number.f9 , 3=March, 4=April

1+MOD((2+INT(((INT(MOD(((INT(JD#+0.5)+(-37+INT(0.5+0.75*INT((INT(JD#+0.5)-4479.5)/36524.25))))-59.25),365.25)))

+0.5)/30.6)),12)

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Astronomical Easter Comparison & Calculation by OP Armstrong 9.5/15

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Look at 135 different years between 4000BC and 2038AD. The average lunar conjunction age at 4pm Easter Sunday was about 19. days, with a minimum of 15.5 days and a max of 22.2 days. Without the postponement rule, then some Easter Sundays would land before a lunar age of 13.5 day This gives a very early Lunar Good Friday of just 12.5 days. Application of the rule "Sunday following the Paschal Moon" keeps Good Friday in better alignment with the 14th lunar day. For at the minimum found above, Good Friday falls more closely on the 14th or 15th lunar day.Recapping the "raised up on 3rd day", Good Friday was day one by inclusive counting as Jesus was laid in grave before sunset on the Sabbath. Then day 2 was Friday after sunset to sunset Saturday, and day 3 inclusive count was Saturday after sunset unto about sunrise Sunday. Thus the reason for sunrise Easter service is to memorialize "Christ our Passover", "a feast by an ordinance for ever." To the end that others may wish to abolish this ".- feast by an ordinance for ever", they neglect the blessings of the Almighty and sadly invite the fires of judgment to blot their memory from off the earth!Adjustment to Jerusalem time can be accomplished by adding 2.33 hours or 0.098 days to the “if” statements and day of week calculations.

Why the Sunday after the Paschal Full Moon?Take a look at either the proleptic Catholic or Astronomical Easters for years 30 and 33AD. For these dates, the proleptic Gregorian Easter dates are April 7 and April 3, respectively. Next determine the Lunar Conjunction (astronomical new moon) age of 17.9 and 17.2 days, respectively, at 4pm Sunday. Given that Jesus died before Friday sunset and was buried before sunset, so 1 day back is, Saturday 4pm and another day back is Friday 4pm. Thus at time of Jesus death, the Lunar days are 15.9 and 15.2 respectively. Given that the visible new crescent or sighted moon is some where about 1 day after conjunction. So on Good Friday the lunar sighted moon of these years is 14 days in age. Thus Good Friday of years 30AD and 33AD would either be on Nissan 14 or 15. However, if this skip week, “after” were not used, then sometimes the Easter would come early to the lunar calendar.Why the Postponement Rule?From this it is seen that reckoning Easter by these methods speaks of "Christ our Passover", Jn18:39, 19:14, 1Cor5:7, Heb11:28, Num9:13, Ex12:14.Since the Catholic Easter concurs the Astronomical Easter in about than 95% of the dates, keeping Good Friday and Easter are keeping "Christ our Passover" as "a memorial; and .... a feast to the LORD throughout your generations; ... feast by an ordinance for ever." Ex12:14. The postponement rule importance is illustrated by calculation. NEXT

Astronomical Easter Comparison & Calculation by OP Armstrong 9.5/15

"And ye shall count unto you from the morrow after the Sabbath, from the day that ye brought the sheaf of the wave offering; seven Sabbaths shall be complete: Even unto the morrow after the seventh Sabbath shall ye number fifty days; and ye shall offer a new meat offering unto the LORD." Lev 23: 15/16. The Fifty days were numbered from a Saturday, so the 50th day falls always on a Sunday, 49days or 7 weeks after Easter SundayFor Christians, the Easter Sunday sets the precedent to find the Sunday in the 7th month. The earliest Easter being 22 March. By this the 7th lunar month starts around the last week of September. The latest Easter falls on 25 April, by which the 7th lunar month looks to fall on last week of October. The 1st Sunday after and a 3rd Sunday would be a logical memorial for the Autumn Feasts.Effect of using Jerusalem as Principle MeridianExercise Caution when the Universal Time new moon moment is on a Saturday night after 21:30 hours. As in 1998, when the Full Moon moment was Saturday at 22:23. The +2h21m offset between GMT and Jerusalem, gives a Paschal full moon on 00:44 Sunday 12 Apr. This astronomical Easter is delayed unto the following Sunday. Compared to a Catholic and/or Universal Time Easter of 12April. This shows the principle difference in the two methods. The Catholic calculation is stepped in days and weeks. The Astronomical method is a moment defined calculation. Thus it depends upon the details of complex astronomical calculations. NEXT

Frequency of VariationFor 24 years, from 2001 to 2025, only once did the Astronomical Easter differ from the Catholic Easter. That being 2019, with Astro Easter on 24March, and Catholic Easter on 21April. Many of the tabulated dates of the table were evaluated for known difficult dates likely to offer discrepancy between the two methods. Even so, only 11 of 60 years show variance between the methods. So most likely, better than 95% of years will show the Catholic Easter and Lunar Easter are same.

Other Feasts: Pentecost, Tabernacles, and The Lord's SupperThe other two of the three main feasts were Pentecost and Tabernacles. For Christians, Pentecost (7 weeks after Easter) celebrates the Holy Spirit. The feast of Tabernacles celebrates being freed from bondages of the flesh, the world, and eternal death, thru election by God the Father. By celebrating these 3 feasts, Passover (hope of a more better resurrection thru Jesus Christ), Pentecost (hope of continual renewal by Holy Spirit), and Tabernacles (hope of election and freedom from bondage thru grace of Father God), the Holy Trinity can be honored by Christians. Because Jesus initiated the Holy Communion, then communion on these days should be held in high esteem. The 1st of the first and seventh lunar months are seen as special days or Sabbath's. Also, the middle of these months are feasts of remembrance.Pentecost is by the definition, always on a Sunday by virtue of the week count, 7th Sunday after Easter. 4

Astronomical Easter Comparison & Calculation by OP Armstrong 9.5/15

Comparison of Three Major Hebrew Feasts The Table at right compares the three feasts set forth by Moses. Two of these feast weeks are routinely celebrated in most churches. The first is Easter Holy week. That starts with Palm Sunday, followed by Good Friday, and lastly, Resurrection Sunday or Easter Sunday. The first of these two Holy Days of Palm Sunday and Good Friday, correspond approximately to the 10th and 15th days of a lunar month. This provisioned that the 1st day of the lunar month falls upon a Friday, the 8th day being a Friday also, the 10th day is then a Sunday, and the 15th day being a Friday. It is provisioned that Jesus died on a Friday and His empty tomb found early Sunday; thus the term Holy Week.The feast of Pentecost is celebrated in most churches 7 weeks after Easter. These first two Mosaic Feasts being celebrated, begs the question? If two are celebrated, then why not the 3rd and if so, then how so? If one remembers the words of the blessed Savior, “When you Fast” they were not in the permissive sense but in the imperative instance. The 40 days of Lent could be taken as something dealing with fasting. However the Master was noted to have kept the Feast of Tabernacles. So then does it not seem proper for churches to also remember this 3rd Feast?The Sunday following Passover is typically Catholic Easter Sunday. As Easter is the Sunday following the first full moon after Spring Equinox, then the start of the lunar month is about 2 weeks prior. A lunar month is about 28.5 days in length. Six lunar months are then 171 days or 24.4 weeks.

The 3 Mosaic Feasts of 1st month, 7th Month Ex23:14, and Pentecost

Reference Nissan, Lev23, Nu28:16 Pentecost, Du16:16-17 Trumpets -Tishari

MonthDay/ date+\- March/April May/June Ex23:14 September/Oct.

1st Day-A Sabbath

Sabbath, 1st Day of 1st Month

15th Nissan + 49D, Easter + 49 days

Sabbath & blow Trumpets 1st of 7th,

New Moon & sin offering

7th Day A Sabbath Lev23:8, Ex12:6 A Sabbath

10th pick passover Lamb, Psalm Sunday

9th evening to 10th evening

day of atonement, fasting

14thPassover: sunset

Deut16:6, kill lamb, Ex12:6

15thunleven bread 7 days, 15th is Good Friday &

17th Easter

Tabernacles for 7 days, start with a

Sabbath21st evening end unleven 22nd offering for 7 day23rd Assembly

Taking out the two and a fraction of weeks elapsed unto Easter, then 22 weeks after Easter corresponds to nearly the start of the seventh lunar month. A comparison of dates 22 weeks after Easter to 1 Tishrei shows the two dates agree within a few days. The odd exceptions being when Hebrew calendar postponement rules are applied. One possible church memorial to this time would be Eucharist 22 and 24 weeks after Easter. BACK NEXT

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Astronomical Easter Comparison & Calculation by OP Armstrong 9.5/15

First. Page

Easterby UTC UTC

YR Astro Cath this astro Ful l Moon Equinox

2038 28Mr 25Ap 28-Mar 2465503.59 2465503.03

2019 24Mr 21Ap 24-Mar 2458563.57 2458563.42

1998 19Ap 12Ap 19-Apr 2450915.43 2450893.33

1967 02Ap 26Mr 2-Apr 2439575.64 2439570.82

1962 25Mr 22Ap 25-Mar 2437744.83 2437744.60

1954 25Ap 18Ap 25-Apr1943 28Mr 25Ap 28-Mar 2430805.42 2430805.00

1927 24Ap 17Ap 24-Apr1876 16Ap 09Ap 9-Apr 2406353.32 2406333.76

1845 23Mr 30Mr 30-Mar 2395014.35 2395011.24

1829 19Ap 26Ap 26-Apr 2389167.08 2389167.36

1825 03Ap 10Ap 10-Apr 2387719.77 2387706.39

1818 22Mr 29Mr 29-Mar 2385151.09 2385149.70

1805 14Ap 21Ap 21-Apr 2380425.49 2380401.54

1802 18Ap 25Ap 25-Apr 2379333.61 2379305.83

1744 29Mr 05Ap 29-Mar1724 09Ap 16Ap 9-Apr1700 04Ap 11Ap 4-Apr550 26Ap 19Ap 26-Apr 1922022.20 1922022.43

-61 me26Mr NoCalc 26-Mar 1698859.401 1698859.395

97 YR's Astro v Catholic Easter Variants

2038AD-1ADOnly one application offers astronomical or ‘uniform’ Easter calculation. Kalendis has not been ported to mobile devices. This Excel spreadsheet will find the Astronomical Easter for years between 4007BC and 3027AD. In Table to right, are differences between this calc and others Astro-Easter. For these, exact values of full Moon and Equinox are input. In all evaluated points, this excel sheet was verified by Kalendis to be correct. The below chart shows variations of my Full Moon Date to Kalendis. The normal range is +/- 1.5 hours for about 7000 years. Beware, not all implementations of mobile Excel have the needed numerical accuracy to evaluate these complex expressions. Only IOS-Numbers and MS-Excel routines could accurately execute these complex calculations.

??????? Microsoft Office Excel

Astronomical Easter Comparison & Calculation by OP Armstrong 9.5/15

Excel Formula for Catholic Easter by Julian Day Number for Calendar Converter or direct Excel CellC var !. Single Input of Gregorian Year, if BC then 1-Yr.BC & find Easter in 7 steps, i.e. 30AD=> 30

.f10 P' =MOD(-8-11*MOD(Yr,19)+INT((Yr-1600)/100)-INT((Yr-1600)/400)-INT((8*INT((Yr-1400)/100))/25),30) 14

.f11 P =P'-IF(P'=29,1,IF((1+MOD(Yr,19))>11,IF(P'=28,1,0),0)) 14

.f12 D.1 =118+INT(365.25*(Yr+4712))-INT(0.75*INT(((Yr)/100)+49)) 1732097

.f13 D.2 =D.1+P 1732111

.f6 D.3 =1+INT(MOD((1.5+D.2),7)) 5

.f14 D.4 =IF(D.3=1,D.2+7,8-D.3+D.2)&"Catholic Easter as Julian Day Number" 1732114

end Estr use D.4 to get Day_of_Month, f.9, &Month#, f.8, &day_of_Week,f.6 as =D&f.n&… D7M4wkd1

Here is the Catholic Easter formulation using Gregorian Year as input to find Easter Date as a Julian Day Number. This simplifies several steps as compared to other methods. The resultant JD# may be used to rapidly find Pentecost Sunday or any number of Easter dependant days. The JD# can be rapidly changes to calendar dates via formula f.6, f.8, & f.9 for historical or future dates. Beware excel dates do not display for years prior to 1901. Thus the above work around. The Easter JD# can be ported to excel date system for years 1901 forward. Simply determine the offset to Excel date number and JD#, then subtract offset to other dates. Apply this method when a wide range of dates are to be reviewed.

Most Easter routines are only valid for a few hundred years after 1901. This is substantial since Christ our Passover was slain from the foundation of the world. Thus there has been a perpetual Easter since the day this world was founded. That date was when Adam sinned, 4000 years prior to Jesus Baptism at river Jordan by Saint John. The day of resurrection was hidden by God and revealed by Christ earthly Easter day in 30AD.

The following list dates when Astronomical Easter is not same date as the Catholic Easter, about 1 in 12 years.

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Astronomical Easter Comparison & Calculation by OP Armstrong 9.5/15

This tabulation covers from years 2050 back to 60BC. A span of about 2100 years. As seen in the above Tabulation some centuries have few discrepancy than others. The cycle of 391-19 or 372 years can be seen in some skip sequences. The average is about 11 of 12 years agree and 1 in 12 years are not in agreement between the two Easter Methods. However the pattern is not uniform. Some centuries have fewer concurrences than others. Next page

Variant Astro Easter Years to Catholic Variant Astro Easter Years to Catholic2049 1700 1457 1206 915 543 254 1903 1558 1351 1074 716 384 732045 1693 1453 1199 895 536 242 1900 1552 1332 1061 685 367 662038 1685 1446 1182 881 523 235 1876 1551 1331 1030 634 343 422019 1680 1429 1162 861 519 218 1873 1527 1328 1003 614 323 221981 1666 1427 1155 854 516 216 1845 1514 1313 998 607 320 151974 1629 1419 1142 846 509 191 1829 1507 1311 979 590 313 -51967 1622 1409 1135 837 496 188 1825 1503 1308 960 588 303 -191962 1609 1408 1128 827 489 178 1818 1487 1294 959 587 292 -291954 1598 1402 1111 817 482 171 1805 1484 1284 941 570 289 -321943 1590 1389 1108 810 474 168 1802 1483 1277 935 569 273 -491927 1582 1375 1101 783 469 144 1778 1473 1237 932 563 269 -531924 1578 1370 1088 736 438 137 1744 1465 1226 922 550 262 -561923 1571 1362 1081 729 411 124 1724 1463 1218

Given the primitive nature of physics and astronomy at the time of the original formulation of the Easter Calendar, the Catholic method mostly agrees with the Astronomical formulation. That being stated, the Paschal Moon of the Catholic Easter is not a true moon. In fact it has a striking similarity to the Molad of the calculated Hebrew Calendar. But the molad event is timed to start around the autumn equinox vs. around or about the Spring Equinox for the Catholic Easter. 8