Astronomical Easter Date by Spreadsheet

Astronomical Easter Comparison & Calculation by OP Armstrong

9.5/15

Table-A Calculation Formula for Astronomical Easter Calculation, Gregorian Year JD# Method A B C D E F YR pEpact JD#1Jan JD#JanNM JD#PFM1 JD#Eqnx -4000 24.3 260090.45 260113.8 260187.8 260170.2 2019 6.0 2458484.8 2458489.8 2458563.8 2458563.4 Yr

G JD#PFM 260187.8 2458563.8

H WkDy 7 5

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)

I

JD# Easter 260188.8 2458566.8 IF(H=1,G+7,8INT(H)+G)

J D#ck 1 1 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 (1) day, verification by a more precise routine is advised. NEXT N3

Astronomical Easter Comparison & Calculation by OP Armstrong

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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*(-4006Yr)),29.5306))-30),(1+MOD((365.242454*(-4006-Yr)),29.5306)))

JD# Jan1.f3

257898.52-365.242454*(-4006-Yr)

JD# Equinox.f4 1st Page

(2457102.448+(Yr-2015)*365.2422)+((-0.0005947871)*((Yr-2015)/1000)^4+(0.00392591)*((Yr-2015)/1000)^3+(0.013808751)*((Yr2015)/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 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

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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.

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Astronomical Easter Comparison & Calculation by OP Armstrong Frequency of Variation For 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 Supper

The 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.

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 Sunday For 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 Meridian Exercise 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.

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Astronomical Easter Comparison & Calculation by OP Armstrong st

th

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The 3 Mosaic Feasts of 1 month, 7 Month Ex23:14, and Pentecost Comparison of Three Major Hebrew Feasts Pentecost, The Table at right compares the three feasts set forth by Reference Nissan, Lev23, Nu28:16 Trumpets -Tishari Du16:16-17 Moses. Two of these feast weeks are routinely celebrated in most churches. The first is Easter Holy week. That starts MonthDay/ March/April May/June Ex23:14 September/Oct. date+\with Palm Sunday, followed by Good Friday, and lastly, Sabbath & blow Resurrection Sunday or Easter Sunday. The first of these 1st Day-A Sabbath, 1st Day of 1st 15th Nissan + 49D, Trumpets 1st of 7th, New Moon & sin two Holy Days of Palm Sunday and Good Friday, correspond Sabbath Month Easter + 49 days offering approximately to the 10th and 15th days of a lunar month.

A Sabbath Lev23:8, This provisioned that the 1st day of the lunar month falls 7th Day A Sabbath Ex12:6 upon a Friday, the 8th day being a Friday also, the 10th day is pick passover Lamb, 9th evening to 10th day of atonement, then a Sunday, and the 15th day being a Friday. It is 10th Psalm Sunday evening fasting provisioned that Jesus died on a Friday and His empty Passover: sunset tomb found early Sunday; thus the term Holy Week. th 14 Deut16:6, kill lamb, The feast of Pentecost is celebrated in most churches 7 Ex12:6 weeks after Easter. These first two Mosaic Feasts being unleven bread 7 days, Tabernacles for 7 th th celebrated, begs the question? If two are celebrated, then 15 15 is Good Friday & days, start with a 17th Easter Sabbath why not the 3rd and if so, then how so? If one remembers st 21 evening end unleven the words of the blessed Savior, “When you Fast� they nd 22 offering for 7 day were not in the permissive sense but in the imperative rd instance. The 40 days of Lent could be taken as something 23 Assembly dealing with fasting. However the Master was noted to Taking out the two and a fraction of weeks elapsed unto have kept the Feast of Tabernacles. So then does it not Easter, then 22 weeks after Easter corresponds to nearly the seem proper for churches to also remember this 3rd Feast? start of the seventh lunar month. A comparison of dates 22 The Sunday following Passover is typically Catholic Easter weeks after Easter to 1 Tishrei shows the two dates agree Sunday. As Easter is the Sunday following the first full moon within a few days. The odd exceptions being when Hebrew after Spring Equinox, then the start of the lunar month is calendar postponement rules are applied. One possible about 2 weeks prior. church memorial to this time would be Eucharist 22 and 24 A lunar month is about 28.5 days in length. Six lunar weeks after Easter.

BACK NEXT months are then 171 days or 24.4 weeks.

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Astronomical Easter Comparison & Calculation by OP Armstrong Only 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.

First. Page

97 YR's Astro v Catholic Easter Variants 2038AD-1AD

YR

2038 2019 1998 1967 1962 1954 1943 1927 1876 1845 1829 1825 1818 1805 1802 1744 1724 1700 550 -61

Astro 28Mr 24Mr 19Ap 02Ap 25Mr 25Ap 28Mr 24Ap 16Ap 23Mr 19Ap 03Ap 22Mr 14Ap 18Ap 29Mr 09Ap 04Ap 26Ap me26Mr

Cath 25Ap 21Ap 12Ap 26Mr 22Ap 18Ap 25Ap 17Ap 09Ap 30Mr 26Ap 10Ap 29Mr 21Ap 25Ap 05Ap 16Ap 11Ap 19Ap NoCalc

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Easter by UTC UTC this astro Ful l Moon Equi nox 28-Mar 2465503.59 2465503.03 24-Mar 2458563.57 2458563.42 19-Apr 2450915.43 2450893.33 2-Apr 2439575.64 2439570.82 25-Mar 25-Apr 28-Mar 24-Apr 9-Apr 30-Mar 26-Apr 10-Apr 29-Mar 21-Apr 25-Apr 29-Mar 9-Apr 4-Apr 26-Apr 26-Mar

2437744.83

2437744.60

2430805.42

2430805.00

2406353.32

2406333.76

2395014.35

2395011.24

2389167.08

2389167.36

2387719.77

2387706.39

2385151.09

2385149.70

2380425.49

2380401.54

2379333.61

2379305.83

1922022.20

1922022.43

1698859.401 1698859.395 6