"According to the Jewish calendar and customs when was Jesus buried to be 3 days and 3 nights in the grave in order to arise on the first day of the week. How does the Gregorian calendar fit in with this?"
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(All quotations from the King James Version unless stated otherwise).
I cannot answer for the Jewish calendar and customs or the Gregorian calendar as neither is reliable. The weight of the evidence in the Bible is that Jesus ate the Passover according to the Law, as the 14th of Nisan ended and the 15th began (approx 6pm). He was arrested about midnight on the 15th of Nisan, crucified at 9am, died at 3pm and was buried before 6pm on the 15th of Nisan. The 15th of Nisan was the preparation day (In Exodus 12:16 it is a holy convocation, but food can be prepared and it is NOT designated a Sabbath) He remained in the tomb on the 16th of Nisan which was the weekly Sabbath and was raised early on the 17th Nisan, the first day of the week.
The single ‘three days and three nights in the heart of the earth’ cannot contradict the 12 plain statements ‘on the third day’ and the 6 plain statements ‘(with)in three days’ and must be understood as idiomatic (as the lexicon used with the Strong’s number suggests).
Below is a chart in which resurrection ON the third day is shown to be undisputable.
On the Third Day
Three days and three nights
Hos 6:2 After two days will he revive us: in the third day he will raise us up, and we shall live in his sight.
Mt 16:21… and be raised again the third day.
Mt 17:23… the third day he shall be raised again…
Mt 20:19… and the third day he shall rise again.
Mt 27:64 Command therefore that the sepulchre be made sure until the third day …
Mr 9:31… he shall rise the third day.
Mr 10:34 …and the third day he shall rise again.
Lu 9:22… and be raised the third day.
Lu 18:33 And they shall scourge him, and put him to death: and the third day he shall rise again.
Lu 24:7… delivered into the hands of sinful men, and be crucified, and the third day rise again.
Lu 24:21… and beside all this, to day is the third day since these things were done.
Lu 24:46… thus it behoved Christ to suffer, and to rise from the dead the third day:
Ac 10:40 Him God raised up the third day, and shewed him openly;
1Co 15:4…he rose again the third day according to the scriptures: (Hos 6:2 above?)
Jon 1:17… Jonah was in the belly of the fish three days and three nights.
Mt 12:40For as Jonas was three days and three nights in the whale’s belly; so shall the Son of man be three days and three nights in the heart of the earth.
Day 2250 hemera: 1) the day, used of the natural day, or the interval between sunrise and sunset, as distinguished from the night; 1a) in the daytime; 1b) metaph., "the day" is regarded as the time for abstaining from indulgence, vice, crime, because acts of the sort are perpetrated at night and in darkness;
2) of the civil day, or the space of twenty four hours (thus including the night) 2a) Eastern usage of this term differs from our western usage. Any part of a day is counted as a whole day, hence the expression "three days and three nights" does not mean literally three whole days, but at least one whole day plus part of two other days.
Idiom used in OT
1 Sam 30:12…for he had eaten no bread, nor drunk any water, three days and three nights.
13… my master left me, because three days agone I fell sick.
In Three Days
After Three Days
Mt 26:61…This fellow said, I am able to destroy the temple of God, and to build it in three days.
Mt 27:40 And saying, Thou that destroyest the temple, and buildest it in three days…
Mr 14:58...I will destroy this temple that is made with hands, and within three days I will build another…
Mr 15:29…Ah, thou that destroyest the temple, and buildest it in three days,
Joh 2:19 Jesus answered and said unto them, Destroy this temple, and in three days I will raise it up.
Joh 2:20…Forty and six years was this temple in building, and wilt thou rear it up in three days?
Mt 27:63 Saying, Sir, we remember that that deceiver said… After three days I will rise again.
Mr 8:31… be killed, and after three days rise again.
Idiom used in OT
2Ch 10:5 And he said unto them, Come again unto me after three days. And the people departed.
12…came to Rehoboam on the third day, as the king bade, saying, Come again to me on the third day.
Below is an explanation by Ignatius of Antioch who lived approximately AD 30-107. He seems to have no problem reconciling the three days and three nights with resurrection ‘on the third day’.
Ignatius of Antioch was the third bishop of the Christian church in Antioch. He lived from approximately 30 A.D. through 107 A.D. In his Epistle to the Trallians, written around 60 A.D., he explained how Christians of his time understood the meaning of Christ's prediction He would be in the grave "three days and three nights."
Chapter 9.—Reference to the history of Christ.
...He also rose again in three days, the Father raising Him up; and after spending forty days with the apostles, He was received up to the Father, and “sat down at His right hand, expecting till His enemies are placed under His feet.” Heb 10:12,13. On the day of the preparation, then, at the third hour, He received the sentence from Pilate, the Father permitting that to happen; at the sixth hour He was crucified; at the ninth hour He gave up the ghost; and before sunset He was buried. During the Sabbath He continued under the earth in the tomb in which Joseph of Arimathæa had laid Him. At the dawning of the Lord’s day He arose from the dead, according to what was spoken by Himself, “As Jonah was three days and three nights in the whale’s belly, so shall the Son of man also be three days and three nights in the heart of the earth.” Matt 12:40. The day of the preparation, then, comprises the passion; the Sabbath embraces the burial; the Lord’s Day contains the resurrection.
The idea that Jesus died on the 14th of Nisan arises from John 18:28:
John 18:28 Then led they Jesus from Caiaphas unto the hall of judgment: and it was early; and they themselves went not into the judgment hall, lest they should be defiled; but that they might eat the passover.
This can be explained in that both the Passover meal and the feast of Unleavened Bread were both called the Passover.
Luke 22:1 Now the feast of unleavened bread drew nigh, which is called the Passover.
It is reasonable to suppose that the Passover lamb had been eaten by the Jews at the same time as Christ ate it with his disciples. It is not reasonable to suggest that the lamb had been killed and Christ had eaten the Passover on the wrong day.
Luke 22:7 Then came the day of unleavened bread, when the passover must be killed. 8 And he sent Peter and John, saying, Go and prepare us the passover, that we may eat.
Matthew 26:19... and they made ready the passover.
Mark 14:16... and they made ready the passover.
Luke 22:13... and they made ready the passover.
Luke 22:15... he said unto them, With desire I have desired to eat this passover with you before I suffer:
It is reasonable to suppose that the Passover that the Jews didn’t want to be barred from eating was the first meal of the feast of unleavened bread which would be eaten late on the 15th of Nisan (as Jesus was being buried). This began a week of feasting in one another’s houses with the uppermost rooms at feasts which they loved (Matthew 23:6).
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May God bless you,