How many days and hours separate the moment of betrayal of Jesus by Judas to the beginning of the crucifixion?
This may be difficult to ascertain with any great degree of certainty, but we may be able to get close.
The Time of Betrayal
If, by the "moment of betrayal", you are referring to the Judas' kiss, then there are a few things we know. We know the disciples were having a hard time staying awake even during the first time Jesus went away to pray, and Jesus went away to pray two more times. Jesus seems to indicate that he had been praying an entire hour when he returned the first time, so it is at least possible that he went away three times, each for roughly an hour of praying.
And taking with him Peter and the two sons of Zebedee, he began to be sorrowful and troubled. Then he said to them, "My soul is very sorrowful, even to death; remain here, and watch with me." And going a little farther he fell on his face and prayed, saying, "My Father, if it be possible, let this cup pass from me; nevertheless, not as I will, but as you will." And he came to the disciples and found them sleeping. And he said to Peter, "So, could you not watch with me one hour? Watch and pray that you may not enter into temptation. The spirit indeed is willing, but the flesh is weak." Again, for the second time, he went away and prayed, "My Father, if this cannot pass unless I drink it, your will be done." And again he came and found them sleeping, for their eyes were heavy. So, leaving them again, he went away and prayed for the third time, saying the same words again. Then he came to the disciples and said to them, "Sleep and take your rest later on. See, the hour is at hand, and the Son of Man is betrayed into the hands of sinners. Rise, let us be going; see, my betrayer is at hand." (Matthew 26:37-46)
So, what time would Jesus have first gone off to pray. They had already eaten the Passover meal, so this was after that. However, this is before both daylight savings time and the invention of the incandescent light bulb, so people probably went to bed earlier, rather than staying up in the dark. They probably arose earlier in the morning as well. Being that is was during Passover, which is typically in March or April. Sunset would be around 6:00 p.m. (without daylight savings time). Sundown is typically when the Sabbath began.
If we assume they began eating at sundown and ate for two hours (this was a very significant Jewish festival), then took an hour to get to the garden, then assume three hours for Jesus to pray, we are already at midnight for the kiss of betrayal. That may be the best we can do.
The Time of Crucifixion
The crucifixion probably began around 9:00 a.m. There is some confusions about this, but this has to do with the different ways in which the Romans and Jews kept time. Darkness came over the land around noon to about 3:00 p.m., at which time Jesus committed His spirit into the hands of the Father.
So, if the betrayal occurred around midnight and the crucifixion began around 9:00 a.m., then that would be around nine hours and a total of 15 hours until the time of death.
Part of me likes the idea of symmetry, and it is perfectly reasonable to think that the betrayal was later in the evening. Thus, it could have been 6 hours from the betrayal to the inception of the crucifixion and another 6 hours to the death of Christ. That's the best I can offer, though.
Tradition says Jesus was betrayed late Thursday night, was crucified and buried before sundown on Friday. Jesus went to the garden of Gethsemane late in the evening, and prayed there for some time. A reasonable guess would be that it was Midnight to 2 AM by the time Judas led the soldiers there to arrest Jesus. Mark 15:25 says it was "the third hour" when they crucified him, which would be around 9 AM give or take an hour. It seems Jesus may have been crucified six to nine hours after He was arrested.
A careful reading of all four Gospels makes me question whether there was time enough for the events described in the nine hour period. It is quite speculative on my part, but it seems to me Jesus might have been in custody for two days. Since God chose to record four independent eyewitness accounts and it is not always clear when things are described in chronological sequence, I could easily be mistaken in some of my conclusions.
Matthew, Mark, Luke and John all agree it was late at night in the garden of Gethsemane when Jesus was arrested, lets say around 2 AM. Then (Mat 26:57, Mar 14:53, Luk 22:54, Joh 18:24) they led Jesus to the house of Caiaphas, the high priest. There was a night-time trial, during which they could find no evidence against Jesus. Then Jesus claimed to be the expected Messiah, and apparently claimed to be God as well. At that point Jesus was declared guilty of blasphemy and worthy of death (Mat 26:63-66, Mar 14:61-64).
According to Jewish law, no death penalty can be rendered at night. The Gospels suggest that after sunrise the Sanhedrin (Jewish ruling council) convened a formal session, and charged Jesus officially (Mat 27:1, Mar 15:1, Luk 22:66-69). Luke alone records the fatal question as occuring during the second trial, "Art thou the Christ? tell us." and the answer, "I AM". Many Christians believe Jesus' answer was equivalent to Yahweh or Jehovah, the covenant name of God, which God Himself described as meaning, "I am that I am". If the members of the Sanhedrin heard it that way, then there were only two choices for them. They could accuse Jesus of "blasphemy", profaning God's Holy Name and worse, claiming to be God when He was not; or they could accept His claim and worship Him.
It was now well after 6 AM, and Jesus was led to Pilate's court. John 18:28 says it was early when they arrived. In verse 30 the clerics said, "If he were not a malefactor, we would not have delivered him up unto thee" which makes me think they thought they had a deal with Pilate to rubber stamp their judgment. According to John, Pilate now took Jesus inside and questioned Him privately, finally deciding Jesus was no threat to the Roman government. By this time I think it would have been 7:30 AM at the earliest.
Only Luke records an additional trial before Herod. Even without it, there would not be enough time for Jesus to be scourged and for Pilate to try to further placate the crowd then send Jesus toward the execution site by 9 AM, much less have Him arrive and be nailed to the cross at that time.
Mark's Gospel makes it clear that the betrayal took place at midnight and the crucifixion was at 9 am, a difference of nine hours. In this, the first New Testament Gospel to be written, the last twenty four hours in the life of Jesus are described in a chiastic structure, in which an opening set of events (A-D) is mirrored by a second set (D'-A'):
A The celebration of the Passover Feast, which becomes the Last Supper, beginning "when it was evening" (Mark 14:17), or when the sun went down: approximately 6 pm and the beginning of the day of the Passover by Jewish reckoning. The Passover meal typically took three hours and was concluded by singing a hymn (Mark 14:26).
B At about 9 p.m. Mark then has Jesus and the disciples go to the Garden of Gethsemane, where Jesus went to pray. He returned three times and each time found the disciples asleep, measuring three hours of time by asking, "Could you not sleep one hour?".
C The betrayal by Judas, the darkest deed in human history, came next, occurring at the stroke of midnight. This will be reflected by the darkness at midday.
D At 3:00 a.m., Jesus was led away for a trial before the high priest and other senior priests and elders.
We know the time of the first trial because Peter's threefold denial of Jesus followed, once each hour until the cock crowed, marking the watch between 3 a.m. and 6 a.m., known as cockcrow.
E When it was 6 o'clock, "As soon as it was morning", Jesus was led by the chief priests, scribes and elders for trial by Pontius Pilate.
D' At 9 o'clock: "It was the third hour when they crucified him."
C' When "the sixth hour had come" (12 noon), darkness covered the whole earth, reflecting the betrayal at 12 midnight.
B' The three hours of darkness, until 3 p.m. mirror the agony in the Garden of Gethsemene. Jesus last words, "My God. My God, why hast thou forsaken me?" reflect the recognition that his prayer in the Garden has not been answered. At 3 o'clock Jesus cried out and gave up the ghost.
A' Joseph of Arimathea then asked Pilate for the body of Jesus, so that he could be buried before the Sabbath began at 6 p.m., when the sun went down.
The Gospels of Matthew and Luke follow this timeline more or less faithfully, although without the chiasm. John's Gospel alters the time of the crucifixion, making it take place at 12:00. We know the evening began at the twelfth hour, equivalent to exactly 6 pm and that first light was at 6 am, regardless of the time of year, as the ancients measured exactly 12 hours of daylight. Hours were of variable length, whereas today we measure a variable number of hours of daylight, always of fixed length.