The date of the crucifixion has been a thorn in the side of New Testament scholars and is widely debated. The two most popular years are 33 AD and 30 AD splitting scholars about 50% for each. The reason for the discrepancy is that the Gospel of John differs from his account of the events of Easter week from the other three synoptic Gospels. This apparent contradiction has been the subject of debate and is a stumbling block for achieving a consensus of a single date. There are many interpretations that resolve this apparent contradiction which I will not go into. Let us just acknowledge that there is a contradiction.
Humphreys starts by establishing a set of facts that can be used to generate a series of dates that can be further scrutinized. The first fact is the range of years that we can be sure that the crucifixion took place. We know that Jesus was crucified under the governorship of Pontius Pilate and during the reign of Tiberius which was between 26 and 36 AD. The second fact that is not disputed is that the crucifixion took place on a Friday at the beginning of Passover. The third fact is not so clear because it takes into account the apparent discrepancy between John and the other Gospels. Assuming the two opposing accounts, the crucifixion either took place on Nisan (a Jewish month) 14 or Nisan 15.
Using these facts and modern astronomical software, he then generates a series of possible dates of the crucifixion. I am oversimplifying the process because the Jewish calendar was an observational one (based on the appearance of a new moon). The software was used to determine when a new moon could have been observed (establishing the month), that Nisan 14 or 15 fell on a Friday (establishing the date), and in the range of years established (establishing the year). Once the series of dates were established, the dates were cross referenced to events in the Bible whose chronology has been more soundly established. Once complete, Humphreys is left with two dates in the years 30 and 33 AD. The final elimination can be done by citing John's Gospel which records three different Passovers (including that at the crucifixion) during Jesus' ministry which effectively eliminates the 30 AD date.
This later date also explains the uncharacteristic behavior of Pilate when it comes to sentencing Jesus. Pilate was known for his toughness, yet when it comes to sentencing Jesus he hesitates. This later date may explain his hesitation. His mentor had been recently executed for mistreating the Jews. Pilate took this execution as a grave warning about mistreating the Jews which is why he hesitated to sentence Jesus. He is subsequently forced to carry out the sentence by the angry mob.
Thus, the final conclusion is that Jesus Christ was crucified by Pontius Pilate on April 3, 33 AD.
Humphrey's then proceeds to examine extra-biblical sources and non-canonical Gospels to corroborate his chosen date. He finds the following passages:
Acts 2 14:21The original passage:
Then Peter stood up with the Eleven, raised his voice and addressed the crowd: "Fellow Jews and all of you who live in Jerusalem, let me explain this to you; listen carefully to what I say. These men are not drunk, as you suppose. It's only nine in the morning! No, this is what was spoken by the prophet Joel: 'In the last days, God says, I will pour out my Spirit on all people. Your sons and daughters will prophesy, your young men will see visions, your old men will dream dreams. Even on my servants, both men and women, I will pour out my Spirit in those days, and they will prophesy.
I will show wonders in the heaven above and signs on the earth below, blood and fire and billows of smoke. The sun will be turned to darkness and the moon to blood before the coming of the great and glorious day of the Lord. And everyone who calls on the name of the Lord will be saved.'
Joel 2:31
The sun shall be turned into darkness, and the moon into blood, before the
great and terrible day of the LORD come.
A New Testament Apocryphal fragment known as the "Report of Pilate" contained the following passage (It should be noted that although much of the Apocryphal cannot be used a as primary historical evidence, Tertullian records that Pilate did in fact write a report of all of the facts of the crucifixion for the Emperor Tiberius. This gives evidence the Apocryphal may be based on an earlier document):
the Sun was darkened; the stars appeared and in all the world people lighted lamps from the sixth hour till evening; the Moon appeared like blood.Humphreys finds other historically established usages of the phrase "moon appeared like blood" and "moon to blood." In each of the chronologically established accounts, the phrase is used to describe a lunar eclipse. Also in each of these accounts, a lunar eclipse can be found to have occurred using NASA's database. Humphrey's then uses that database to determine if any lunar eclipses have occurred during the years that Pilot was governor that could be seen from Jerusalem. He finds that in for all of the years surveyed there is only a single lunar eclipse that could have been seen from Jerusalem. This eclipse took place on April 3, 33 AD.
The preceding is an admittedly superficial account of the lecture (from memory). Humphreys published his findings in Nature if you are interested in reading a more detailed account of the findings.
Crucifixion Article