NOTE: I HAVE ADDED A NUMBER OF LINKS AT THE END OF MY POST
I found this site a few days ago while researching the vexed question of whether Luke was right in saying that Christ was born during the census of Quirinius. I will move swiftly on to try and answer the question about when John the Baptist's preaching began, but to solve the apparent 'Quirinius contradiction', this is resolved simply if one accepts an equally valid translation of the original Greek as "This was the first census, before Quirinius was appointed governor of Syria".
I see that you welcome posts that answer the question and those with many sources listed. I shall probably fail the second criterion.
A poster above said: "Either Luke or Tertullian was wrong, or both were using different methods of counting years". I agree with this formulation. The burden of my post is that Luke was correct. I do not say that Tertullian was wrong, but he must have had in mind some other dating procedure.
I am going to frame my answer with a summary of the chronology of the life of Christ, from which it may hopefully be understood that Luke's statement that that John the Baptist's ministry began 'in the fifteenth year of Tiberius Caesar' is correct.
Recent research has brought about a probable answer to the chronology of Christ's life, resolving most of the controversies.
First, the information about the time when it was Zechariah’s lot to burn incense in the temple (Luke 1 v 8), and other data in Luke Chapters 1 to 3, tell us that Christ was probably born at the time of the Feast of Tabernacles (“He tabernacled amongst us”). This places His birth in late September/early October.
Next, we can date the year of Christ’s birth as 1 BC. Most scholars have hitherto followed Emil Schuerer’s ‘History of the Jewish People in the Time of Jesus Christ’ in dating the death of Herod in 4BC. This was based on the Jewish historian Josephus stating that Herod died weeks after a lunar eclipse. However, a far more prominent eclipse occurred on 29 December 1 BC, which places Herod’s death probably in 1 AD. This harmonises with Christ’s birth months before Herod’s death, in line with Matthew Chapter 1.
This date for Christ’s birth gives us precisely 33½ years until His crucifixion on a commonly accepted date: 3 April 33 AD. This was also the 14th day in the first month of the Jewish year, Nisan, thus precisely fulfilling the Passover day of the killing of the spotless lamb (Exodus 12 vv 6-7). Christ had entered Jerusalem on a donkey four days earlier, the 10th of Nisan, thus fulfilling Exodus 12 vv 1-5.
The beginning of Christ’s 3½ year ministry can then by dated be reference to Luke 3 vv 1-2: “In the fifteenth year of the reign of Tiberius Caesar…the word of God came unto John the son of Zacharias in the wilderness”. Augustus, Tiberius’ predecessor, died on 19 August 14 AD, Tiberius’s reign officially beginning on 18 September. So, given the ordinary meaning of ‘in the fifteenth year', this places the beginning of John the Baptist’s ministry between 18 September 28 AD and 18 September 29 AD. That harmonises with John baptising Christ in the autumn of 29 AD, by which time Christ would have fulfilled his 30 years’ service, required under Levitical rules to enter the priesthood (Numbers 4 vv 3 and 23).
Worthy of additional note is Pontius Pilate’s letter to Tiberius, in which he described the night before Christ’s crucifixion in these terms: “The moon was like blood…it did not shine all night long though it was at the full…the moon lost its brightness as though tinged with blood”. Remarkable confirmation of this can be seen today on NASA’s website, which lists all historical lunar eclipses. There is one that began at 33 minutes past midnight on 3 April AD 33 and lasted for 2 hours 50 minutes.
For information I declare that I accept that the human authors of the Bible were inspired by God to write the words that they did and that therefore all the historical information in the Bible is without error.
One reference I have used for this answer is: "Jesus: An Uncommon Journey – Studies on the Historical Jesus", by Armand Puig i Tarrech (2010), LINK:
LINKS ADDED ON 12 MARCH 2018
[ EDIT: I apologise for my lack of references. I will add a number of references I used here:
On the subject of the ‘eclipse of Herod’, here are some references about the two eclipses in 1BC, one in January 1 BC, the other in December 1BC. I tend to prefer the arguments of those who select the date of 29 December 1 BC for the eclipse. This would place Herod’s death probably in 1 AD and I would suggest Christ’s death in the autumn of 1 BC. This would make the beginning of Christ’s ministry in 29 AD and, assuming a 3½-year ministry with his ministry spanning four Passovers including the Passover of the Crucifixion, His crucifixion on 3 April 33 AD.
Of the two 1 BC eclipses, the first was apparently a full eclipse but IIRC began very late (about midnight). The one in December was only a 53% eclipse but because it started about dusk it is claimed that it would have been far more memorable and talked about:
http://www.biblearchaeology.org/post/2017/07/29/How-Lunar-and-Solar-Eclipses-Shed-Light-on-Biblical-Events.aspx (also deals with the year of the Crucifixion)
The date of the Crucifixion was I think calculated as 3 April 33 AD by Sir Isaac Newton. (I would also be interested to know what date the great Bishop Ussher assigned to it). I think most of the references to this date are readily available.
On the subject of the lunar eclipse in the early morning of 33 AD, here is the reference to the NASA site:
https://eclipse.gsfc.nasa.gov/LEhistory/LEhistory.html >>> scroll down to the section ‘ 1CE to 2000 CE’.
On the subject of Pilate’s letters, including the one referring to the blood moon, I looked at this reference:
http://www.orthodox.cn/patristics/apostolicfathers/herpilat.htm (Letters from Pilate)
It is titled ‘LETTERS OF HEROD AND PILATE’ and explains that they “connect Roman history with the death of Christ at Jerusalem. These letters occur in a Syriac manuscript in the British Museum, dated in the sixth or seventh century. There is a Greek copy in a Paris museum”.
I found this reference in ‘The Reports of Pilate, Anaphora Pilati’:
“Pilate observed in his correspondence sent to Tiberius Caesar that there was seen a blood moon eclipse at dusk — ‘…and the moon that was like blood..’; ‘And the moon, which was like blood, did not shine all night long though it was at the full, ‘; ‘…and the moon lost its brightness as though tinged with blood ‘; ‘ and the moon, as if turned into blood ‘; → The Reports of Pilate, Anaphora Pilati”.
I also googled - Reports of Pilate Anaphora Pilati and got this link:
The Reports of Pilate, Anaphora Pilati.
Then I found this link:
…which on a Google search comes up with:
by AC Baudoin - 2016
22 May 2017 - Rome: the Anaphora Pilati, or “The Report of Pilate.” I shall first briefly intro duce this text and then focus on the paragraph that opens it in some manuscripts, prior to the first person narration. In a second part of the paper, I shall bring to. —————. 1 Baudoin 2012. 2 The creation of a German word reflects ...
This article from one of the young earth creationist groups throws some doubt on whether the lunar eclipse of 3 April 33 AD produced the ‘blood moon’ effects but suggests another possible cause. It is worth a read: