A couple of things.
None of my three kids got to 282. The closest was around 270 and the others around 260.
You DO get the point that no one believes it is 9 months mathematically exact, it is a good reference, and in the case of Jesus, a (supposed) miracle. It is much neater to say 9 months (and so 25/3 to 25/12) than 282 days .
You should see the napkin rings.
The 280+ figures also include a couple weeks before actual conception, and I believe the plus/minus is like two weeks.
APB is correct. Saturnalia of course was celebrated long before JC was born. But not on Dec 25th, note. Usu Dec 21st- but the Roman calendar was WAY off almost every year until Ceasar became Dictator & changed to the Julian calendar, and so it is hard to come up with exact dates. Besides- there were so many holidays on the roman calendar- than any day selected for JC’s birthday would be close to one.
As to Sol Invictus- actual archealogists & their studies of Mitraism have far more lacunae in their knowledge of this SECRET faith than modern neo-pagans & such would have you beleive. But in general- Mitraism did not become a popular Roman faith until well after the death of JC. It SEEMS (note this word) that Mitraism borrowed more from Christianity that the other way.
In any case, early Christians were already arguing dates for Christmas long before Sol Invictus became common. It APPEARS that the Dec date (along with a Jan 6th date) was argued before any large celebrations of Sol Invictus. (Saturnalia was still around but dying off).
To be honest- we have no idea when JC was born- Dec 25th was as good as any. We also don’t know why they settled on Dec 25th out of all the calculated dates- and it could well be that they picked Dec 25th OUT OF THE VARIOUS ARGUED DATES- to compete with Sol Invictus. But that was already very likely one of the dates that was a strong contender. (as Rodrigo and his cite says)
So- we really don’t know, but it seems pretty certain that they didn’t JUST select Dec 25 “as there was already a Pagan Holiday there”- although that could very well have been the “tie-breaker” so to speak.