History of calender dating
The day is the commonest and most straightforward measure of time.
But days are not equal in length because the earth's orbit is elliptical; when the earth is on the steeper part of its curve, it gets a bit further round the sun in one rotation than when it is on the shallow part of its orbit.
1 January is not the date of Christ's birth, but the feast of the circumcision.
This meant a lot to the early generations of Christians within the Jewish tradition, but after the victory of Roman-style Christianity this was ignored in favour of a birthday commemoration fixed to the pagan midwinter feast of 25 December, timed to mark the approximate point where the days start getting longer after the winter solstice.
The day, at least, is universally recognised on earth. The week of seven days is a purely human invention, with no equivalent in the motions of the heavens; its widespread use testifies only to the enormous influence on history of the ancient Babylonians, who invented it.
There are other uncertainties about the start of the Christian era.
The time measured on a sundial can be anything up to a quarter of an hour ahead or behind the time measured by a clock, the amount varying with the seasons.
Our day is an average day, accurate by the clock only four times a year.
I will try to offer straightforward answers, based on historical rather than merely mathematical or rational perspectives. The end-of-the-millennium question shows the limits of a purely rationalist approach to the calendar.
The more you look at these questions, the more complicated they get.
Search for history of calender dating:
The slippage of the seasons meant that it usually did not, and this apparent error in the practice of the Christian world was becoming an embarrassment.