No. rotations does the earth make on a single orbit of sun?

How many rotations does the earth make on it's own axis in a single orbit around the Sun?

Is the earliest sun set and the last sun rise on the winter solstice?

Darragh

How many rotations does the earth make on it's own axis in a single orbit around the Sun?

Almost exactly 365 and a quarter.

Is the earliest sun set and the last sun rise on the winter solstice?

Darragh

No, they are offset by about a week but I can't remember offhand which is which.

The start of the day continues getting later for about a week after the
solstice, but the days start getting longer almost immediately
(the rate of change is small at the solstice itself, though, changing
to about 4 min/day later)

How many rotations does the earth make on it's own axis in a single orbit around the Sun?

That's the same as asking how many days are in a year.

1 day = 24h00m
1 Earth rotation = 23h56m

The 4min difference arises because the day is measured relative to the Sun so that the Sun is at the highest point in the sky at the same time each day, but during the course of one rotation about its axis (siderial day) the Earth moves 1/365.25 of the way around the Sun. Note that 4 mins = approx 1/365.25th day.

So in fact the answer is that the Earth rotates about its own axis more times in a year than the number of days in a year! In fact, logic suggests that the answer is 366.25 times.

Am I right?

365.25

Thats what i've always been told.