In the Northern Hemisphere, December has the fewest
hours of daylight and the most darkness because at that
time the tilt of the Earth's axis is pointing the Northern
Hemisphere away from the Sun. However, as
counter-intuitive as it might sound, December actually
has the longest days of the year. Modern clocks,
of course, think every day is 86,400 seconds long,
but that just the average length of a solar day over the
course of the year. A solar day is what you actually
measure with a sundial, or equivalently it's the time it
takes for a line of longitude on the Earth to rotate back
to face the Sun again. This actually requires slightly
more than 360 degrees of rotation because the Earth
isn't just sitting in space rotating, it's also moving
around the Sun so it has to rotate roughly 361 degrees
before the Sun comes back perfectly overhead a
particular place on consecutive days. If the Earth's orbit
were perfectly circular and its axis were perfectly
upright, that would be the end of the story. However, the
Earth's orbit is elliptical, so sometimes the Earth is
slightly closer to the Sun, and the peculiarities of gravity
mean it moves faster when it's closer to the Sun, so it
goes farther around the Sun in 24 hours so the Earth has
to rotate slightly farther before the Sun comes back
right overhead. 0.033 degrees farther, to be precise.
More rotation takes more time, so when the Earth is
closest to the Sun, the real sundail measured day length
is lengthened by about eight seconds. Plus the Earth's
axis is tilted, which is what gives rise to the seasons,
but also means that at the time of year when the tilt
points towards or away from the sun, narrower slices of
longitude are aimed directly at the sun. So as the Earth
moves in its orbit, it has to rotate slightly farther in order
for a particular line of longitude to catch up with the
changing direction to the Sun. 0.088 degrees farther, to
be precise. And again more rotation takes more time, so
when the Earth is tilted towards the Sun, the real sundial
measured day length is lengthened by about 21
seconds. Now by a strange coincidence, we live during
a time in geologic history when the Earth's closest
approach to the Sun happens almost perfectly to
coincide with one of the two times of year when the
Earth's tilt is oriented directly towards the Sun. So these
two day lengthening effects add up. And on December
22nd, the length of a solar day as measured by a sundial
will be the longest it is all year. 86,430 seconds, for a
grand total of 30 extra seconds.
Oh, and in case you're wondering where those 30 extra
extra seconds on December 22nd go, well they get
pushed into December 23rd, and the extra seconds from
the 23rd get pushed into the 24th, and so on which is
why solar noon, or the time which the Sun is directly
overhead, shifts about 30 seconds later every day
around the solstice. This increasing disparity between
solar time and clock time is also why, in the Northern
Hemisphere, the earliest sunset happens a few weeks
before the solstice, and the latest sunrise happens a
few weeks after.