Today is the day of the earliest sunset, next month is when sunrise is latest, why is that?

Hello, Scythian!

It's because of the eccentricity (e ≈ 0.0167) of the Earth's orbit (and the amount of the discrepancy in sunset/rise extremum dates depends on your latitude). I suspect you're smart enough to figure out the rest, but for others who may read this, here goes.

The Earth's rotation rate is extremely steady/uniform (not absolutely perfect, but much better than its orbital speed). The Earth's revolution rate -- its angular velocity in orbit about the Sun -- varies more substantially. Near perihelion (Earth closest to Sun), it goes faster, sweeping out more than 1/365.26 revolution in a day, while near aphelion (Earth farthest from Sun), it goes slower, sweeping out less than 1/365.26 revolution in a day.

Meanwhile, throughout the year, the rotation remains steady. This means that near perihelion (which is Jan. 4 or so), the rotation falls behind the orbital motion, and it takes a bit more than 24 hr for the Sun to return to the same place in your sky; but then, near aphelion (early July), it catches back up again.

Now if you're at, say, 40ºN latitude, and you were to record the exact time each day that the Sun crosses your meridian in the sky (your longitude circle projected up onto the sky; which is also the quarter-circle connecting your horizon's south-point to your zenith), you'd see that it would happen earlier than average during part of the year, and later than average the rest. And because the December solstice occurs close to the Earth's aphelion date, the Sun has been "running ahead" for a few months by then. This causes both sunrise and sunset at that time of year to occur several minutes earlier than if the Earth's orbit were perfectly circular. Similarly, around the date of the June solstice, sunrise and sunset both occur several minutes later than "normal."

The upshot is, that for mid-northern latitudes:

• the date of earliest sunset is in early December (7th)

• the date of latest sunrise is in early January (4th)

• the date of latest sunset is in mid June (14th)

• the date of earliest sunrise is in late June (27th)

[dates given are for 2014]

EDIT:

If you're like me, a pictorial representation is much more informative. If you can get hold of the January issue (actually, of any year) of Sky & Telescope magazine, it always includes a separate, folded sheet titled, "Skygazer's Almanac 40ºN <year>". It depicts a bunch of astronomical events for the year, with time of night on the horizontal axis, and day-of-year on the vertical. The left and right boundaries are basically vertical plots [ x,time = f(y,date) ] of the time of sunset and sunrise, respectively, throughout the year.

do a search for "analemma".

astronomically clueful people know that the dates of earliest sunset, latest sunrise and shortest day do not coincide, and know why.