Why don't the latest sunrise and earliest sunset occur on the same day, instead of almost a month apart?

Answer 1

It's actually a pretty complex thing. It has to do with the fact that Earth's orbit is elliptical, and the fact that Earth's rotational axis is tilted.

The elliptical orbit causes Earth to move slower and faster at different points in its orbit. Specifically, Earth moves fastest right around now, when we are closest to the Sun. Earth moves slowest about 6 months from now, when we are farthest from the Sun. The speed of Earth's rotation doesn't change, but while we are rotating we're also moving around the Sun, and that speed changes.

There's a great website that explains this in lots of detail, with excellent animations: http://www.analemma.com/Pages/framesPage.html