As I write, we're only a few hours from the winter solstice, the point when the North Pole is tilted furthest away from the Sun. This year, the solstice is at 23:03 GMT, so make sure you get your Yule log burning tonight... otherwise Thor will get very upset 😉
There's a fascinating article on the BBC website today, which I think is very well written. It explains why the Sun will continue to rise later in the morning up until 2 January, and how the earliest sunset was on 11 December. Some nice explanations from Prof Ian Morison as well.
Suffice to say that this can all be explained by the "equation of time", a formula for which was first provided by none other than John Flamsteed, who published tables back in 1673. This was before he became the first Astronomer Royal in 1675.
The article can be read here: http://www.bbc.co.uk/news/magazine-30549149
I found this site http://www.analemma.com   There are two applications that can be downloaded.
It has some graphics showing the movement of the sun/earth orbit. It also goes through some of the mathematics to calculate sunrise/sunset and the true position of the sun. (Fortunately, I found this site before I sent a letter to NASA telling them their calculations of the angles for the solar eclipse were wrong. That could have been embarrassing!) If you are reading the item quickly remember, it uses e as the eccentricity of an ellipse not e = 2.718281828459045235360287471352662497757...
Hope this helps,
Bill O'Brien
It also goes through some of the mathematics to calculate sunrise/sunset and the true position of the sun. (Fortunately, I found this site before I sent a letter to NASA telling them their calculations of the angles for the solar eclipse were wrong. That could have been embarrassing!)
Glad you got this sorted!