A diagram of how the Sun moves through the sky on the winter solstice. Click on image for full size (49K GIF)

The upper panel shows that on the winter solstice (which occurs around December 21), the northern half of the Earth is tilted away from the Sun. Notice that the Sun is south of the equator. For you in Topeka, the altitude of the Sun at noon is 26.5°, which is pretty low in the sky. That is the lowest the Sun gets at that latitude. It has been getting lower and lower in the sky since the summer solstice and through the autumnal equinox. The bottom panel shows how the Sun moves through the sky for someone standing on the ground in Topeka.

So, on the winter solstice, the northern hemisphere is getting less direct sunlight than the southern hemisphere. This is winter for people in the northern hemisphere. During the winter, the Sun is also above the horizon for a shorter time than it is during the summer (the nights are long). The winter solstice is the shortest day of the year.

At this same time, the southern half of the Earth is tilted toward the Sun. If you were living in Valdivia, Chile (about -40° S latitude) you would be enjoying a nice warm summer.

How high the Sun get's in your sky, and how long it is above the horizon during the day, depend not only on the season, but also on your latitude.