So which way does the Little Dipper appear to rotate around Polaris?
Every time I consider that question I come up with two different answers, and they both make perfect sense.
Still, I figure it has to be counter-clockwise. It has to be. If you're laying flat on your back at the north end of the Earth's axis of rotation, you are rotating clockwise. Therefore the Little Dipper will appear to rotate counter-clockwise.
The problem is very easily reducible if you confine it to the simplest cases--either at the axis of rotation, or at the equator--but when you live at around 45° of latitude it becomes a lot less intuitive.
Motion of the celestial bodies doesn't make much sense anyway. If you look at a plot of the sun's track across the sky in summer and winter, the angle of that track with respect to the ground doesn't change. The Earth maintains a more-or-less constant 23.5° tilt with respect to the ecliptic, and this is what gives us our seasons; the sun appears to move north and south over the course of a typical year. But while it stays in the sky longer in summer than in winter, the arc it makes merely translates across the compass: from a southeast to southwest track, to a northeast to northwest track. Its angle doesn't change.
The sun is always in the ecliptic, of course, and the planets largely confine themselves to that plane--so if there are planets visible, you can trace it out at night. If you can see sun and moon in the daytime, you can trace it out then, too.
Here's an interesting fact that took me years to figure out: since both the sun and the moon are on the ecliptic, they switch positions in summer and winter. When the moon is full, in winter, it's high in the sky; but in summer, it'll be low in the sky. The sun is naturally low in the sky in winter, but high in the sky in summer. It's because the moon, when full, is always at opposition to the sun--ie on the opposite side of the sky.
Mercury and Venus can never be at opposition, because their orbits lie between the Earth and the sun. But all the planets can be in conjunction--hidden in or behind the sun--and never fail to be in conjunction at least once per year.
Whenever I really start to think about the structure of our solar system I realize how smart the ancient astrologers really were. Without even knowing how to calculate the orbits of the planets, they were able to predict the motions of the planets through the sky; they had only arithmetic, no calculus or even algebra to help them with their astrological calculations. Here I am with a computer, astronomy software, and all kinds of technology, and I can't even keep the rotation of the Earth straight.
Kepler and Galileo were genuises in their own right. Kepler figured out how orbital motion works and why it works that way, without calculus. Galileo's insistence on a sun-centric solar system was a defining moment in the history of the Renaissance, for crying out loud.
But the astrologers gave us a lot of knowledge about the motions of the planets, much the same way alchemists gave us a lot of knowledge about the interactions of chemicals--though both sciences have their foundations in superstition and mystique, they have risen above that.
I had an opportunity to play around with "Distant Suns" Special Edition--the freeware demo version available for download from the company's web site. I can't recommend it, though. While I was fiddling with it, it crashed so hard that I couldn't shut down my computer! When I tried to shut it down, I'd get an error message claiming that RUNDLL32 had caused an error in GDI.EXE and the progam would terminate. Yahoo, that really makes me want to shell out money for the non-crippled version!