This beautiful time-lapse video was taken from the world's highest revolving restaurant atop a mountain in the Swiss Alps. It shows the stately procession of stars as they move through the night sky. So why are some stars not moving?
The answer, of course, is that some of these points of light only look like far distant stars. In reality, they are satellites in geostationary orbit, moving around Earth at precisely the same speed as the planet rotates. This is only really possible from a very narrow range of distances from Earth, which Newton's Laws tell us is right around 22,236 miles up (for an explanation as to just why it's that particular distance, go here). This distance is a couple orders of magnitude greater than that of the International Space Station, which is only about 240 miles above sea level. This also means only a limited number of satellites can operate in geostationary orbit at any given time.
The idea of placing satellites in geostationary orbit was first proposed by Austrian rocket scientist Herman Potočnik in 1928, but the idea only really took off when legendary science fiction author Arthur C. Clarke pointed out the orbit's usefulness for radio broadcasts in a 1945 paper. The advantage of such an orbit is that antennae on Earth never have to move to track down their satellite - they know the satellite will always be in the exact same spot above the Earth. The geostationary orbit is sometimes known as the Clarke Orbit in his honor.
For more on this video, check out NASA.