The center of mass of the Earth-Moon system is actually located inside the Earth. Each of the approximately 25 satellites in orbit contains an atomic clock, as does the hand-held receiver. The satellites send signals in the microwave portion of the electromagnetic spectrum, so the receiver can only get data from satellites in its line of sight. Signals from a minimum of 4 satellites are needed to compute longitude, latitude, and altitude. The instructor actually brought a GPS receiver to class, and showed data taken on the roof of the physics building.
Many modern elevators contain a counterweight.