GPS

NO GPS WITHOUT RELATIVITY

Global Positioning Systems are only possible where one makes two types of adjustments based on relativity theory. Not to do so would lead to errors of the magnitude of tens of meters every day. Where are dealing here with a concrete application of space-time and the curvature of space. On the one hand, a satellite in space travels at 3,874 km\s with respect to earth. The correction to be made is in the square of the speed of the satellite over the square of the speed of light, thus on the order of 10^-10 (0,...ten zeros before the 1). This may seem ridiculously little but it translates into some ten meters after 5 minutes of operations. The positioning error for a day would thus be 2 kilometers if this were not corrected. To this simple relativistic correction should be added one from General Relativity. Earth curves space-time in its vicinity, which entails a diference in period for two clocks situated at different altitudes within the gravitational field of the planet. A clock on board a satellite goes a bit more quickly than the same on earth, for the gravitational field is weaker at high altitude. The difference is appreciable, 46 microseconds per day: the effect from gravitation is here more important than that for the speed of the satellite with respect to that of the earth. The two effects go in opposite directions, but the resulting temporal imbalance of 39 us per day is not negligeable. The satellite moved by 15 centimeters during that time. Within a few days, Global Positioning Systems would become totally useless without the help of relativistic equations.

from: Deiber, André et al, La Physique pour les nuls, éditions First 2009.