Friday, 12th December, 2008

Relativity is Real in GPS

We may think that relativity is abstract and far removed from everyday life and the “real” world. Time, for instance, is said to run differently depending on our speeds or environments, but is it so tiny as not to be noticeable in everyday life?

Philip Yam, in Scientific American, 2004, page 39, knows differently.

gps satellite.jpg

It is relevant, and it is noticeable. Global positioning systems, which we use in cars, planes and ships, depend on measuring the time radio waves take to reach us from a satellite of known position; this enables the receiver, which measures the travel time of the radio signal, to work out the distance from the satellite. Once four satellites have been measured, we can find our position.

Now if the satellite clocks were to run at a slightly wrong speed, say losing 2 nanoseconds a day (that’s 2 billionths of a second per day), then the satellites would appear to be 60cm further away each day, and we would soon have a build-up of error.

The times on the satellite clocks thus have to very accurate indeed,and any small effects (such as those due to relativity) can have a real effect on the navigation abilities of GPS systems.

There are in fact two relativistic effects: the speed of the satellite relative to the ground slows its clock by 7 microseconds per day (that’s 7000 nanoseconds per day); on the other hand, the weaker gravitational field up at the satellite orbit means that clocks run faster by 45 microseconds per day. The net effect is therefore that the clocks on the satellites run faster by (45-7), or 38 microseconds per day. That’s 38000 nanoseconds, or a cumulative error of over 11 kilometres per day! That’s a large error for such a non-real, airy-fairy theory that isn’t supposed to affect real life.

Cheer up. The people who run the systems know about this, and build in corrections so that you won’t try to drive the car into one of the craters on the Moon.

 

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