Relativity and GNSS Satellites.

I saw 'Interstellar' a few months back in the IMax. Excellent film. 

There is a scene in it (spoiler alert) where the shuttle arrives at a planet that is orbiting a dwarf star, or some such object that exhibits a massive gravitational pull. The crew debate and briefly explain the issue of relativity before going down to the surface. Time passes more slowly depending on gravity, and this is dependant on your proximity to the body exhibiting the gravititational pull. During the 15 minutes spent by the four crew on the planet surface the single crew member left on the shuttle in orbit will experience about 1 year and have aged accordingly. To cut a long story short, the crew that go down to the planet run into trouble, get knocked around by a few waves and barely get away with their lives.

Understandably this has delayed them slightly and when they get up to the ship the guy who was left has aged by about 20 years. See, he has a beard.

The maths behind this is beyond me but the principle was pretty easy to follow during the movie. I was left very entertained and thinking how it will never effect me, right? Obviously I'm unlikely to be orbiting a massive star or part of a planetary exploration mission anytime soon.

Wrong.

I came across a very real surveying example only a few weeks after seeing the movie. GNSS satellites must be able to tell their time to extremely high tolerances and there are atomic clocks on board each satellite for this very reason. However, due to the proximity to the body emitting the larger gravitation pull, 1 second recorded by the clock on earth is slower than 1 second recorded by the clock on a satellite. Added to this, the direction the satellite orbits around the large body exhibiting the gravitational pull can also add or subtract to the effect. The bottom line is that the two clocks will diverge by 38 microseconds per day and this has to be built into the satellite clock when calibrating it before launch!

More info here and here for anyone interested.