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What is the speed of the Earth's rotation?

So the two planes fly at

The factor for each plane should be straightforward to compute, but in practice may cause a problem with some calculators. For the Red plane, we try

but because , some calculators will yield . In such cases, we need to use tricks based on the binomial theorem. First, for ,

so

Second, again for ,

and thus

That means that we can turn the expression for into a form that we can handle easily - as long as we keep expressing it as 1 plus something''. Watch:

How long does it take the Red Plane, travelling around the world (a distance of about 40,000 km) at a speed of 710 m/s, to complete its journey? According to an observer motionless in space above the Earth's North Pole,

somewhat less than a day. On board the Red Plane, however, the clock will run slower by a factor of so that it reads

The difference between the two clocks will be

If you look at the papers describing this experiment, you'll see that the special relativistic effect indeed has roughly this size.

Michael Richmond 2003-12-05