There are many subtle effects that must be taken into account incalculations involving GPS satellites. Estimate just the effect ofthe time dilation of special relativity.
(a) Find the speed of a GPS satellite (height is 20,200 km abovethe surface of Earth). Hence, find the time difference between aclock in the satellite and one on the ground after one completeorbit, assuming they were originally synchronized (ignore alleffects except time dilation).
(b) Suppose we forgot to allow for this time difference.Estimate the resulting error in the calculation of ourposition.
