Find the speed of a GPS satellite (height is 20,200 km above the surface of Earth). Hence find the time difference between a clock in the satellite and one on the ground after one complete orbit, assuming they were originally synchronized (ignore all effects except time dilation). (b) Suppose we forgot to allow for this time difference. Estimate the resulting error in the calculation of our position. (c) Do the same m, but taking account of JUST the gravitational red shift instead of time dilation (note: the formula near Earth was Df/f = gh/c2 , but now g varies so instead of gh you should use the integral of g dh, where g is the acceleration due to gravity)
There are many subtle effects that must be taken into account in calculations involving GPS satellites. Here you are to estimate just the effect of the time dilation of
(a) Find the speed of a GPS satellite (height is 20,200 km above the surface of Earth). Hence find the time difference between a clock in the satellite and one on the ground after one complete orbit, assuming they were originally synchronized (ignore all effects except time dilation).
(b) Suppose we forgot to allow for this time difference. Estimate the resulting error in the calculation of our position.
(c) Do the same m, but taking account of JUST the gravitational red shift instead of time dilation (note: the formula near Earth was Df/f = gh/c2 , but now g varies so instead of gh you should use the integral of g dh, where g is the acceleration due to gravity)
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