Review. A global positioning system (GPS) satellite moves
Chapter 39, Problem 65(choose chapter or problem)
Review. A global positioning system (GPS) satellite moves in a circular orbit with period 11 h 58 min. (a) Determine the radius of its orbit. (b) Determine its speed. (c)The nonmilitary GPS signal is broadcast at a frequency of 1 575.42 MHz in the reference frame of the satellite. When it is received on the Earths surface by a GPS receiver (Fig. P39.65 on page 1230), what is the fractional change in this frequency due to time dilation as described by special relativity? (d) The gravitational blueshift of the frequency according to general relativity is a separate effect. It is called a blueshift to indicate a change to a higher frequency. The magnitude of that fractional change is given by Df f 5 DUg mc 2 where Ug is the change in gravitational potential energy of an objectEarth system when the object of mass m is moved between the two points where the signal is observed. Calculate this fractional change in frequency due to the change in position of the satellite from the Earths surface to its orbital position. (e) What is the overall fractional change in frequency due to both time dilation and gravitational blueshift?
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