A global positioning system (GPS) satellite moves in a circular orbit with perio

Question

A global positioning system (GPS) satellite moves in a circular orbit with period 11 h 58 min. (Assume the mass of the earth is 5.98 x 24 kg, and the radius of the earth is 6.37 x 106 m (a) Determine the radius of its orbit. 6570801.43 m (b) Determine its speed. m/s 3875.33 (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 Earth's surface by a GPS receiver (see figure above), w hat is the fractional change in this frequency due to time dilation as described by special relati vity? E0 0.000000000 (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 Af AU, mc2 where Ug s the change in gravitational potential energy of an object-Earth system when the object of mass m s 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 Earth's surface to its orbital position (e) W hat is the overall fractional change in frequency due to both time dilation and gravitational blueshift Af

Explanation / Answer

d) M is the mass of the earth

R is the radius of the earth

m is the mass of the satellite

r is the radius of the satellite

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