GPS and relativity. The Global Positioning System (GPS) consists of a network of about 30 satellites in orbit, each carrying atomic clocks on board. The orbital radius of the satellites is about four Earth radii (26,600 km). The orbits are nearly circular, with a typical eccentricity of less than 1%. The on board atomic clocks keep highly accurate time, and oscillators produce signals at several different frequencies. The frequency used by nonmilitary GPS receivers is 1575.42 MHz. Two relativistic corrections must be made to this signal so that accurate position readings on the Earth are possible: first, special relativity predicts that moving clocks will appear to tick slower than non-moving ones, and second, general relativity predicts that clocks in a stronger gravitational field will tick at a slower rate. Determine 

(a) The orbital period and 

(b) The orbital speed of these satellites. 

(c) Apply special relativity to determine the correction to the frequency of the signal received on the Earth. 

(d) Applying general relativity and following the method described in Problem 69, determine the correction to the frequency of the signal received on Earth.