The Navstar Global Positioning System (GPS) utilizes a group of 24 satellites or

Question

The Navstar Global Positioning System (GPS) utilizes a group of 24 satellites orbiting the Earth. Using "triangulation" and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational "fixes." The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical mile = 1.852 km = 6076 ft].
(a) Determine the speed of each satellite.
m/s___________
(b) Determine the period of each satellite.
s ____________

Explanation / Answer

mass of earth M = 5.97*10^ 24 kg radius of earth R_E = 6.37*10^ 6 m stellite orbit at an altitude of h = 11000 nautical miles                                               =11000*1.852 km                                               = 2.0372*107 m speed of each satellite is                     v = G M / ( RE + h )                        = (6.674*10-11 )(5.97*1024 kg ) / ( 6.37*106 m + 2.037*107 m )                        = 3860 m/s time period of each satellite is                     T = 2r / v                        = 2 (  6.37*106 m + 2.037*107 m ) / 3860 m/s                        = 42427 s

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