Determine the true weight of an object located in a geostationary satellite, assuming it weighed exactly 10.0 N at the north pole.

Step-by-step solution

The true weight of an object at the north pole is given by the gravitational force: W = GMm R^2 = 10.0 N For a geostationary satellite, the time period of revolution is T = 24 hours = 86400 s . The radius r of its orbit is obtained from Kepler's third law: T^2 = 4 ^2 r^3 GM r = ( GMT^2 4 ^2 )^ 1/3 = ( gR^2T^2 4 ^2 )^ 1/3 Substituting g = 9.8 m/s ^2 , R = 6.37 10^6 m , and T = 86400 s : r ( 9.8 (6.37 10^6)^2 (86400)^2 4 ^2 )^ 1/3 4.22 10^7 m The true weight of the object in the geostationary satellite is the actual