A satellite is projected vertically upwards from an earth station. Determine the height above the earth's surface at which the force exerted on the satellite by the earth is reduced to half of its value at the earth station. (The radius of the earth is 6400 km .)

Step-by-step solution

The force exerted by the earth on the satellite at the earth's surface is given by F = GMm R^2 . The force at a height h above the surface is F' = GMm (R+h)^2 . Given that F' = F 2 , we have: GMm (R+h)^2 = 1 2 GMm R^2 (R+h)^2 = 2R^2 R+h = 2 R h = ( 2 - 1)R Substituting R = 6400 km and 2 1.414 : h = (1.414 - 1) 6400 h = 0.414 6400 = 2649.6 km This is approximately 2650 km .