A satellite of a mass `m` orbits the earth at a hight `h` above the surface of the earth. How much energy must be expended to rocket the satellite out of earth's gravitational influence? (where `M_(E)` and `R_(E)` be mass and radius of the earth respectively)

Explanation

Total energy of the satellite, `E = P.E. + K.E.`
`= - (GM m)/((R + h)) + (1)/(2) m upsilon^(2)`
or `E =- (GM m)/((R + h)) + (GM m)/(2(R + h)) [:' upsilon = sqrt((GM)/(R + h))]`
`= - (GM m)/(2(R + h))`
thus, the energy to be expended to rocket the satellite out of the earth's gravitational field `= - E`
`= (GM m)/(2(R + h)) = ((6.67 xx 10^(-11)) xx 6.0 xx 10^(24) xx 250)/(2(6.4 xx 10^(6) + 5 xx 10^(5)))`
`= 7.25 xx 10^(9) J`