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 orbiting satellite at a height `h`
`= - (GM m)/((R + h)) + (1)/(2) m upsilon^(2) = - (GM m)/((R + h)) + (1)/(2) m (GM)/((R + h)) = (-GM m)/(2(R + h))`
Energy expended to rocket the satellite out of Earths's gravitational field
= - (total energy of the orbiting satellite)
`= (GM m)/(2(R + h)) = ((6.67 xx 10^(-11)) xx (6 xx 10^(24)) xx 200)/(2 (6.4 xx 10^(6)+ 4 xx 10^(5))) = 5.9 xx 10^(9) J`