A Satellite orbits the earth at a height of 400 km above the surface . How much energy must be expended to rocket the satellite out of the gravititional influence of earth? Mass of the satellite is 200 kg , mass of the earth = `6.0xx10^24` kg , radius of the earth =`6.4xx10^6` m , `G=6.67xx10^(-11) Nm^2 kg^(-2)`

Explanation

Total energy of orbiting satellite at a height
`h=(-GMm)/(2(R+h))`
Energy expended to rocket the satellite out of the earth.s gravititional field = - (total energy of the satellite)
`=(GMm)/(2(R+h))=((6.67xx10^(-11))xx(6xx10^24)xx200)/(2(6.4xx10^6+4xx10^5))=5.9xx10^9` J