A satellite orbits the earth at a height of `400km` above the surface. How much energy must be expanded to rocket the satellite out of the gravitational influence of earth? Mass of the satellite is `200kg,` mass of earth `=6.0 xx 10^(24) kg,` radius of earth `=6.4 xx 10^6 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 at satellite out of the earth.s gravitational field =-(Total energy of the satellite )`=(GMm)/(2(R+h))`
`=((6.67xx10^(-11))xx(6xx10^(24))xx200)/(2(6.4xx10^(6)+4xx10^(5))0=58.85xx10^(8)J`