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 gravitational influence of earth ? Mass of the satellite is 200 kg, mass of the earth = 6.0 xx 10^(24) kg radius of the earth = 6.4 xx 10^(6)m, G = 6.67 xx 10^(-11) Nm^(2) kg^(-2).

A satellite orbits the earth at a height of 400 km above the surface.

1.	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 gravitational influence of earth ? Mass of the satellite is 200 kg, mass of the earth = 6.0 xx 10^(24) kg radius of the earth = 6.4 xx 10^(6)m, G = 6.67 xx 10^(-11) Nm^(2) kg^(-2).
Answer» Solution :TOTAL energy of ORBITING SATELLITE at a HEIGHT `h = (-GMM)/(2(R+h))` Energy expended to rocket the satellite out of the earth.s gravitational field = -(total energy of the satellite) `= (GMm)/(2(R+h)) = ((6.67 xx 10^(-11)) xx (6 xx 10^(24)) xx 200)/(2(6.4 xx10^(6) + 4 xx 10^(5))) = 5.9 xx 10^(9) J`