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 earth’s gravitational influence? Mass of the satellite = 200 kg; mass of the earth = 6.0 ×1024 kg; radius of the earth = 6.4 ×106 m; G = 6.67 × 10–11 N m2 kg–2.
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 earth’s gravitational influence? Mass of the satellite = 200 kg; mass of the earth = 6.0 ×1024 kg; radius of the earth = 6.4 ×106 m; G = 6.67 × 10–11 N m2 kg–2.
Mass of the Earth, M= 6.0 × 1024 kg
Mass of the satellite,m = 200 kg
Radius of the Earth, Re= 6.4 × 106 m
Universal gravitationalconstant, G = 6.67 × 10–11 Nm2kg–2
Height of thesatellite, h = 400 km = 4 × 105 m = 0.4 ×106m
Total energy of thesatellite at height h
Orbital velocity of thesatellite, v = 
Total energy of height,h
The negative signindicates that the satellite is bound to the Earth. This is calledbound energy of the satellite.
Energy required to sendthe satellite out of its orbit = – (Bound energy)
Mass of the Earth, M= 6.0 × 1024 kg
Mass of the satellite,m = 200 kg
Radius of the Earth, Re= 6.4 × 106 m
Universal gravitationalconstant, G = 6.67 × 10–11 Nm2kg–2
Height of thesatellite, h = 400 km = 4 × 105 m = 0.4 ×106m
Total energy of thesatellite at height h
Orbital velocity of thesatellite, v =
Total energy of height,h
The negative signindicates that the satellite is bound to the Earth. This is calledbound energy of the satellite.
Energy required to sendthe satellite out of its orbit = – (Bound energy)
