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A satellite orbits the Earth at a height...

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 Earth `=6.0xx10^(24)` kg, radius of the Earth `=6.4xx10^(6)m, G=6.67xx10^(-11) N-m^(2)//kg^(2)`.

Text Solution

Verified by Experts

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
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