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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 the earth=`6.0xx10^(24)`kg, radius of the earth=`6.4xx10(6)`m, G=`6.67xx10^(-11)Nm^(2)Kg^(-2)`.

Text Solution

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Total energy of a satellite in an orbit at a height h from earth.s surface is
`T.E. = P.E. + K.E.`
`= -(GMm)/(R+h) + (GMm)/(2(R+h)) " "[because v_(0) = sqrt((GM)/(R+h))]`
`= -(GMm)/(2(R+h))`
Energy required to take the satellite out from gravitational influence of earth
`E = -T.E. = (+GMm)/(2(R+h))`
`= (6.67 xx 10^(-11) xx 6 xx 10^(24) xx 200)/(2(6.4 xx 10^(6) + 0.4 xx 10^(6)))`
`= (80.04 xx 10^(15))/(13.6 xx 10^(6)) = 5.885 xx 10^(9) J`
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