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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 expected to Rocket the satellite out of Earth ' s gravitational influence ? Mass of the satellite = 200 kg , mass of Earth `=6.0xx10^(24)kg,` radius of Earth `=6.4xx10^(6)m,G=6.67xx10^(-11)Nm^(2)kg^(-2)`

Text Solution

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`h=400 km , m = 200 kg , M = 6xx10^(24)kg`
`R=6.4xx10^(6)m,G=6.67xx10^(-11)Nm^(2)kg^(-2)`
Here `1/2 mv_(e) ^(2)- (GMm)/(R+h)=0`
Energy required is `(GMm)/(R+h)=(6.67xx10^(-11)xx6xx10^(24)xx200)/((6400+400)10^(3))=(GMm)/(R+h)=(6.67xx6xx200xx10^(13-3))/(6.8xx10^(3))`
Energy `= 1.177 xx10^(10)J`
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