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Taking the earth to be a uniform sphere ...

Taking the earth to be a uniform sphere of radius `6400 km` and the value of g at the surface to be `10ms^(-2)`, calculate the energy needed to raise a satellite of mass `2000 kg` to a height of `800 km` a above the earth's surface and to set it into circular orbit at that altitude.

Text Solution

Verified by Experts

The correct Answer is:
`7.1xx10^(10)J`
Initial energy of the satellite
`E_(1)=-(GMm)/r` (since initial `KE=0)`
Final energy of the satellite
Energy needed,
`/_\E=E_(2)-E_(1)`
`=-(2GMm)/(2(R+h))=(-(GMm)/R)=GMm(1/R-1/(2(R+h)))`
but `GM=R^(2)g`
`/_\E=R^(2)gM(1/R-1/(2(R+h)))=mgR[1-1/(2(1+h/R))]`
`=7.1xx10^(10)J`
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