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The ratio of energy required to raise a ...

The ratio of energy required to raise a satellite to a height `h` above the earth surface to that required to put it into the orbit is

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The correct Answer is:
2
m = mass of satellite
`E_(1)` = Energy required to raise the satellite to height h
`= (-GMm)/((R+h))-(-GMm)/(R )`
`= GMm(-(1)/(R+h) + (1)/(R ))`
`= (GMmh)/(R(R+h))`
Energy required to put satellite in orbit is
`E_(2) = (1)/(2) mv_(0)^(2) = (1)/(2)m(GM)/(R+h) = (GMm)/(2(R+h))`
`(E_(1))/(E_(2)) = (GMmh)/(R(R+h)).(2(R+h))/(GMm)`
`= (2h)/(R )`
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