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In a two stage launch of a satellite, th...

In a two stage launch of a satellite, the first stage brings the satellite to a height of 150 km and the `2^(nd)` stage gives it the necessary critical speed to put it in a circular orbit. Which stage requires more expenditure of fuel? Given mass of earth `=6.0xx10^(24)kg` radius of earth `=6400 km`.

Text Solution

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Work done on satellite in first state `=W_(1)=PE` at 150 km -PE at the surface
`W_(1)= (GMm)/(R+h)-(-(GMm)/(R ))`
`=(GMmh)/(R(R+h))`
Work done on satellite in `2^(nd)" stage "W_(2)` = energy required to give orbital velocity `v_(0)`
`=(1)/(2)mv_(0)^(2)= (1)/(2)((GMm)/(R+h))`
`(W_1)/(W_2)=(2h)/(R )= (2xx150)/(6400)= (3)/(64) lt 1`
`W_2 gt W_1`, so second stage require more energy.
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