In a sub - stage lunch of a satellite, the first stage brings the satellite to a height of 150 km and the second stage gives it the necessary critical speed to put . It in a circular orbit around the Earth , which stage requires more expenditure of fuel ?
(Given , `M_(E)=6.0xx10^(24)kg,R=6.4xx10^(6)m,G-6.67xx10^(-11)Nm^(2)kg^(-2)).`

Explanation

Work done on a satellite in first stage
`W_(1)` = Potential energy at a height of 150 km
`= (-GMm)/(R+h) - ((-GMm)/(R ))`
`= GMm ((1)/(R ) - (1)/(R+h)) = (GMmh)/(R(R+h))` …(i)
Work done on satellite in second stage
`W_(2)` = Energy needed to give orbital speed
`= (1)/(2) m v_(0)^(2) = (1)/(2)m((GM)/(R+h)) = (1)/(2)((GMm)/(R+h))` ...(ii)
Dividing (i) by (ii),
`(W_(1))/(W_(2)) = (2h)/(R ) = (2 xx 150)/(6,400) = 0.0469 lt 1`
So, work done in second stage is more.