(a) Does it take more energy to get a satellite upto `1500 km` above earth than to put in circular orbit once it is there.
(b) What about `3185 km` ?
(c ) What about `4500 km`? (Take `R_(e) = 6370 km`)

Answer

A, B, C

Explanation

`W_(1) = DeltaU = - (GMm)/((R + h)) + (GMm)/(R )=(GMmh)/(R(R + h))`
`W_(2) = (1)/(2) m nu^(2) = (1)/(2) m (sqrt((GM)/(r)))^(2)`
`= (1)/(2) m ((GM)/(R + h)) = (GMm)/(2(R + h))`
`W_(1) gt W_(2)`
If `(h)/(R ) gt (1)/(2)` or `h gt (R )/(2)`
or `h gt (6370)/(2) km`
or `h gt 3185 km`