A sky lab of mass `2 xx 10^(3)kg` is first launched from the surface of earth in a circular orbit of radius `2R` and them it is shifted from this circular orbit to another circular orbit of radius `3R`. Calculate the energy required
(a) to place the lab in the first orbit,
(b) to shift the lab from first orbit to the second orbit. `(R = 6400 km`, `g = 10 m//s^(2))`

Answer

`1.04xx10^(10)J`

Explanation

Total energy of sky laboratory `E=-(GMm)/(2r)`
`E_(1)=-(GMm)/(2(2R))` and `E_(2) =-(GMm)/(2(3R))`
Therefore the energy required
`/_\E=E_(2)-E_(1)=GMm(1/(4R)-1/(6R))=(GMm)/(12R)`
`((R^(2)g)m)/(12R)=(mgR)/12=1.04xx10^(10)J`