A sky lab of mass `2 xx 10^(3)kg` is first lauched 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

A, B

Explanation

(a) `W =` energy of satellite in first orbit - energy of satellite on the surface of earth
`= - (GMm)/(2(2R)) - ((-Gmm)/(R))`
`= (3)/(4) (GMm)/(R )`
`= (3)/(4) mgR = (3)/(4) xx 2 xx 10^(3) xx 10 xx 6.4 xx 10^(6)`
`= 9.6 xx 10^(10) J`
(b) `W =` enargy of satellite in second orbit - energy in first orbit
` = - (GMm)/(2(3R)) - [(-Gmm)/(2(2R))]`
`= (1)/(2) (GMm)/(R) = (1)/(2) mgR`
`= (1)/(2) xx 2 xx 10^(3) xx 10 xx 6.4 xx 10^(6)`
`= 1.07 xx 10^(10)J`