Question

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 1

Given :

Mass = 2×10³ kg

Radius (R1) =2R

Radius (R2) = 3R

To find :

Energy required

a)To place the lab in the first orbit

b)To shift the lab from first orbit to the second orbit

Solution :

a)   W= energy in first orbit - energy on the earth surface

     = -GMm/2(2R) - (-GMm/R)

     =3/4 (GMm/R)

     =3/4mgR = 9.6 ×10¹⁰

Energy required is  9.6 ×10¹⁰J

b)  W=energy in second orbit - energy in first orbit

        = -GMm/2(3R) - (-GMm/2(2R))

        = GMm/2R

        =mgr/2 = 1.07×10¹⁰J

 Energy required is  1.07×10¹⁰J