A satellite is launched into a circular orbit of radius R around earth while a second satellite is launched into an orbit of radius 1.02R. The percentage difference in the time periods of the two satellites is

Options

(a) 0.7
(b) 1
(c) 1.5
(d) 3

Correct Answer:

3

Explanation:

Apply Kepler’s third law, T²r³=constant
To study the small changes in T and r, take logs and differentiate.
2logT-3logr=log(constant)
2.dT/T-3.dr/r=zero
dT/T=3/2.dr/r
Now change in the radius of the satellite
dR=1.02R-R=0.02R
Percentage change in time period of second satellite with respect to the time period of the first satellite
dT/Tx100%=-3/2 .(0.02R)/Rx100%=3%