The period of a satellite in a circular orbit of radius R is T. What is the period of another satellite in a circular orbit of radius 4 R ?

Options

A. 64hrs
B. 32hrs
C. 16 hrs
D. 8 hrs

Answer

B

Explanation

Radius of orbit of the first satellite
`R_(1)=R`
Time period of the first satellite T=4 hrs. and radius of orbit of second satellite =4r
Time period of satellite is given by
`T prop r^(3/2)`
hence `(T_(2))/(T_(1))=((r_(2))/(r_(1)))^(3/2)=((4r)/r)^(3/2) =8`
`T_(2)=8xx4=32 ` hours