Two small satellies move in a circular orbits around the earth, at disatnce `r` and `(r + dr)` from the centre of the earth. Their time periods of rotation ate `T` and `T + dT (Delta r lt lt r, DeltaT lt lt T)`. Then

Options

A. `DeltaT=3/2T(Deltar)/r`
B. `DeltaT=3/2T(Deltar)/r`
C. `DeltaT=2/3T(Deltar)/r`
D. `DeltaT=T(Deltar)/r`

Answer

B

Explanation

`(T+Delta)/T=((r+Deltar)/r)^(3//2)=(1+(Deltar)/r)^(3//2)=1+3/2 (Deltar)/r`
`DeltaT=3/2T (Deltar)/r`