Question

For a given density of planet the orbital period of a satellite near the surface of planet of radius R is proportional to

• A. $R^{\frac{1}{2}}$
• B. $R^{\frac{3}{2}}$
• C. $R^{-\frac{1}{2}}$
• D. $R^0$

Answer 1

The correct option is D

$R^0$

$T=\frac{2\pi r^{\frac{3}{2}}}{\sqrt{GM}}$

For $r\approx R$

and $M=\frac{4}{3}\pi R^3\rho$ ($\rho$ = density of planet)

We see that $T=\sqrt{\frac{3\pi }{\rho G}}$

i.e., T is independent of R.