Question

Show that period of a satellite revolving around the Earth depends upon mass of the Earth.

Answer 1

Let the satellite of mass $m_s$ is revolving around the Earth of mass $m_e$ at a distance of r then the centripetal force will be given by:

$F_c=\frac{m_s{v}^2}{r}$

where v is velocity of satellite. This force is equal to gravitational force between satellite and earth. Therefore

$\frac{m_s{v}^2}{r}=G\frac{m_s{m}_e}{r^2}$

$v=\sqrt{\frac{G{m}_e}{r}}$

Now, period of the satellite is given by:

$T=\frac{2\pi r}{v}=2\pi \sqrt{\frac{r^3}{G{m}_e}}$

Therefore time period of satellite(T) depends on the mass of earth($m_e$).