Question

The time period of an earth's satellite in a circular orbit is independent of

• A. the mass of the satellite
• B. radius of its orbit
• C. both the mass and radius of the orbit
• D. neither the mass of the satellite nor the radius of its orbit

Answer 1

The correct option is A the mass of the satellite

Time period of a satellite in terms of orbital speed is given by:
$T=\frac{2\pi r}{v_o}=\frac{2\pi r}{\sqrt{\frac{GM}{r}}}=2\pi \sqrt{\frac{r^3}{GM}}$
From the above equation, we can see that $T$ depends on radius of the orbit, '$r$' but not on its mass of the satellite, '$m$'.