Question

The time period of a satellite moving in a circular orbit around a planet is independent of

• A. the mass of the planet.
• B. the radius of the planet.
• C. the mass of the satellite.
• D. all the three parameters.

Answer 1

The correct option is C the mass of the satellite.

Time period in terms of orbital speed is given by

$T=\frac{2\pi r}{v_o}=\frac{2\pi r}{\sqrt{\frac{GM}{r}}}=2\pi \sqrt{\frac{r^3}{GM}}$
where, T = time period of satellite
M = mass of the planet
r = radius of the orbit of the satellite

From the above equation, we can see that T depends on radius of the orbit and the mass (density) of the planet but not the mass of the satellite.