Question

A satellite is orbiting very close to planet. Its time period depends only upon:

• A. the density of the planet
• B. mass of the planet
• C. the radius of the planet
• D. mass of the satellite

Answer 1

The correct option is A the density of the planet

A time period of a satellite is the time taken by the satellite to go once around the earth.

$T=2\pi \sqrt{\frac{r^3}{MG}}$, where $r=R+D$,

if D is very small wrt to R so D can be neglected .

So $T=2\pi \sqrt{\frac{1}{M\sigma }}$, where $\sigma$ is density of the planet.

so here clearly we can see if the orbit of the satellite is very close to the planet then its period depends only on the density of the planet.

hence best possible answer is A.