Question

The time period of an earth satellite in circular orbits is independent of

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

Answer 1

The correct option is C the mass of the satellite

$\frac{m{v}^2}{R+x}=\frac{GmM}{(R+x{)}^2}$
$x=$ height of satellite from earth surface
$m=$ mass of satellite
$\Rightarrow v^2=\frac{GM}{(R+x)}$ or $v=\sqrt{\frac{GM}{R+x}}$
$T=\frac{2\pi (R+x)}{v}=\frac{2\pi (R+x)}{\sqrt{\frac{GM}{R+x}}}$
which is independent of mass of satellite