Two heavenly bodies $S_1$ and $S_2$,not far from each other,are seen to revolve in orbits:

The radius of a planet is $R$. $A$ satellite revolves around it in a circle of radius $r$ with angular velocity $\omega_0$. The acceleration due to gravity on the planet's surface is

An artificial satellite is revolving around a planet of radius $R$ in a circular orbit of radius $a$. If the time period of revolution of the satellite $T \propto a^{3/2} g^x R^y$,then the values of $x$ and $y$ are respectively. [Note: $g$ is the acceleration due to gravity at the surface of the planet.]

$A$ geostationary satellite is orbiting the earth at a height of $6R$ above the surface of the earth,where $R$ is the radius of the earth. The time period of another satellite at a height of $2.5R$ from the surface of the earth is

Which of the following statements is correct in respect of a geostationary satellite?

$A$ spherical asteroid having the same density as that of Earth is floating in free space. $A$ small pebble is revolving around the asteroid under the influence of gravity near the surface of the asteroid. What is the approximate time period of the pebble?