Two satellites of masses $m$ and $3\,m$ revolve around the earth in circular orbits of radii $r$ and $3r$ respectively. The ratio of orbital speeds of the satellites respectively is:

Assuming that the earth is revolving around the sun in a circular orbit of radius $R$,the angular momentum is directly proportional to $R^{n}$. The value of $n$ is

Earth is moving around the sun in an elliptical orbit as shown. The ratio of $OB$ and $OA$ is $R$. Then the ratio of Earth's velocities at $A$ and $B$ is

Who decides the upward direction in an artificial satellite?

$A$ geostationary satellite is orbiting around an arbitrary planet $P$ at a height of $11R$ above the surface of $P$,where $R$ is the radius of $P$. The time period of another satellite in hours at a height of $2R$ from the surface of $P$ is $........$. The planet $P$ has a rotation period of $24\, \text{hours}$.

The time period of a geostationary satellite is (in $\text{ h}$)