$A$ 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 motion of planets in the solar system is governed by which of the following conservation laws?

The angular momentum of a planet of mass $M$ moving around the sun in an elliptical orbit is $\overrightarrow{L}$. The magnitude of the areal velocity of the planet is:

Why does a satellite not have an escape velocity?

$A$ planet is moving in a circular orbit. It completes $2$ revolutions in $360$ days. What is its angular frequency?

$A$ satellite is to be placed in an equatorial geostationary orbit around the Earth for communication.
$(a)$ Calculate the height of such a satellite.
$(b)$ Find out the minimum number of satellites that are needed to cover the entire Earth,so that at least one satellite is visible from any point on the equator.
Given: $M = 6 \times 10^{24} \ kg$,$R = 6400 \ km$,$T = 24 \ h$,$G = 6.67 \times 10^{-11} \ N \cdot m^2/kg^2$.