The orbital velocity of an artificial satellite in a circular orbit just above the Earth's surface is $v$. For a satellite orbiting at an altitude of half of the Earth's radius,the orbital velocity is

$A$ satellite $S$ is moving in an elliptical orbit around the Earth. The mass of the satellite is very small compared to the mass of the Earth.

$A$ satellite is in an elliptical orbit around a planet $P.$ It is observed that the velocity of the satellite when it is farthest from the planet is $6$ times less than that when it is closest to the planet. The ratio of distances between the satellite and the planet at closest and farthest points is $......$

Match the types of satellites in Column-$I$ with their applications in Column-$II$.

Column-$I$	Column-$II$
$(1)$ Polar satellite	$(a)$ Telecommunication
$(2)$ Geostationary satellite	$(b)$ Spying
	$(c)$ Weather forecasting

Two stars of masses $m$ and $2m$ at a distance $d$ rotate about their common centre of mass in free space. The period of revolution is

Given below are two statements:
Statement $I$: $A$ satellite is moving around the Earth in an orbit very close to the Earth's surface. The time period of revolution of the satellite depends upon the density of the Earth.
Statement $II$: The time period of revolution of the satellite is $T = 2\pi\sqrt{\frac{R_e}{g}}$ (for a satellite very close to the Earth's surface), where $R_e$ is the radius of the Earth and $g$ is the acceleration due to gravity.
In the light of the above statements, choose the correct answer from the options given below: