$A$ geostationary satellite orbits around the earth in a circular orbit of radius $36000\, km$. Then,the time period of a satellite orbiting a few hundred kilometres above the earth's surface $(R_{\text{Earth}} = 6400\, km)$ will approximately be ....... $hours$.

What are the orbital period of the Moon around the Earth and the rotational period of the Moon about its own axis?

$A$ satellite is moving in a low nearly circular orbit around the earth. Its radius is roughly equal to that of the earth's radius $R_e$. By firing rockets attached to it,its speed is instantaneously increased in the direction of its motion so that it becomes $\sqrt{\frac{3}{2}}$ times larger. Due to this,the farthest distance from the centre of the earth that the satellite reaches is $R$. The value of $R$ is $....R_e$.

$A$ satellite is orbiting around the Earth with an areal speed $v_a$. At what height from the surface of the Earth is it rotating,if the radius of the Earth is $R$?

If $\rho$ is the density of the planet,the time period of a nearby satellite is given by

Two satellites $A$ and $B$ revolve around the same planet in coplanar circular orbits. Their periods of revolution are $1\, h$ and $8\, h$,respectively. The radius of the orbit of $A$ is $10^{4}\, km$. The speed of $B$ relative to $A$ when they are closest is (in $km/h$):