The orbital velocity of a planet revolving close to the Earth's surface is:

Let us assume that our galaxy consists of $2.5 \times 10^{11}$ stars, each of one solar mass. How long will a star at a distance of $50,000 \; ly$ from the galactic centre take to complete one revolution? Take the diameter of the Milky Way to be $10^{5} \; ly$.

$A$ satellite of the earth is revolving in a circular orbit with a uniform speed $v$. If the gravitational force suddenly disappears,the satellite will

Write the equation for the orbital velocity of a satellite revolving very close to the surface of the Earth.

$A$ 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 $R$?

$A$ planet of mass $M$ has two natural satellites with masses $m_1$ and $m_2$. The radii of their circular orbits are $R_1$ and $R_2$ respectively. Ignore the gravitational force between the satellites. Define $v_1, L_1, K_1$ and $T_1$ to be,respectively,the orbital speed,angular momentum,kinetic energy,and time period of revolution of satellite $1$; and $v_2, L_2, K_2$ and $T_2$ to be the corresponding quantities of satellite $2$. Given $m_1/m_2 = 2$ and $R_1/R_2 = 1/4$,match the ratios in List-$I$ to the numbers in List-$II$.

List-$I$	List-$II$
$P. \frac{v_1}{v_2}$	$1. \frac{1}{8}$
$Q. \frac{L_1}{L_2}$	$2. 1$
$R. \frac{K_1}{K_2}$	$3. 2$
$S. \frac{T_1}{T_2}$	$4. 8$