Two satellites $A$ and $B$ move around the Earth in the same orbit. The mass of $A$ is twice the mass of $B$. The quantity which is the same for the two satellites will be:

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

Two stars of equal masses $M$ are orbiting in a circle of radius $R$. Their orbital time period is proportional to

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

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

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