Two satellites $A$ and $B$ are orbiting in circular paths of radii $4R$ and $R$ respectively. If the orbital velocity of satellite $A$ is $3V$,what is the orbital velocity of satellite $B$ (in $V$)?

$A$ planet of mass $m$ moves in an elliptical orbit around an unknown star of mass $M$ such that its maximum and minimum distances from the star are equal to $r_1$ and $r_2$ respectively. The angular momentum of the planet relative to the centre of the star is

Earth is moving around the sun in an elliptical orbit as shown. The ratio of $OB$ and $OA$ is $R$. Then the ratio of Earth's velocities at $A$ and $B$ is

$A$ body moves in a circular orbit of radius $R$ under the action of a central force. The potential due to the central force is given by $V(r) = kr$ ($k$ is a positive constant). The period of revolution of the body is proportional to:

Two satellites $A$ and $B$ rotate around a planet in orbits having radii $4R$ and $R$ respectively. If the speed of satellite $A$ is $3V$,then the speed of satellite $B$ is: (in $V$)

Express the constant $k$ of $T^{2}=k(R_{E}+h)^{3}$ in days and kilometres. Given $k = 10^{-13} \; s^{2} \; m^{-3}$. The moon is at a distance of $3.84 \times 10^{5} \; km$ from the earth. Obtain its time period of revolution in days.