$A$ planet of mass $M$ has a satellite of mass $m$,revolving around the planet in a circular orbit of radius $r$ and time period $T$. The mass $(M)$ of the planet is

$A$ satellite revolving around the earth at a certain height experiences acceleration due to gravity equal to $\frac{16}{49} g_0$,where $g_0$ is the acceleration due to gravity on the earth's surface. If $R$ is the radius of earth,then the square of time period of the satellite's revolution is equal to $K\left[\frac{\pi^2 R^3}{G M}\right]$. The value of $K$ is

Two satellites $A$ and $B$ go round a planet in circular orbits having radii $4 R$ and $R$ respectively. If the speed of $A$ is $3 v$,the speed of $B$ will be:

$A$ satellite is to revolve around the Earth in a circle of radius $8000\, km$. The speed at which this satellite must be projected into an orbit will be......... $km/s$.

An artificial satellite of mass $500 \ kg$ is orbiting the Earth. If its areal velocity is $4 \times 10^4 \ m^2s^{-1}$,find its angular momentum.

The percentage increase in the energy for an artificial satellite to shift it from an orbit of radius $r$ to an orbit of radius $\frac{3r}{2}$ is