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

An artificial satellite is moving around the Earth in a circular orbit with a speed equal to one-fourth the escape speed of a body from the surface of the Earth. The height of the satellite above the Earth's surface is ............ ($R$ is the radius of the Earth). (in $R$)

Two satellites $A$ and $B$ having ratio of masses $3: 1$ are revolving in circular orbits of radii $r$ and $4r$. The ratio of total energy of satellites $A$ to that of $B$ is

The orbital velocity of an Earth satellite near the surface is $7 \, km/s$. When the radius of the orbit is $4$ times the radius of the Earth,the orbital velocity in that orbit is ......... $km/s$.

If the height of a satellite from the earth is negligible in comparison to the radius of the earth $R$,the orbital velocity of the satellite 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: