Two satellites $A$ and $B$ are revolving around the earth in orbits of heights $1.25 R_E$ and $19.25 R_E$ from the surface of the earth respectively,where $R_E$ is the radius of the earth. The ratio of the orbital speeds of the satellites $A$ and $B$ is (in $: 1$)

Two particles of identical mass are moving in circular orbits under a potential given by $V(r) = K r^{-n}$,where $K$ is a constant. If the radii of their orbits are $r_1$ and $r_2$ and their speeds are $v_1$ and $v_2$,respectively,then:

If the orbital speed of a body revolving in a circular path near the surface of the earth is $8 \ km s^{-1}$,then the orbital speed of a body revolving around the earth in a circular orbit at a height of $19,200 \ km$ from the surface of the earth is (Radius of the earth $R = 6400 \ km$). (in $km s^{-1}$)

Two satellites are launched at a distance $R$ from a planet of negligible radius. Both satellites are launched in the tangential direction. The first satellite launches correctly at a speed $v_0$ and enters a circular orbit. The second satellite,however,is launched at a speed $\frac{1}{2}v_0$. What is the minimum distance between the second satellite and the planet over the course of its orbit?

Imagine a light planet revolving around a very massive star in a circular orbit of radius $R$ with a period of revolution $T$. If the gravitational force of attraction between the planet and the star is proportional to $R^{-5/2}$,then ${T^2}$ is proportional to:

Earth revolves around the sun in a circular orbit of radius $R$. The angular momentum of the revolving earth is directly proportional to