Two satellites are revolving around the Earth with orbital velocities $v_1$ and $v_2$ at radii $r_1$ and $r_2$ respectively,where $r_1 > r_2$. Then:

The orbital speed of an artificial satellite very close to the surface of the Earth is $V_o$. What is the orbital speed of another artificial satellite at a height equal to three times the radius of the Earth (in $,V_o$)?

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,

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?

$A$ particle moves in a circular orbit of radius $r$ under a central attractive force $F = -\frac{k}{r^2}$,where $k$ is a constant. The time period of its motion shall be proportional to

The time period of a $1500 \,kg$ satellite is equal to the time period of rotation of the earth. The altitude of the satellite is nearly