The orbital velocity of an artificial satellite in a circular orbit just above the earth's surface is $v$. For a satellite orbiting at an altitude of half the earth's radius above the surface,the orbital velocity is:

$A$ satellite is in an elliptic orbit around the Earth with an aphelion of $6R$ and a perihelion of $2R$,where $R = 6400 \, km$ is the radius of the Earth. Find the eccentricity of the orbit. Find the velocity of the satellite at apogee and perigee. What should be done if this satellite has to be transferred to a circular orbit of radius $6R$? $(G = 6.67 \times 10^{-11} \, SI \text{ units and } M = 6 \times 10^{24} \, kg)$

$A$ planet is revolving around the sun in an elliptical orbit. Its closest distance from the sun is $r_{min}$,and the farthest distance from the sun is $r_{max}$. If the orbital angular velocity of the planet when it is nearest to the sun is $\omega$,then the orbital angular velocity at the point when it is at the farthest distance from the sun is:

At which height from the surface of the Earth does a polar satellite revolve around the Earth?

Two satellites $A$ and $B$ of same mass are moving around a planet at an altitude of $3R$ and $5R$ respectively. Select the correct statement.

Which of the following is the evidence to show that there must be a force acting on the earth and directed towards the sun?