$A$ planet revolves around the Sun in an elliptical orbit. When it is closest to the Sun,its distance from the Sun is $1.6 \times 10^{12} \ m$ and its velocity is $60 \ m/s$. What is its velocity in $m/s$ when it is farthest from the Sun,given its distance is $8 \times 10^{12} \ m$?

$A$ satellite of the earth is revolving in a circular orbit with a uniform speed $v$. If the gravitational force suddenly disappears,the satellite will

Two satellites $A$ and $B$ revolve around the same planet in coplanar circular orbits. Their periods of revolution are $1\, h$ and $8\, h$,respectively. The radius of the orbit of $A$ is $10^{4}\, km$. The speed of $B$ relative to $A$ when they are closest is (in $km/h$):

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 particles of equal mass $m$ go around a circle of radius $R$ under the action of their mutual gravitational attraction. The speed of each particle with respect to their centre of mass 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 $6R$? $(G = 6.67 \times 10^{-11} \, SI \text{ units and } M = 6 \times 10^{24} \, kg)$