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

The radii of circular orbits of two satellites $A$ and $B$ of the earth are $4R$ and $R,$ respectively. If the speed of satellite $A$ is $3V,$ then the speed of satellite $B$ will be ...... $V$.

$A$ 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 $6R$? $(G = 6.67 \times 10^{-11} \, SI \text{ units and } M = 6 \times 10^{24} \, kg)$

$A$ geostationary satellite is taken to a new orbit such that its distance from the centre of the earth is doubled. Find the time period of this satellite in the new orbit.

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

The largest and the shortest distance of the earth from the sun are ${r_1}$ and ${r_2}$ respectively. What is its distance from the sun when it is at a position perpendicular to the major axis of the orbit drawn from the sun?