Two satellites $P$ and $Q$ go round a planet in circular orbits having radii $3R$ and $R$ respectively. If the speed of satellite $P$ is $2V$,what will be the speed of satellite $Q$?

What is the time period of a satellite orbiting at a height $R$ above the Earth's surface?

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

$A$ satellite can be in a geostationary orbit around a planet at a distance $r$ from the centre of the planet. If the angular velocity of the planet about its axis doubles,a satellite can now be in a geostationary orbit around the planet if its distance from the centre of the planet is

Select the correct statement from the following:

The mass density of a spherical galaxy varies as $\frac{K}{r}$ over a large distance $r$ from its centre. In that region,a small star is in a circular orbit of radius $R$. Then the period of revolution,$T$ depends on $R$ as