Consider two satellites $S_{1}$ and $S_{2}$ with periods of revolution $1\, hr$ and $8\, hr$ respectively,revolving around a planet in circular orbits. The ratio of the angular velocity of satellite $S_{1}$ to the angular velocity of satellite $S_{2}$ is:

Which of the following statements is correct in respect of a geostationary satellite?

$A$ 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 $S$ moves around a planet $P$ in an elliptical orbit as shown in the figure. The ratio of the speed of the satellite at point $a$ to that at point $b$ is:

Consider a binary star system of star $A$ and star $B$ with masses $m_{A}$ and $m_{B}$ revolving in a circular orbit of radii $r_{A}$ and $r_{B}$,respectively. If $T_{A}$ and $T_{B}$ are the time periods of star $A$ and star $B$,respectively,then -

Suppose the gravitational force varies inversely as the $n^{th}$ power of the distance. Then,the time period of a planet in circular orbit of radius $R$ around the sun will be proportional to