Two satellites $S_{1}$ and $S_{2}$ are revolving in circular orbits around a planet with radii $R_{1} = 3200 \, km$ and $R_{2} = 800 \, km$ respectively. The ratio of the speed of satellite $S_{1}$ to the speed of satellite $S_{2}$ in their respective orbits is $\frac{1}{x}$,where $x =$

If $g \propto \frac{1}{R^3}$ (instead of $\frac{1}{R^2}$),then the relation between the time period $T$ of a satellite near the Earth's surface and the radius $R$ will be:

The maximum and minimum distances of a comet from the Sun are $1.6 \times 10^{12} \ m$ and $8.0 \times 10^{10} \ m$ respectively. If the speed of the comet at the nearest point is $6 \times 10^{4} \ m/s$,the speed at the farthest point is ......... $\times 10^{3} \ m/s$.

What are the conditions necessary for a satellite to appear stationary? What is the direction of rotation of a geostationary satellite?

Two satellites $A$ and $B$ go round a planet $P$ in circular orbits having radii $4R$ and $R$ respectively. If the speed of the satellite $A$ is $3V$,the speed of the satellite $B$ will be ........ $V$.

$A$ 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: