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

$A$ satellite $S$ is moving in an elliptical orbit around the Earth. The mass of the satellite is very small compared to the mass of the Earth.

Choose the correct statement from the following: The radius of the orbit of a geostationary satellite depends upon

Which of the following is the evidence to show that there must be a force acting on the earth and directed towards the sun?

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 $x =$

Two planets,$A$ and $B$,are orbiting a common star in circular orbits of radii $R_A$ and $R_B$,respectively,with $R_B = 2 R_A$. The planet $B$ is $4 \sqrt{2}$ times more massive than planet $A$. The ratio $\left(\frac{L_B}{L_A}\right)$ of angular momentum $(L_B)$ of planet $B$ to that of planet $A$ $(L_A)$ is closest to integer . . . . . . .