Two satellites $A$ and $B$ having ratio of masses $3: 1$ are revolving in circular orbits of radii $r$ and $4r$. The ratio of total energy of satellites $A$ to that of $B$ is

If a satellite has to orbit the earth in a circular path every $6 \text{ hrs}$, at what distance from the surface of the earth should the satellite be placed (in $\text{ km}$)? (Radius of earth $R_e = 6400 \text{ km}$)
(Assume $\frac{GM}{4\pi^2} = 8 \times 10^{12} \text{ m}^3\text{s}^{-2}$, where $G$ and $M$ are the gravitational constant and mass of earth, and $10^{1/3} = 2.1$)

Consider a light planet revolving around a massive star in a circular orbit of radius $r$ with time period $T$. If the gravitational force of attraction between the planet and the star is proportional to $r^{-7/2}$,then $T^2$ is proportional to:

Which force is responsible for the necessary centripetal force of a satellite revolving around the Earth?

The orbital period of a geostationary satellite is (in $\,h$)

$A$ satellite is revolving very close to a planet of density $\rho$. The period of revolution of the satellite is