$A$ geostationary satellite is orbiting the earth at a height of $5R$ above the surface of the earth,where $R$ is the radius of the earth. The time period of another satellite in hours at a height of $2R$ from the surface of the earth is:

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 . . . . . . .

The time period of a $1500 \,kg$ satellite is equal to the time period of rotation of the earth. The altitude of the satellite is nearly

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 $10^{1/3} = 2.1$)

The orbital speed of Jupiter is

Two small,equal masses are attached by a light rod. This object orbits a planet; the length of the rod is smaller than the radius of the orbit,but not negligible. The rod rotates about its axis in such a way that it remains vertical with respect to the planet. Determine the state of the rod (tension or compression) and the stability of the equilibrium with respect to a small angular perturbation.