On a hypothetical planet,a satellite can only revolve in quantized energy levels,i.e.,the magnitude of the energy of a satellite is an integer multiple of a fixed energy. If two successive orbits have radii $R$ and $\frac{3R}{2}$,what could be the maximum radius of the satellite (in $R$)?

If the gravitational constant $G$ is decreasing with time,what will remain unchanged for a satellite orbiting around the Earth?

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

If the mass of a satellite is doubled and the time period remains constant,the ratio of the orbital radii in the two cases will be:

Two satellites of masses $m$ and $4m$ are revolving in the same orbit around the Earth. Which one of the following statements is correct?

$A$ satellite is revolving around a planet in a circular orbit close to its surface. Let $\rho$ be the mean density and $R$ be the radius of the planet. Then the period of the satellite is ($G=$ universal constant of gravitation).