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 $R$)?

Two satellites of masses $m_1$ and $m_2$ $(m_1 > m_2)$ are revolving around the Earth in circular orbits of radii $r_1$ and $r_2$ $(r_1 > r_2)$ respectively. Which of the following statements is true regarding their speeds $v_1$ and $v_2$?

The time period of revolution of a satellite orbiting very close to a planet of radius $R$ is $T$. What is the period of revolution around another planet,whose radius is $3R$ but having the same density?

$A$ satellite is moving in a low nearly circular orbit around the earth. Its radius is roughly equal to that of the earth's radius $R_e$. By firing rockets attached to it,its speed is instantaneously increased in the direction of its motion so that it becomes $\sqrt{\frac{3}{2}}$ times larger. Due to this,the farthest distance from the centre of the earth that the satellite reaches is $R$. The value of $R$ is $....R_e$.

Which of the planets is nearest to the Sun?

$A$ spaceship orbits around a planet at a height of $20 \, km$ from its surface. Assuming that only the gravitational field of the planet acts on the spaceship, what will be the number of complete revolutions made by the spaceship in $24 \, hours$ around the planet? [Given: Mass of planet $= 8 \times 10^{22} \, kg$, Radius of planet $= 2 \times 10^6 \, m$, Gravitational constant $G = 6.67 \times 10^{-11} \, N \cdot m^2/kg^2$]