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

The distance between two stars of masses $3 M_S$ and $6 M_S$ is $9 R$. Here $R$ is the mean distance between the centers of the Earth and the Sun,and $M_S$ is the mass of the Sun. The two stars orbit around their common center of mass in circular orbits with period $n T$,where $T$ is the period of Earth's revolution around the Sun. The value of $n$ is. . . . .

$A$ satellite revolving around a planet in a stationary orbit has a time period of $6 \text{ hours}$. The mass of the planet is one-fourth the mass of the Earth. What is the radius of the orbit of the satellite? (Given: Radius of the geostationary orbit for Earth is $4.2 \times 10^4 \text{ km}$)

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

$A$ planet is moving around the sun in an elliptical orbit at different positions $A, B, C, D$. The maximum kinetic energy of the planet is at position:

Two satellites $A$ and $B$ of masses $200 \, kg$ and $400 \, kg$ are revolving around the Earth at heights of $600 \, km$ and $1600 \, km$ respectively. If $T_{A}$ and $T_{B}$ are the time periods of $A$ and $B$ respectively,then find the value of $T_{B} - T_{A}$.
[Given: Radius of Earth $R = 6400 \, km$,Mass of Earth $M = 6 \times 10^{24} \, kg$,$G = 6.67 \times 10^{-11} \, Nm^{2}/kg^{2}$]