An earth satellite $S$ has an orbit radius which is $4$ times that of a communication satellite $C$. The period of revolution of $S$ is ........ $days$.

Kepler's third law states that the square of the period of revolution $(T)$ of a planet around the sun is proportional to the cube of the average distance $(r)$ between the sun and the planet,i.e.,$T^2 = Kr^3$,where $K$ is a constant. If the masses of the sun and the planet are $M$ and $m$ respectively,then according to Newton's law of gravitation,the force of attraction between them is $F = \frac{GMm}{r^2}$,where $G$ is the gravitational constant. The relation between $G$ and $K$ is:

If the angular momentum of a planet of mass $m$,moving around the Sun in a circular orbit is $L$,about the center of the Sun,its areal velocity is

The period of a satellite in a circular orbit of radius $R$ is $T$. The period of another satellite in a circular orbit of radius $4R$ is:

$A$ Saturn year is $29.5$ times the Earth year. How far is Saturn from the Sun if the Earth is $1.50 \times 10^{8} \; km$ away from the Sun?

$A$ satellite $S_1$ of mass $m$ is moving in an orbit of radius $r$. Another satellite $S_2$ of mass $2m$ is moving in an orbit of radius $2r$. The ratio of the time period of satellite $S_2$ to that of $S_1$ is