The mean radius of the earth's orbit around the sun is $1.5 \times 10^{11} \ m$. The mean radius of the orbit of Mercury around the sun is $6 \times 10^{10} \ m$. Mercury will revolve around the sun in:

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:

The distances of two planets from the Sun are $10^{11} \ m$ and $10^{10} \ m$ respectively. Find the ratio of their orbital periods.

$A$ satellite is launched into a circular orbit of radius $R$ around Earth,while a second satellite is launched into an orbit of radius $1.02 R$. The percentage difference in the time periods of the two satellites is:

If a planet revolves around the sun with an angular velocity $(\omega)$ and distance $(r)$,then the areal velocity of the planet is proportional to which of the following?