The average distance of the Earth from the Sun is $L_{1}$. If one year of the Earth is $D$ days, then one year of another planet whose average distance from the Sun is $L_{2}$ will be:

State and prove Kepler's second law (Law of Areas) of planetary motion.

If $A$ is the areal velocity of a planet of mass $M$,its angular momentum is

$A$ planet is revolving around the sun in an elliptical path as shown. The orbital velocity of the planet will be minimum at:

Which graph best represents the variation of radius $r$ of a circular orbit of a satellite against its time period $T$?

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: