Two planets revolve round the sun with frequencies ${N_1}$ and ${N_2}$ revolutions per year. If their average orbital radii be ${R_1}$ and ${R_2}$ respectively, then ${R_1}/{R_2}$ is equal to

Kepler's second law (law of areas) is nothing but a statement of

The angular momentum of a planet of mass $M$ moving around the sun in an elliptical orbit is $\overrightarrow{ L }$. The magnitude of the areal velocity of the planet is:

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

The maximum and minimum distances of a comet from the Sun are $1.6 \times 10^{12}\, m$ and $8.0 \times 10^{10}\, m$ respectively. If the speed of the comet at the nearest point is $6 \times 10^{4}\, ms ^{-1},$ the speed at the farthest point is ……… $\times 10^{3}\, m / s$