In planetary motion the areal velocity of position vector of a planet depends on angular velocity $(\omega )$ and the distance of the planet from sun $(r)$. If so the correct relation for areal velocity is

The relative uncertainty in the period of a sateilite orbiting around the earth is $10^{-2}$. If the relative uncertainty in the radius of the orbit is negligible, the relative uncertainty in the mass of the earth is

Given below are two statements: one is labelled as Assertion $(A)$ and the other is labelled as Reason $(R)$.

$Assertion$ $(A)$ : The angular speed of the moon in its orbit about the earth is more than the angular speed of the earth in its orbit about the sun.

$Reason$ $(R)$: The moon takes less time to move around the earth than the time taken by the earth to move around the sun.

In the light of the above statements, choose the most appropriate answer from the options given below:

A planet revolves around sun whose mean distance is $1.588$ times the mean distance between earth and sun. The revolution time of planet will be ……….. $ years$

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