The distance between the Sun and the Earth is $R$. What will be the duration of the year if the distance between the Sun and the Earth becomes $3R$?

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 $6 \times 10^{10} \ m$. The mercury will rotate around the sun in

Given below are two statements: one is labelled as Assertion $(A)$ and the other is labelled as Reason $(R)$.
Assertion $(A):$ The radius vector from the Sun to a planet sweeps out equal areas in equal intervals of time and thus the areal velocity of the planet is constant.
Reason $(R):$ For a central force field,the angular momentum is a constant.
In the light of the above statements,choose the most appropriate answer from the options given below:

Suppose there existed a planet that went around the sun twice as fast as the earth. What would be its orbital size as compared to that of the earth?

Kepler discovered

Match Column-$I$ with Column-$II$.

Column-$I$	Column-$II$
$(1)$ Kepler's first law	$(a)$ Law of periods
$(2)$ Kepler's second law	$(b)$ Law of orbits
$(3)$ Kepler's third law	$(c)$ Law of areas