The period of revolution of planet $A$ around the sun is $8$ times that of planet $B$. How many times is the distance of planet $A$ from the sun greater than that of planet $B$ from the sun (in $times$)?

Two planets $A$ and $B$ of equal mass have periods of revolution $T_{A}$ and $T_{B}$ such that $T_{A} = 2 T_{B}$. These planets are revolving in circular orbits of radii $r_{A}$ and $r_{B}$ respectively. Which of the following is the correct relationship between their orbital radii?

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

If $J$ is the angular momentum of a planet revolving around the Sun,what is the areal velocity of the planet?

If the earth is at one-fourth of its present distance from the sun,the duration of the year will be

In planetary motion,the areal velocity of the position vector of a planet depends on the angular velocity $\omega$ and the distance of the planet from the sun $r$. The correct relation for areal velocity is: