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

$Assertion$ : For the planets orbiting around the sun,angular speed,linear speed and $K.E.$ change with time,but angular momentum remains constant.
$Reason$ : No torque is acting on the rotating planet. So its angular momentum is constant.

If the angular momentum of a planet of mass $m$,moving around the Sun in a circular orbit is $L$,about the center of the Sun,its areal velocity is

$A$ planet $(P_1)$ is moving around a star of mass $2M$ in an orbit of radius $R$. Another planet $(P_2)$ is moving around another star of mass $4M$ in an orbit of radius $2R$. The ratio of the time periods of revolution of $P_2$ and $P_1$ is . . . . . . .

$A$ planet moving around the Sun sweeps out an area $A_{1}$ in $2$ days,$A_{2}$ in $3$ days,and $A_{3}$ in $6$ days. Then,the relation between $A_{1}, A_{2}$,and $A_{3}$ is

An artificial satellite of mass $m$ is moving along an elliptical path around the earth. The areal velocity of the satellite is proportional to