According to the law of conservation of angular momentum, angular momentum $(J)$ of a planet is constant.
$\Rightarrow m u_{A} r_{A} \sin \theta_{A}=m u_{B} r_{B} \sin \theta_{B}$
or $ \frac{u_{A}}{v_{B}}=\frac{r_{B}}{r_{A}} \frac{\sin \theta_{B}}{\sin \theta_{ A }}$
Given, $r_{A}=90 \times 10^{6} km , r_{B}=60 \times 10^{6} \,km$
$\theta_{A}=30^{\circ}, \theta_{B}=60^{\circ}$
or $\frac{u_{A}}{u_{B}}=\frac{60 \times 10^{6}}{90 \times 10^{6}} \times \frac{\sin 60^{\circ}}{\sin 30^{\circ}}$
$4=\frac{2}{3} \times \frac{\sqrt{3} / 2}{1 / 2}$
or $ \frac{u_{A}}{u_{B}}=\frac{2}{\sqrt{3}}$
Hence, the ratio of velocities of the planet is $2 \sqrt{3}$
Rotational motion can be defined as the motion of an object around a circular path, in a fixed orbit.
The wheel or rotor of a motor, which appears in rotation motion problems, is a common example of the rotational motion of a rigid body.
Other examples: