In planetary motion,the areal velocity of the | vedclass

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(C) The areal velocity of a planet is given by the rate of change of area swept by the position vector,which is $\frac{dA}{dt} = \frac{1}{2} r^2 \omeg

Vedclass · Accepted Answer

$\frac{dA}{dt} \propto \omega r^2$

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(C) The areal velocity of a planet is given by the rate of change of area swept by the position vector,which is $\frac{dA}{dt} = \frac{1}{2} r^2 \omega$.Since the angular momentum $L = mvr = mr^2\omega$ is constant for a central force,the areal velocity is $\frac{dA}{dt} = \frac{L}{2m}$.From the expression $\frac{dA}{dt} = \frac{1}{2} r^2 \omega$,it is clear that $\frac{dA}{dt} \propto \omega r^2$.Therefore,the correct relation is $\frac{dA}{dt} \propto \omega r^2$.

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 $(r)$. If so,the correct relation for areal velocity is:

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