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  4. Kepler’s second law regarding constancy of areal velocity of a planet is a consequence of the law of conservation of

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Q. Kepler’s second law regarding constancy of areal velocity of a planet is a consequence of the law of conservation of

BITSATBITSAT 2019

Solution:

Areal velocity $\frac{ d A }{ dt }$ & angular momentum $L$ of a planet are related by equation $\frac{ d A }{ dt }=$
$\frac{L}{2 M}$, where $M$ is the mass of planet. Since in planetary motion $\bar{L}$ is constant
$\left(\bar{\tau}_{\text {ext. }}=0\right)$,
hence $\frac{ d A }{ dt }$ is also constant.