Question

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

• A. Energy
• B. Angular momentum
• C. Linear momentum
• D. None of these

Answer 1

Answer: (B)

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