Kepler's second law (law of areas) is nothing but a statement of

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Aicharya · Accepted Answer

According to Kepler's second law of planetary motion, the radius vector joining planet to the sun sweeps out equal areas, in equal interval of time. i.e., \(\frac{\Delta A}{\Delta t}=\text { constant }\)

According to figure, \(\mathbf{r}\) be the position vector of the planet w.r.t sun and \(\mathbf{F}\) be the gravitational force on the planet due to the sun. Then, torque exerted on the planet by this force about the sun is \(\begin{aligned} \tau=\mathbf{r} \times \mathbf{F}=0 \\ \quad[\because \mathbf{r} \text { and } \mathbf{F} \text { are oppositely directed }] \end{aligned}\) But \(\begin{array}{ll} \text {But } & \tau=\frac{d \mathbf{L}}{d t} \\ \therefore & \frac{d \mathbf{L}}{d t}=0 \Rightarrow \mathbf{L}=\text { constant } \end{array}\) Angular momentum \(=\) constant Hence, Kepler's second law (law of areas) is equivalent to law of conservation of angular momentum.

Kepler's second law (law of areas) is nothing but a statement of

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