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  4. A planet of mass m is in an elliptical orbit about the sun (m < < M textsun) with an orbital period T . If A be the area of orbit, then its angular momentum would be

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Q. A planet of mass $m$ is in an elliptical orbit about the sun $\left(m < < M_{\text{sun}}\right)$ with an orbital period $T$ . If $A$ be the area of orbit, then its angular momentum would be

NTA AbhyasNTA Abhyas 2022

Solution:

using Kepler's IInd law ; areal velocity = constant = $\frac{L}{2 m}$
⇒ $\frac{d A}{d t}$ = $\frac{L}{2 m}$
⇒ $L=2m\frac{d A}{d t}$
$L=\frac{2 m A}{T}$