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  • The angular momentum of planet of mass M moving around the sun in an elliptical orbit is . The magnitude of the areal velocity of the planet is: Option: 1<

The angular momentum of planet of mass M moving around the sun in an elliptical orbit is \overrightarrow{L}. The magnitude of the areal velocity of the planet is:
Option: 1 \frac{L}{2M}
Option: 2 \frac{2L}{M}
Option: 3 \frac{L}{M}
Option: 4 \frac{4L}{M}

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\text{For small displacement ds of the planet its area can be written as}

\begin{array}{l} d A =\frac{1}{2} rd \ell \\ \\ =\frac{1}{2} r d \sin \theta \\ \\ Areal \ velocity =\frac{ d A }{ dt }=\frac{1}{2} r \sin \theta \frac{ ds }{ dt }=\frac{ Vr \sin \theta}{2} \\ \\ \frac{ d A }{ dt }=\frac{1}{2} \frac{ mV r \sin \theta}{ m }=\frac{ L }{2 m } \end{array}

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Deependra Verma

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