(A) According to Kepler's second law,the areal velocity of a planet is constant and is given by the relation: $\frac{dA}{dt} = \frac{L}{2m}$,where $L$

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(A) According to Kepler's second law,the areal velocity of a planet is constant and is given by the relation: $\frac{dA}{dt} = \frac{L}{2m}$,where $L$ is the angular momentum and $m$ is the mass of the planet.For a complete orbit,the total area swept is $A$ and the time taken is the orbital period $T$. Thus,the average areal velocity is $\frac{A}{T}$.Equating the two expressions: $\frac{A}{T} = \frac{L}{2m}$.Solving for $L$,we get: $L = \frac{2mA}{T}$.

Class 11 Physics Gravitation Kepler’s laws of Planetary Motion

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$A$ planet of mass $m$ is in an elliptical orbit about the sun $(m \ll M_{sun})$ with an orbital period $T$. If $A$ is the area of the orbit,then its angular momentum is:

A
$\frac{2mA}{T}$
B
$mAT$
C
$\frac{mA}{2T}$
D
$2mAT$

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Kepler’s laws of Planetary Motion

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$A$ planet of mass $m$ is in an elliptical orbit about the sun $(m \ll M_{sun})$ with an orbital period $T$. If $A$ is the area of the orbit,then its angular momentum is:

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$A$ planet of mass $m$ is moving in an elliptical orbit about the sun with time period $T$. If $A$ is the area of the orbit,then its angular momentum is:

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