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An artificial satellite of mass $m$ is moving along an elliptical path around the earth. The areal velocity of the satellite is proportional to
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Verified Answer
The correct answer is:
$m^0$
Areal velocity, $\frac{d A}{d t}=$ constant
$$
\frac{d A}{d t}=\frac{L}{2 m}
$$
(where, $L$ is angular momentum)
$$
=\frac{m v r \sin \theta}{2 m}=\frac{v r \sin \theta}{2}
$$
This shows areal velocity does not depends on mass.
So,
$$
\frac{d A}{d t} \propto m^0
$$
$$
\frac{d A}{d t}=\frac{L}{2 m}
$$
(where, $L$ is angular momentum)
$$
=\frac{m v r \sin \theta}{2 m}=\frac{v r \sin \theta}{2}
$$
This shows areal velocity does not depends on mass.
So,
$$
\frac{d A}{d t} \propto m^0
$$
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