Question:
Kepler?? second law regarding constancy of areal velocity of a planet is a consequence of the law of conservation of
Kepler?? second law regarding constancy of areal velocity of a planet is a consequence of the law of conservation of
Updated On: Jul 28, 2022
- Energy
- Angular momentum
- Linear momentum
- None of these
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The Correct Option is B
Solution and Explanation
Areal velocity $\frac{ d A }{ dt }$ & angular momentum $L$ of a planet are related by equation $\frac{ d A }{ dt }=$
$\frac{L}{2 M}$, where $M$ is the mass of planet. Since in planetary motion $\bar{L}$ is constant
$\left(\bar{\tau}_{\text {ext. }}=0\right)$,
hence $\frac{ d A }{ dt }$ is also constant.
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Concepts Used:
Keplers Laws
Kepler’s laws of planetary motion are three laws describing the motion of planets around the sun.
Kepler First law – The Law of Orbits
All the planets revolve around the sun in elliptical orbits having the sun at one of the foci.
Kepler’s Second Law – The Law of Equal Areas
It states that the radius vector drawn from the sun to the planet sweeps out equal areas in equal intervals of time.
Kepler’s Third Law – The Law of Periods
It states that the square of the time period of revolution of a planet is directly proportional to the cube of its semi-major axis.
T2 ∝ a3