Question:
A planet is moving around the sun in an elliptic orbit. Its speed
A planet is moving around the sun in an elliptic orbit. Its speed
Updated On: Jul 5, 2022
- is the same at all points of the orbit
- is maximum when it is farthest from the sun
- is maximum when it is nearest to the sun
- is maximum at the two points in which the orbit is intersected by the line which passes through the focus of the orbit and which is perpendicular to its major axis
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The Correct Option is C
Solution and Explanation
According to Kepler's II law of planetary motion, the areal velocity of the planet around the sun is constant ie, $\frac{d \vec{A}}{d t}=\frac{\vec{L}}{2 m}=$ constant where $\vec{L}$ is the angular momentum of the planet and $m$ is its mass.
But $L=m v r$
$\therefore \frac{d A}{d t}=\frac{m v r}{2 m}=\frac{v r}{2}=$ constant or $v \propto \frac{1}{r}$
Therefore, the speed of a planet is maximum when it is nearest to the sun.
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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