The figure shows a planet in an elliptical orbit around the sun S
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The figure shows a planet in an elliptical orbit around the sun S.
At which position of the planet will its kinetic energy be maximum?
A. <span class="math-tex">\(P_1\)</span>
B. <span class="math-tex">\(P_2\)</span>
C. <span class="math-tex">\(P_3\)</span>
D. <span class="math-tex">\(P_4\)</span>
Please scroll down to see the correct answer and solution guide.
Right Answer is: A
SOLUTION
CONCEPT:
- Kepler’s First law: Every planet revolves around the Sun in an elliptical orbit and Sun is situated at one of its two foci. It is also termed as ‘the Law of Orbits’.
- Conservation of Angular Momentum: The velocity and distance from the Sun both change as the planet moves in an elliptical orbit, but the product of the velocity times the distance stays constant.
L = m v r,
Where m is the mass of the planet, v is the planet's orbital velocity and r is the distance can be taken as the semi-major axis of the orbit (the distance between sun and planet).
EXPLANATION:
- As from the law of conservation of angular momentum; we can say that the speed of the mercury will be the maximum when its distance from the sun is the minimum;
∴ m v r = constant
- So, the speed (v) of the planet will be maximum at ‘P1 because the distance between the sun and the planet is the lowest at ‘P1S’ in the figure.
Kinetic energy = (1/2) m v2
- Thus kinetic energy will be maximum at p1. So option 1 is correct.
