Which of the following quantity of a planet revolving around the sun remains constant

Which of the following quantities remain constant in a planetary motion (consider elliptical orbits) as seen from the sun?

Speed
Angular speed
Kinetic Energy
Angular momentum.

Angular momentum.

In planetary motion, the net external torque on the planet is zero. Therefore, angular momentum will remain constant.

Concept: Newton’s Universal Law of Gravitation

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A planet is revolving around the sun in an elliptical orbit. Which of the following remains constant?a.Linear momentum.B.Angular momentum.C.Kinetic energyD.Potential energy.

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The answer is (b) According to Kepler's second law, the angular momentum of the planet is constant. The angular momentum of the planet does not vary, i.e. the aerial velocity of the planet remains constant.

Answer (Detailed Solution Below)

Option 2 : Angular momentum

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10 Qs. 10 Marks 10 Mins

CONCEPT:

Kepler’s laws of planetary motion:

The law of Orbits: Every planet moves around the sun in an elliptical orbit with the sun at one of the foci.

The law of Area: The line joining the sun to the planet sweeps out equal areas in equal interval of time. i.e. areal velocity is constant.
According to this law, the planet will move slowly when it is farthest from the sun and more rapidly when it is nearest to the sun. It is similar to the law of conservation of angular momentum.
The law of periods: The square of the period of revolution (T) of any planet around the sun is directly proportional to the cube of the semi-major axis of the orbit i.e. T2 ∝ r3

EXPLANATION:

From above it is clear that the planet will move slowly when it is farthest from the sun and more rapidly when it is nearest to the sun. Therefore speed is not constant.
According to this law, the planet will move slowly when it is farthest from the sun and more rapidly when it is nearest to the sun. It is similar to the law of conservation of angular momentum. Therefore option 2 is correct.
In an elliptical orbit, the magnitude and direction of velocity keep on changing. Therefore, momentum and kinetic energy do not remain constant.