Kepler's Laws Of Planetary Motion

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According to Kepler's second law, a planet sweeps out equal areas in equal times as it moves around the Sun. Which physical quantity of the planet remains constant because of this?

RankGuru · Accepted Answer

NCERT Class 11, Chapter 8 (Gravitation) explains that Kepler's law of areas is a direct consequence of the conservation of angular momentum. The areal velocity is $\dfrac{dA}{dt} = \dfrac{L}{2m}$, where $L$ is the planet's angular momentum about the Sun and $m$ its mass. Because gravity is a central force, always pointing toward the Sun, it exerts no torque about the Sun, so $L$ stays constant; this fixed $L$ makes the areal velocity constant, which is exactly the equal-areas statement. Linear speed is not constant: the planet moves faster at perihelion and slower at aphelion to keep $L$ unchanged. Kinetic energy likewise varies along the orbit, being largest when the planet is nearest the Sun. The distance from the Sun continuously changes in an elliptical orbit. As a plausibility check, only a quantity tied to the central nature of gravity, namely angular momentum, can remain conserved while speed and distance both vary, confirming the correct choice.

Kepler's Laws Of Planetary Motion

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