Question

prove the law of areas ie.. kepler's 2nd law
provide elaborate explanation, and also a list of the assumptions that are made, make sure to provide mathematical expressions.
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Answer 1

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Kepler's Second Law, or The Law of Equal Areas in Equal Time — The line between a planet and the sun sweeps out equal areas in the plane of the planet's orbit over equal times. ... It is often called the Law of Harmony because it shows a harmonic relation between distances and periods.

Kepler's Second Law Revisited. "Equal areas in equal times" means the rate at which area is swept out on the orbit (dA/dt) is constant. So Kepler's Second Law Revised: The rate at which a planet sweeps out area on its orbit is equal to one-half its angular momentum divided by its mass (the specific angular momentum).

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