Question

Prove that angular momentum of particle is twice the product of its mass and areal velocity how does it leads to kepler's 2nd law

Answer 1

Proof of the Kepler's second law.

According to the geometrical meaning of angular momentum, the angular momentum of a planet of mass "m" Orbiting around sun is,

L = 2m × areal velocity

Therefore

Areal velocity = L/2m

But torque = dL/dt = r × F = 0

( theta = 0°)

Hence angular momentum L is a constant

Therefore

Areal velocity = L/2m = a constant

Thus Kepler's second law is proved.

Hope you understand

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