Kepler's second law regarding the constancy of areal velocity of a planet is a consequence of the law of conservation of

Options

A. Angular momentum
B. Energy
C. Linear momentum
D. Mass

Answer

A

Explanation

For the motion of the planet, both v and r change continuosly.
Assuming SAB to be a triangle, `dA=(1)/(2)(vdt)r`
`therefore` Areal velocity `=(dA)/(dt)=(1)/(2).("vdtr")/(dt)=(1)/(2)vr` …..(1)
But the angular momentum, `L = I omega = mvr`
`therefore vr = (L)/(m) " " therefore (dA)/(dt)=(1)/(2)(L)/(m)`
As L and m are constant, the areal velocity of the radius vector remains constant.