The motion of planets in the solar system is an exmaple of the conservation of

Options

A. mass
B. linear momentum
C. energy
D. angular momentum

Answer

D

Explanation

From Kepler's second law a line joining any about to the sun sweeps out equal areas in equal times, that is, the areal speed of the planet remains constant.

`dA`= area of curved triangle `SAB`
`=1/2(ABxxSA)`
`=1/2(r d thetaxxr)=1/2r^(2)d theta`
The instantaneous areal speed of the planet is
`(dA)/(dt)=1/2 r^(2) (d theta)/(dt)=1/2r^(2) omega`
Where `omega` is an angular spped. Let `J` be angular momentum of planet about sun
`J =Iomega=mr^(2) omega`
`(dA)/(dt)=J/(2m)`
From kepler's law areal speed is constant, therefore angular momentum `J` is constant.
Hence, Kepler's second law is equivalent to conservation of angular momentum