Question

The law of areas can be understood as a consequence of

• A. conservation of angular momentum
• B. conservation of energy
• C. conservation of linear momentum
• D. Both (a) and (b)

Answer 1

Answer: (A)

The law of areas (Kepler's second law) says that areal velocity is constant, i.e. the line joining the planet sweeps out equal areas in equal interval of time.
The area swept out by the planet of mass $m$ in time interval $\Lambda t$ is given as
$\Delta A=\frac{1}{2}r(vdt)$
then arcal velocity $-\frac{dA}{dt}=\frac{d}{dt}\left[\frac{1}{2}r(vdt)\right]-\frac{1}{2}rv$
$=\frac{mvr}{2m}=\frac{L}{2m}=$ constant
i.e. angular momentum is conserved. So, we can say that the law of areas can be understood as a consequence of conservation of angular momentum.