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Q.
Kepler's second law states that the straight line joining the planet to the sun sweeps out equal areas in equal times. This statement is equivalent to saying that
A planet moves around the sun under the effect of a purely radial force. Therefore, areal velocity of the planet must always remains constant.
= $\frac{\Delta A}{\Delta t}=\frac{L}{2m}$ = constant vector
Therefore, Kepler's 2nd law is the consequence of the principle of conservation of angular momentum (L)
$\tau=\frac{dL}{dt}=0$
Now, $\tau=I\alpha$
= $I\alpha=0 or \alpha=0$
or $a_T = r\alpha = 0$
ie, tangential acceleration is zero.