Question

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. Total acceleration is zero
• B. Tangential acceleration is zero
• C. Longitudinal acceleration is zero
• D. Radial acceleration is zero

Answer 1

The correct option is B Tangential acceleration is zero

Earth and all other planets move around the sun under the effect of gravitational force., This force always acts along the line joining the centre of the planet and the sun and is directed towards the sun. In other words, a planet moves around the sun under the effect of a purely radial force. Therefore, areal velocity of the planet must always remain constant.
$\therefore \frac{△\overrightarrow{A}}{△t}=\frac{\overrightarrow{L}}{2m}=$ a 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, $\tau =I\alpha$
$\therefore I\alpha =0$ or $\alpha =0$
or $aT=r\alpha =0$
ie, tangential acceleration is zero.