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Q.
A planet is moving around the sun in an elliptical path as shown in the figure. The linear speed of the planet is minimum at
Gravitation
Solution:
By Kepler's second law of planetary motion, for a moving planet around the sun, angular momentum remains conserved.
i.e. $ m_{1} v_{1} r_{1} =m_{2} v_{2} r_{2} $
but $ m_{1} =m_{2}$
$ \therefore v_{1} r_{1} =v_{2} r_{2} $
$\Rightarrow \frac{v_{1}}{v_{2}} =\frac{r_{2}}{r_{1}}$
For points $R$ and $P, \frac{v_{R}}{v_{P}}=\frac{r_{P}}{r_{R}}$
Since, $ r_{R} >r_{P}$
$\therefore v_{R} < v_{P}$
Hence, linear speed of planet is minimum at $R$.
