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

Question

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 (A) P (B) S (C) Q (D) R

Tardigrade Admin · Accepted Answer

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}

∴ 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}

∴ v_{R} < v_{P}

Hence, linear speed of planet is minimum at

R

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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