Question

A planet is revolving in an elliptical orbit around the Sun. Its closest distance from the Sun is $r_{min}$ and the farthest distance is $r_{max}$. If the velocity of the planet at the distance of the closest approach is ${\nu }_1$ and that at the farthest distance from the Sun is ${\nu }_2$ , then { ${\nu }_1$ }/{ ${\nu }_2$ }

• A. $\frac{r_{max}}{r_{min}}$
• B. $\frac{r_{min}}{r_{max}}$
• C. $\frac{r_{min}+r_{max}}{r_{max}-r_{min}}$
• D. none

Answer 1

The correct option is A $\frac{r_{max}}{r_{min}}$

As there is no external torque, so the angular momentum remains constant.

Thus, $mvr=$ constant $⟹{\nu }_1{r}_{min}={\nu }_2{r}_{max}$

Thus, $\frac{{\nu }_1}{{\nu }_2}=\frac{r_{max}}{r_{min}}$