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 $v_1$ and that at the farthest distance is $v_2$ from the Sun, then $\frac{v_1}{v_2}$ is

• A. $\frac{r_{max}}{r_{min}}$
• B. $\frac{r_{min}}{r_{max}}$
• C. $\frac{r_{min}+r_{max}}{r_{max}-r_{min}}$
• D. None of the above

Answer 1

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

Angular momentum is given by,
$L=mrv$
By using the law of conservation of angular momentum, we get,
$L_1=L_2$
$\Rightarrow m{v}_1{r}_{min}=m{v}_2{r}_{max}$

$\Rightarrow \frac{v_1}{v_2}=\frac{r_{max}}{r_{min}}$