Question

A planet is revolving around the Sun in an elliptical orbit. Its closest distance from the Sun is $r_{\min }$ and the farthest distance from the Sun is $r_{\max }$. If the orbital angular velocity of the planet when it is nearest to the Sun is $\omega$, then the orbital angular velocity at the point when it is at the farthest distance from the Sun is

• A. $\omega \sqrt{\frac{r_{\min }}{r_{\max }}}$
• B. $\omega \sqrt{\frac{r_{\max }}{r_{\min }}}$
• C. $\frac{r_{\max }^2}{r_{\min }^2}\omega$
• D. $\frac{r_{\min }^2\omega }{r_{\max }^2}$

Answer 1

Answer: (D)

Conserving angular momentum
$m\cdot r_{\min }^2\cdot \omega =m\cdot r_{\max }^2\cdot {\omega }^{\prime }$
$\Rightarrow {\omega }^{\prime }=\frac{r_{\min }^2}{r_{\max }^2}\omega$