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
$m \cdot r_{\min }^{2} \cdot \omega=m \cdot r_{\max }^{2} \cdot \omega'$
$\Rightarrow \omega'=\frac{r_{\min }^{2}}{r_{\max }^{2}} \omega$