Question

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

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

Answer 1

The correct option is D ${\left(\frac{r_{min}}{r_{max}}\right)}^2\omega$

As there is no external torque, thus $L$ is conserved.

i-e, $L=mvr=m{r}^{2}w=constant$

Thus $r^{2}w=constant$

Letorbital angular velocity at the point when it is at the farthest distance from the sun be $w_1$

$r_{max}^2{w}_1=r_{min}^{2}w$

$⟹w_1=(\frac{r_{min}}{r_{max}}{)}^{2}w$