Question

A planet has an elliptical orbit around the sun . Let $v_{P}$ and $v_{A}$ be speed of the planet when at point $P$ and $A$ respectively. Which of the following relations is correct?

• A. $\frac{r_{P}}{r_{A}}=\frac{v_{A}}{v_{P}}$
• B. $\frac{r_{P}}{r_{A}}=\frac{v_{P}}{v_{A}}$
• C. $\frac{r_{P}}{r_{A}}=\sqrt{\frac{v_{P}}{v_{A}}}$
• D. $\frac{r_{P}}{r_{A}}=\sqrt{\frac{v_{A}}{v_{P}}}$

Answer 1

Answer: (A)

Angular momentum of planet at $P,L_{P}=m_{P}v_{p}r_{p}$ where $m_{p}$ is the mass of the planet.
Angular momentum of planet at A,
$L_{p}=L_{A}; \, m_{p}v_{p}r_{p}= \, m_{p}v_{A}r_{A}$ or $\frac{r_{p}}{r_{A}}=\frac{v_{A}}{v_{P}}$