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

Question

A planet has an elliptical orbit around the sun . Let vP and vA be speed of the planet when at point P and A respectively. Which of the following relations is correct? <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-xqm81qht3xk7jivw.jpg" /> (A) (rP/rA)=(vA/vP) (B) (rP/rA)=(vP/vA) (C) (rP/rA)=√(vP/vA) (D) (rP/rA)=√(vA/vP)

Tardigrade Admin · Accepted Answer

Angular momentum of planet at P,LP=mPvprp where mp is the mass of the planet. Angular momentum of planet at A, Lp=LA; mpvprp= mpvArA or (rp/rA)=(vA/vP)

Q. 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?

$\frac{r _{P}}{r _{A}} = \frac{v _{A}}{v _{P}}$

$\frac{r _{P}}{r _{A}} = \frac{v _{P}}{v _{A}}$

$\frac{r _{P}}{r _{A}} = \frac{v _{P}}{v _{A}}$

$\frac{r _{P}}{r _{A}} = \frac{v _{A}}{v _{P}}$

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 $\frac{r _{p}}{r _{A}} = \frac{v _{A}}{v _{P}}$

Q. A planet has an elliptical orbit around the sun . Let vP​ and vA​ be speed of the planet when at point P and A respectively. Which of the following relations is correct?

rA​rP​​=vP​vA​​

rA​rP​​=vA​vP​​

rA​rP​​=vA​vP​​​

rA​rP​​=vP​vA​​​

Angular momentum of planet at P,LP​=mP​vp​rp​ where mp​ is the mass of the planet. Angular momentum of planet at A, Lp​=LA​;mp​vp​rp​=mp​vA​rA​ or rA​rp​​=vP​vA​​

Q. 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?

$\frac{r _{P}}{r _{A}} = \frac{v _{A}}{v _{P}}$

$\frac{r _{P}}{r _{A}} = \frac{v _{P}}{v _{A}}$

$\frac{r _{P}}{r _{A}} = \frac{v _{P}}{v _{A}}$

$\frac{r _{P}}{r _{A}} = \frac{v _{A}}{v _{P}}$

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 $\frac{r _{p}}{r _{A}} = \frac{v _{A}}{v _{P}}$