Question

A planet is revolving in an elliptical orbit around the sun. Its closest distance from the sun is $r$ and the farthest distance is $R$. If the velocity of the planet nearest to the sun be $v$ and that farthest away from the sun be $V$, then $v/V$ is :

• A. $\frac{R^2}{r^2}$
• B. $\frac{r^2}{R^2}$
• C. $\frac{R}{r}$
• D. $\frac{r}{R}$

Answer 1

The correct option is C $\frac{R}{r}$

Lets consider,

$R_1=r=$ closest distance of planet from the sun with velocity, $V_1=v$

$R_2=R=$ farthest distance with velocity, $V_2=V$

$\frac{v}{V}=?$

From the conservation of angular momentum,

$I_1{\omega }_1=I_2{\omega }_2$

$M_1{R}_1^2{\omega }_1=M_2{R}_2^2{\omega }_2$

$M{R}_1{V}_1=M{R}_2{V}_2$ ($\omega =\frac{v}{R}$)

$vr=VR$

$\frac{v}{V}=\frac{R}{r}$

The correct option is C.