Question

A planet of mass $m$ is revolving around the sun of mass $M$ in an elliptical orbit. If $r$ and $R$ are the minimum and maximum distances of the planet from the sun respectively, $v$ and $V$ are the minimum and maximum speed of the planet respectively, then

• A. $vr=VR$
• B. $mvr=MVR$
• C. $\frac{m{v}^2}{2}=\frac{M{V}^2}{2}$
• D. $vR=Vr$

Answer 1

The correct option is D $vR=Vr$

Point $\text{P}$ is the point of minimum seperation between the sun and the planet, so it will have maximum speed.

Similarly, point $\text{Q}$ is the point of maximum seperation between the sun and the planet, so it will have minimum speed.
Now, applying angular momentum conservation principle between points $\text{P}$ and $\text{Q}$ we have,

$mVr=mvR$

$\Rightarrow Vr=vR$

Hence, option $\left(D\right)$ is the correct answer.