Question

The minimum and maximum distances of a planet revolving around sun are $r$ and $R$. If the minimum speed of planet on its trajectory is $v_0$, then its maximum speed will be:

• A. $\frac{v_{0}R}{r}$
• B. $\frac{v_{0}r}{R}$
• C. $\frac{v_0{R}^2}{r^2}$
• D. $\frac{v_0{r}^2}{R^2}$

Answer 1

The correct option is A $\frac{v_{0}R}{r}$

By Kepler's law, the areal velocity $=\frac{L}{2m}$ is a constant and hence L (angular momentum) is constant.

$mvr=$ constant (at any point of trajectory)

Minimum speed ($v_0$) is possible at the maximum distance ($R$) from sun and maximum

speed ($v^{\prime }$) is possible at the minimum distance ($r$) from the sun.

$m{v}_{0}R=m{v}^{\prime }r$

$v^{\prime }=\frac{v_{0}R}{r}$