Question

A planet is revolving in an elliptical orbit around the sun as shown in figure.The areal velocity (area swapped by the radius vector with respect to sun in unit time) is :

• A. $\frac{1}{4}(r_1+r_2)v_1$
• B. $\frac{1}{2}{r}_2{v}_2$
• C. $\frac{1}{2}\frac{v_{1}r{{}_1}^2}{r_2}$
• D. dependent on the position of planet from sun

Answer 1

The correct option is B $\frac{1}{2}{r}_2{v}_2$

Kepler's law of periods says that the area swept by a planet for a certain time interval is constant.
i.e $\frac{dA}{dt}=\frac{L}{2m}$; where $L$ is the angular momentum and is constant.

Therefore, $\frac{dA}{dt}$ is constant.
$\frac{dA}{dt}=\frac{L}{2m}=\frac{m{v}_2{r}_2}{2m}=\frac{1}{2}{v}_2{r}_2$