Question

For a planet around the sun in an elliptical orbit of semi - major and semi - minor axes a and b, respectively and period T.

• A. The torque acting on the planet about the sun is non - zero
• B. The angular momentum of the planet about the sun is constant
• C. The areal velocity is $\pi ab/T$
• D. The planet moves with a constant speed around the sun

Answer 1

The correct option is B The angular momentum of the planet about the sun is constant

Keplers law of area

Areal velocity $=\frac{\text{Area swept}}{\text{Time}}=\frac{\frac{1}{2}r\left(rd\theta \right)}{dt}$ $=\frac{1}{2}{r}^2\frac{d\theta }{dt}=$ constant

Hence, $\frac{1}{2}{r}^2\omega =$ constant

or $m{r}^2\omega =$ constant

where $m{r}^2=M$ of the planet relative to $\mathrm{Sun}=I$

$I\omega =$ constant or $\overrightarrow{L}=$ constant

Hence, The angular momentum of the planet about the sun is constant