Question

A planet of mass$m$is in an elliptical orbit about the sun $(m$≪ $M_{sun}$) with an orbit period $T$. If $A$ be the area of orbit, then its angular momentum would be :

• A. $\frac{mA}{\text{2T}}$
• B. $mAT$
• C. $2mAT$
• D. $\frac{2mA}{T}$

Answer 1

The correct option is D $\frac{2mA}{T}$

$\text{From Keplers law Area swept per unit time is}\frac{\text{A}}{\text{T}}=\frac{1}{2}{r}^2\omega \text{m}\frac{\text{A}}{\text{T}}=\frac{1}{2}{\text{mr}}^2\omega \text{m}\left(\frac{A}{T}\right)=\frac{1}{2}\text{L}\left(\text{As Angular momentum}\right(L)=I\omega =m{r}^2\omega )\therefore \text{L}=\frac{\text{2mA}}{\text{T}}$