First slide

Gravitational force and laws

Question

The angular momentum of a planet of mass M moving around the sun in an elliptical orbit is $\vec{L}$ . The magnitude of the areal velocity of the planet is $\frac{L}{n M}$ .
Find the value of n.

Moderate

A

$\frac{4 L}{m}$
B

$\frac{L}{2 m}$
C

$\frac{L}{m}$
D

$\frac{2 L}{m}$

Solution

Assuming SAB a triangle
$d A = \frac{1}{2} (V d t) r$
Areal velocity momentum $L = m v r$ $\Rightarrow v r = \frac{L}{m}$ $\Rightarrow \frac{d A}{d t} = \frac{L}{2 m}$

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