Question 158: Gravitation

Question

The angular momentum of a planet of mass M moving around the sun in an elliptical orbit is $${\overrightarrow L }$$. The magnitude of the areal velocity of the planet is :

Accepted Answer

Gravitational force line passes through the sun so torque about sun always zero for the planet.
$$ 	herefore $$ Angular momentum about sum is constant.
$$\overrightarrow L $$ = Constant
we know, L = M$${v_ \bot }$$ r
Now,
$$dA = {1 \over 2}$$ $$	imes$$ base $$	imes$$ height
$$ = {1 \over 2} 	imes r 	imes {v_ \bot }dt$$
$$ \Rightarrow {{dA} \over {dt}} = {{r{v_ \bot }} \over 2} = {r \over 2} 	imes {L \over {Mr}} = {L \over {2M}}$$

Answer

$${{2L} \over M}$$

Answer

$${{L} \over 2M}$$

Answer

$${{L} \over M}$$

Answer

$${{4L} \over M}$$

Gravitation

The angular momentum of a planet of mass M moving around the sun in an elliptical orbit is ${\overrightarrow L }$. The magnitude of the areal velocity of the planet is :

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