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:

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: (A) (4 L / M ) (B) ( L / M ) (C) (2 L / M ) (D) ( L /2 M )

Tardigrade Admin · Accepted Answer

For small displacement ds of the planet its area can be written as

d A =(1/2) rd ℓ =(1/2) rd sin θ A ⋅ vel =( d A / dt )=(1/2) r sin θ ( d s/ dt )=( Vr sin θ/2) ( d A / dt )=(1/2) ( mVr sin θ/ m )=( L /2 m )

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

$\frac{4 L}{M}$

$\frac{L}{M}$

$\frac{2 L}{M}$

$\frac{L}{2 M}$

For small displacement ds of the planet its area can be written as

$d A = \frac{1}{2} r d ℓ$
$= \frac{1}{2} r d sin θ$
$A \cdot v e l = \frac{d A}{d t} = \frac{1}{2} r sin θ \frac{d s}{d t} = \frac{V r s i n θ}{2}$
$\frac{d A}{d t} = \frac{1}{2} \frac{mV r s i n θ}{m} = \frac{L}{2 m}$

Q. The angular momentum of a planet of mass M moving around the sun in an elliptical orbit is L. The magnitude of the areal velocity of the planet is:

M4L​

ML​

M2L​

2ML​