The motion of planets in the solar system is | vedclass

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(C) According to Kepler's second law of planetary motion, the line joining any planet to the sun sweeps out equal areas in equal intervals of time

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Angular momentum

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(C) According to Kepler's second law of planetary motion, the line joining any planet to the sun sweeps out equal areas in equal intervals of time.
Let the planet be at position $A$ at any instant $t$. The area $dA$ swept out by the radius vector $r$ in a small time interval $dt$ is given by the area of the triangular sector $SAB$.
$dA = \frac{1}{2} 	imes 	ext{base} 	imes 	ext{height} = \frac{1}{2} 	imes (r d	heta) 	imes r = \frac{1}{2} r^2 d	heta$.
The areal speed is given by $\frac{dA}{dt} = \frac{1}{2} r^2 \frac{d	heta}{dt} = \frac{1}{2} r^2 \omega$.
Since the angular momentum $J$ of the planet is $J = I\omega = mr^2\omega$, we can write $\omega = \frac{J}{mr^2}$.
Substituting this into the areal speed expression: $\frac{dA}{dt} = \frac{1}{2} r^2 \left(\frac{J}{mr^2}ight) = \frac{J}{2m}$.
Since the gravitational force exerted by the sun on the planet is a central force, the torque acting on the planet is zero. Consequently, the angular momentum $J$ remains constant. Thus, the motion of planets is an example of the conservation of angular momentum.

The motion of planets in the solar system is an example of the conservation of

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