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(A) Kepler's second law (law of areas) is a direct consequence of the conservation of angular momentum,which holds for any central force. Since the fo

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Kepler's law of areas still holds.

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(A) Kepler's second law (law of areas) is a direct consequence of the conservation of angular momentum,which holds for any central force. Since the force remains a central force,the torque $	au = r 	imes F$ is zero,meaning angular momentum $L$ is conserved. Therefore,Kepler's law of areas still holds.Kepler's third law (law of periods) states that $T^2 \propto r^3$. This is derived specifically for an inverse-square law $(F \propto 1/r^2)$. If the force follows an inverse-cube law $(F \propto 1/r^3)$,the centripetal force requirement $mv^2/r = k/r^3$ implies $v^2 \propto 1/r^2$,or $v \propto 1/r$. Since $v = 2\pi r/T$,we get $1/r \propto r/T$,which leads to $T \propto r^2$,or $T^2 \propto r^4$. Thus,the law of periods does not hold.

Suppose the law of gravitational attraction suddenly changes and becomes an inverse cube law,i.e.,$F \propto 1/r^3$,but still remains a central force. Then:

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