The original form of Kepler's third law is P² = a³, where P is the period of the orbital motion and a is the semimajor axis of the elliptical orbit. Newton's form of the third law, however, is $P^{2}=\left[\frac{4 \pi^{2}}{G\left(m_{1}+m_{2}\right)}\right] a^{3}$ , where m₁ and m₂ are the masses involved. Three of the motions listed below can be analyzed with the original form of the law, and one requires Newton's form. Which one requires Newton's form?

Question

Quizplus · Accepted Answer

The motion of two binary stars orbiting each other involves two masses, so Newton's form of the third law is required. The other three motions involve only one mass, so Kepler's original form of the law can be used.

The Original Form of Kepler's Third Law Is P2 = P2=[4π2G(m1+m2)]a3P^{2}=\left[\frac{4 \pi^{2}}{G\left(m_{1}+m_{2}\right)}\right] a^{3}P2=[G(m1​+m2​)4π2​]a3

The Original Form of Kepler's Third Law Is P² = $P^{2}=\left[\frac{4 \pi^{2}}{G\left(m_{1}+m_{2}\right)}\right] a^{3}$