# Does Kepler's law only apply to planets?

Does Kepler's law only apply to planets? If so why doesn't it apply to other objects undergoing circular motion?

By Kepler's law I'm referring to $T^2 \propto r^3$

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you write: "By Kepler's law I'm referring to $T^2 \propto r^2$". Do you mean $t^2 \propto r^3$ (Keppler's third law)? –  Johannes Jan 3 at 15:51
Yes sorry, that was a typo. I really should triple check my questions when I'm on an iPad... –  Todd Davies Jan 3 at 15:58

Kepler's third law, the so-called harmonic law, was published by Johannes Kepler in 1619, ten year after he published his first two laws. Not long thereafter, in 1643, the Flemish astronomer Godefroy Wendelin noted that Kepler's third law not only applies to the planets, but also to the moons of Jupiter.

Now we know that this law describes the motion of any two bodies in gravitational orbit around each other. In fact, all you need really is an inverse square central attractive force between the two bodies. This law still holds approximately also if there are other bodies present, as long as their gravitational influence on the smaller of the two bodies is minor compared to the gravity of the larger of the two bodies.

Stretching this law to cover Coulombic systems is perfectly ok. Kepler's third law is also observed in Rydberg atoms.

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Thank you, I just didn't know if it applied to other instances circular motion, such as a plane doing loop the loop etc. –  Todd Davies Jan 3 at 16:18
Since all you need is an inverse square central attractive potential between two bodies, then it applies to any two oppositely charged particles as well, because the Coulomb Force is essentially the same form as the Gravitational Force. –  QEntanglement Jan 3 at 16:29
Correct. In Rydberg atoms one observes the square of the Kepler frequency to be inversely proportional to the cube of the radius of the orbit. Have added a remark to that effect. –  Johannes Jan 3 at 16:44