Kepler's third law

Also called Law of periods, Kepler's law of harmonies

The rule that the square of a circular orbit's period is proportional to the cube of its radius, with the constant of proportionality set only by the mass of the central body. AP writes it as T squared equals 4 pi squared R cubed divided by GM.

Look for this in the orbits unit and you will not find it. AP puts it in the circular-motion topic of Unit 2, in both courses that cover it: AP Physics 1 learning objective 2.9.B and AP Physics C: Mechanics learning objective 2.10.B both read "Describe circular orbits using Kepler's third law", and both attach the same derived equation:

T^2 = \frac{4\pi^2}{GM}R^3

The reasoning behind it is one substitution. Gravity supplies the whole centripetal acceleration, so $GMm/R^2 = m(4\pi^2 R/T^2)$ , and $m$ cancels.

Which mass survives is the point. $M$ is the central body. The orbiting object's mass is gone, so every satellite of the same planet shares one value of $T^2/R^3$ . That is why the law works as a ratio: comparing two orbits around the same body gives $T_1^2/R_1^3 = T_2^2/R_2^3$ with no constants to look up.

Not printed on either sheet. Neither the AP Physics 1 nor the AP Physics C: Mechanics table of information carries it, and both CEDs mark it derived. Bring the reasoning, not the memory.

The other two laws are out of scope. A boundary statement in each course says the same thing: AP Physics 1 does not expect students to know Kepler's first or second laws of planetary motion, and AP Physics C: Mechanics does not either. Ellipses and equal areas in equal times are background, not exam content.

The R in the equation is a circular orbit radius here. See orbital velocity for the speed that goes with it.

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