Kepler's 3rd Law

Fake Constant

This is a constant that is a relative constant. It is only constant if the object being orbited around is the same. Every object orbiting the sun will have the same Kepler’s constants. But, an object orbiting a sun and an object orbiting a random rock are going to have different Kepler’s constants.

Formula

Through empirical methods, Kepler found that $R^3\propto T^2$

• Where $R$ is the orbital radius
• And $T$ is the orbital period $K=\frac{R^3}{T^2}$ $K=\frac{4{\pi }^2}{GM}$

Kepler’s Constant for Heavy Orbiting Masses

If the orbiting mass is $\ge$ 20% as heavy as the orbited mass, then the Kepler’s constant does not hold entirely true. The modified constant is: $K=\frac{G(M+m)}{4{\pi }^2}$