What is Newton's version of Kepler's third law?

Newton's version of Kepler's third law is defined as: T²/R³ = 4Ï€²/G * M1+M2, in which T is the period of orbit, R is the radius of orbit, G is the gravitational constant and M1 and M2 are the two masses involved. This is a more precise version of Kepler's third law.

The simplified version of Kepler's third law is:

T² = R³

This approximation is useful when T is measured in Earth years, R is measured in astronomical units, or AUs, and M1 is assumed to be much larger than M2, as is the case with the sun and the Earth, for example.

Newton's expanded version is useful when M1 and M2 are more comparable in size, such as when a planet and its moon, or a planet and a binary star system, are compared.