Many other methods have been used to date the Earth, with many different sets of radioactive nuclides (and other methods).They are all consistent with Patterson’s measurement. The mathematical details of the lead-lead isotopic clock are less straightforward than those of the Rb-Sr method.Though the Rb and Sr concentrations differ, it’s safe to assume that the isotopic makeup of Sr and of Rb is the same everywhere.
It naturally has different concentrations of Rb and Sr in different parts of the rock because these don’t necessarily mix perfectly. Once it cools all the way and crystallizes, it is considered "born" and atoms can no longer come in or out of the system.
At this point, its radiometric clock starts ticking.
As time goes on, the Rb87 in the rock slowly turns into Sr87.
Parts of the rock that have more Rb87 will end up with more Sr87.
Several radioactive nuclides exist in nature with half-lives long enough to be useful for geologic dating.