Let's go back to the evidence for the age of the Earth, shall we? There are many ways that the age of the Earth has been determined, historically. For centuries, scholars have tried to determine the age of the Earth. But the solution ultimately depended on geological observation and careful laboratory work.
In 1660, Steno formulated the only physical law that can be credited to geologic study - the law of superposition. The law states that any horizontally lying, undisturbed formation of sediments will have the oldest sediments at the bottom and the youngest at the top.
In the 18th century, Hutton came up with the idea of cyclic deposition and uplift, from which came the concept of uniformitarianism, which, simply put, means that the processes at work in the present were also at work in the past. What that means is that we can look at how sediments are laid down today and compare them with sediments laid down in the remote past, and correlate their depositional environments.
Using Steno's law, And Hutton's uniformitarianism, geologists were able to develop geologic columns for many rock outcrops, and correlate them into a larger regional stratigraphic column, and eventually conduct these correlations on a worldwide basis. From this work, they were able to produce data that gave relative geologic ages for any rock type. Now, relative ages don't tell us how old the Earth is, but they give us a vital starting point, and definitely show that the Earth is very old.
Enter the atomic age. When radioactivity was discovered and studied, it was determined that all elements on the periodic table have 'daughter" elements, known as isotopes. These isotopes were shown to be unstable, that is, they decay. What's more, they were shown to decay at constant rates that were dependent on the type of isotopes being studied. What was useful in talking about decay rates is determining their half-life, that is, how long it takes for half of the isotope to decay to another product. Below is a table of various important isotopes, the type of decay, and their half-lifes:
Carbon, the first on the list, was found to be a very good indicator of the age of sediments containing carbon that were laid down within the past 50,000 years. And so the Earth cannot be younger than these sediments. Strontium-rubidium curve is useful for determining the age of rocks and minerals and meteorites since 87Rb decays into the ground state of 87Sr with a half-life of 4.7 x 10^10 years. Using this method, scientists were able to determine the age of five chondritic meteorites; and they were determined to be 4.54 billion years old. And since it can be shown that these meteorites were not altered since they were first formed, they are believed to have formed at the time of the formation of the solar system, and so likely at the same time that the Earth formed.
And so bracketing the age of the Earth, it is important that we narrow down the possibilities. One way of doing that is to analyze unaltered Moon rocks. Apollo gave us that opportunity, and from those analyses, we find that the oldest Moon rock is at least 4.5 billion years. More over, we determined that the Moon is compositionally nearly identical to the Earth, and therefore, formed roughly at the same time as the Earth.