Final answer:
Accurate scientific estimates of the Earth's age were unavailable until the 1960s and 1970s due to earlier technological and scientific limitations. The analysis of lunar rocks brought back by astronauts for radioactive age-dating helped to determine that Earth and the Moon are about 4.5 billion years old.
Step-by-step explanation:
We did not have accurate scientific estimates of the age of the Earth until the 1960s and 1970s because prior technologies and scientific understanding did not allow for precise dating. During the 19th century, the age of Earth was thought to be much younger until geologists and physicists discovered that it was much older, leading them to seek out an unknown source of energy to account for the age discrepancy. It was only after the lunar rocks were brought back by astronauts and underwent radioactive age dating at scientists confirmed the age of Earth and the Moon is approximately 4.5 billion years old.