The space exploration activity that has most significantly contributed to determining the age of the Moon is the Apollo program, particularly the Apollo Lunar Sample Return missions (Apollo 11, 12, 15, 16, and 17). During these missions, astronauts collected and brought back rock and soil samples from the lunar surface.
The analysis of these samples, particularly the radiometric dating of isotopes such as uranium-lead and potassium-argon, has allowed scientists to establish the age of the Moon. The most widely accepted age for the Moon is about 4.5 billion years, suggesting that it formed shortly after the formation of the solar system.
Additionally, the study of lunar geology and impact cratering has provided insights into the Moon's history, helping to refine models of its age and evolution. Overall, the Apollo missions were crucial in advancing our understanding of the Moon's age and geological history.