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Short answer - The moon is about four and a half billion years old. About the same age as Earth.

Full answer - Nobody is completely certain of the age of the moon, but its age is currently pretty well constrained to be within 100 million years after the formation of the Earth.

The best data we have on the age of the Earth is 4.5-4.6 billion years ago. Rock samples returned from the lunar missions show dates with a maximum of around 4.4 and 4.5 billion years.

It is a matter of current research, but various models have been developed based on the formation of the Moon as the result of the collision of planet-sized object with Earth in the first 100 million years of the formation of Earth. Needless to say the computer modeling of planetary collisions and subsequent reformation is a complex process that is evolving in accuracy.

There are several hypotheses of the origin of the Moon.

The Moon may have been "born" about the same time that Earth was, about 4.5 billion years ago. Or the Moon might have accidentally wandered in from somewhere else and been captured in the Earth's gravity.

The newer explanation, which is supported a little by the evidence of the lunar rocks brought back by the Apollo astronauts, is that the Moon was created by the result of a titanic collision between some other body, perhaps the size of Mars, and the proto-Earth that had formed in the early solar system.

The collision, the theory goes, caused the Earth to spin and threw off so much material that it formed a ring of rock and dust orbiting the Earth which then coalesced under gravity to form the Moon.

There may be no way to know exactly how the Moon formed, but all of these theories place the Moon's age at about 4-5 billion years.

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8y ago

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