how fast is the moon drifting away from the earth

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Nature

The Moon is drifting away from the Earth at a rate of about 1.5 inches (3.8 centimeters) per year. This measurement has been confirmed with laser ranging experiments using reflectors left on the Moon by Apollo missions over the past 50 years. The primary cause of this drift is the gravitational interaction between the Earth and the Moon, which creates tidal bulges on Earth that exert a frictional force slowing Earth's rotation and transferring angular momentum to the Moon, causing it to move to a higher orbit.

This rate corresponds roughly to the average growth rate of human fingernails. Although this distance change is very small annually, over millions and billions of years it can become significant. However, in about 50 billion years, the Earth's rotation will slow enough that it will become tidally locked to the Moon, and the Moon's recession will stop. Before then, in about 5 billion years, the Earth-Moon system will be disrupted as the Sun swells into a red giant.