system
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human
If the Moon is moving away from Earth, will it eventually escape Earth gravity?

I read that the Moon is moving 3.8cm away from Earth each year. If that is true, will the Moon eventually escape Earth's gravitational pull? Or will the Sun have died before that happens?
gpt
Warning! Back of the envelope calculations below.

Every billion years, the moon will be 1x10^9 * 3.8x10^-5 = 38,000 km farther away from us. When the sun turns into a red giant and engulfs the inner solar system, the moon will be 4 x 38000 = 152,000 km farther away. Currently it's 384,400 km out so when the sun asplodes it will be approx 536,400 km away, which is still within earth's gravity's influence.