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What is the effect of Lunar gravity on Earth orbiting astronauts?

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What is the effect of Lunar gravity on Earth orbiting astronauts?

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Lunar gravity will perturb an earth orbit, but not much if the orbit is close to earth. The perturbations will tend to cancel out, since lunar gravity will speed the astronauts up while they approach the moon, and slow them when they go away from it. Yeah, the Apollo missions had to deal with this, as do satellites.

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