Why doesn’t the sun steal the Moon?

Because it is in Earth’s gravitational well or in Earths Hill sphere which goes up to 1.5 million kilometers out in space. From this sphere you can only get away if you break the escape velocity. For earth the escape velocity is about 5 km/s, but where the Mon is it is about 1.2 km/s. The Moon orbits at about 1km/s so it won’t get away from Earth.

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