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The motion of the Moon would change if the mass of Earth increased, because the Earth's gravity would increase.

The change in the gravitational force between Earth and Moon would affect the orbital path of the Moon.

More details, if wanted:

The Moon would be pulled towards the Earth.

It's possible that the Moon would collide with Earth, depending on the strength of the Earth's new gravity.

The other possibility is that the Moon would simply go into a new, more elliptical, orbital path.

The Moon's speed would be greater than before at its closest approach to Earth. Its orbital speed at its furthest point would be similar to its original speed.

I think that's right. I've checked my answer with a website, but I haven't seen any mathematics on the problem.

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Why would the motion of the moon change if the mass of the earth increase?

The motion of the Moon would change if the mass of Earth increased, because the Earth's gravity would increase. The change in the gravitational force between Earth and Moon would affect the orbital path of the Moon. More details, if wanted: The Moon would be pulled towards the Earth. It's possible that the Moon would collide with Earth, depending on the strength of the Earth's new gravity. The other possibility is that the Moon would simply go into a new, more elliptical, orbital path. The Moon's speed would be greater than before at its closest approach to Earth. Its orbital speed at its furthest point would be similar to its original speed. I think that's right. I've checked my answer with a website, but I haven't seen any mathematics on the problem.


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