[spriggig (OP)]

Our universe consists of the Earth and the Moon.

Both bodies are still in relation to each other and not rotating--completely still.

Stop time.

Put the Moon in contact with the Earth.

Start time.

What happens? Does the gravitational attraction crush the two together? Are they dense enough that they simply remain touching?

[Pmb]

Our universe consists of the Earth and the Moon.

Both bodies are still in relation to each other and not rotating--completely still.

Stop time.

Put the Moon in contact with the Earth.

Start time.

What happens? Does the gravitational attraction crush the two together? Are they dense enough that they simply remain touching?

The system would collapse to form one system consisting of a single spherical planet. If the body is rotating then it will be an ellipsoid of revolution.

[syhprum]

How can I put this  ? I think the softer outer parts of the two bodies would smear together while the denser cores would tunnel thru and unite at the centre.
A great amount of energy would be liberated.

[Pmb]

A great amount of energy would be liberated.

Why do you say this?

[syhprum]

A large body 1/81 the mass of the Earth has its centre of gravity about 1500 km above the Earth , this is a large store of potential energy which presumably will be converted into to heat when the two bodies merge into one.
Or did you mean why did I feel it appropriate to mention this ?

[Pmb]

A large body 1/81 the mass of the Earth has its centre of gravity about 1500 km above the Earth , this is a large store of potential energy which presumably will be converted into to heat when the two bodies merge into one.
Or did you mean why did I feel it appropriate to mention this ?

No. Your answer was exactly what I needed to know to understand it. When you say that a great amount of energy will be liberated you mean that the potential energy will be changed to kinetic energy. Thanks for clarifying that for me. It makes perfect sense now.

[evan_au]

This would cause a mass extinction.
It is questionable whether microbes or deep-ocean life on the other side of the Earth would survive it...