What's the science behind acoustic dispersion?

Supposing alien science were to move the Earth to another solar system, but left Earth's moon behind.  What orbit would the moon then follow?

• I'm aware that no known force could do this without massively disrupting the entire solar system.  But it might be that a sufficiently advanced technology could get round this - Earth just goes, maybe abandoning human settlements beyond Earth.   My own guess is that the EarthMoon would continue on much the same orbit round the sun, but with irregularities because its own motion round the Earth was suddenly not balanced by Earth's gravity.   And that it would make a difference where the moon was on its orbit.   As an extension, one could imagine that the same thing were done to Jupiter, just gone without disruption.  I figure there would be little direct effect on Earth, but Jupiter's huge collection of moons would go off in different directions.   (And Earth meantime would carry on in its new home, but have much smaller tides because only the solar effect would apply.  But it is mostly the EarthMoon that concerns me.)   Update - re-worded the question it to make it clear, I want to know what the moon's orbit would be in such a  case.

• Answer:

  My guess is that two things might happen: The Earth would suffer a larger number of impacts from incoming space debris, since there would be no Moon to deflect/absorb all that. The Moon tends to stabilize the Earth's tilt, so without it the Earth would probably wobble around a lot more on its axis. This would probably cause drastic change in seasons, climate patterns, etc.