Relative Motion (A Thought Experiment)

At first I'd say no. All motion is relative, and if there is nothing to relate the earth to, then it can't be said to be moving.HOWEVER (there's always a 'however,' isn't there? ) it's not clear that there really is such a thing as a "single thing" in reality. Even elementary particles don't have well-defined existences in space-time. They're more like little "blurs" of probabilities which interfere with eachother and in that sense can be said to have relation or relativity. In actuality they are described as waves, and the peaks and valleys of a wave move in relation to eachother. Yes. The act of firing the engines actually propels billions of little particles AWAY from you out of your engines, and you are therefore moving relative to them. I think this is really a trick question. If the earth is spinning and the orbit of the moon is in perfect sync with rotation of the earth so that the moon sits in one place over the earth the whole time, the fact still remains that the moon is circling the earth even though it doesn't look like it from the earth or the moon. That's enough to maintain an orbit like it has presently.

I know you didn't, and forgive me if you feel accused. To inhabitants on the earth, it would have no meaning. To them, it wouldn't appear that there is any orbiting at all, and more or less all motion *IS* is a matter of appearances. I think it's best regarded as an abstraction. It's the continuum of associations that we make in our minds between our memories of the past and our observations and the present. If we didn't know that they were orbiting (which, since you stated the they were, is what made your question tricky ) there would be no way to discern that they were moving absent some additional point of reference moving non-uniformly to the earth-moon system. I'd say no.