These very simple-sounding questions can be the hardest ones to answer.
People used to think that there was a big thing- the Earth- which was not moving. Then you could say that something was ’in motion’ if its distances to various points on Earth were changing in time.
The problem is that there’s no real sense in which the Earth is not moving. In fact, Einstein argued successfully (following Galileo) that there are no physical effects at all which can tell us if something is moving or not. So we shouldn’t even bother to ask.
What we can ask is whether two objects are in relative motion. From your point of view, you could lay out grids of points which are at fixed distances from you, and also not spinning around. If some other object is going from one point to another on that grid, then it’s in motion relative to you.
It gets more complicated in General Relativity because you have to be clear about what it means for the grid to stay rigid, but probably we’ve already been more complicated than you wanted.
Mike W.
(published on 10/22/2007)
