In sailing and shipping, another vessel is set for a collision course for you if and only if its direction from you doesn't change (assuming both keep constant

In sailing and shipping, another vessel is set for a collision course for you if and only if its direction from you doesn't change (assuming both keep constant speed). Is this roughly the same for orbiting bodies? If so, it would seem that things on a collision course would be harder to detect, as they're indistinguishable from bodies far away that don't move. Possibly orbital mechanics change this significantly, but over the course of a few days the earth's trajectory is pretty much straight.