> If Bob is floating in space in a capsule, and a very heavy asteroid floats past, the amount that Bob's capsule is moved is dependent on the speed of the aster

> If Bob is floating in space in a capsule, and a very heavy asteroid floats past, the amount that Bob's capsule is moved is dependent on the speed of the asteroid? Yes > Does that sort of thing have to be considered when planning the orbits of probes etc? Yes, it's a primary concern when sending probes to other planets > Is Earth traveling fast enough, from the viewpoint of Alice floating near the sun, to have a gravity "tail" or "wake" trailing after it? If I understand you correctly, then classically (i.e. ignoring relativity), no. Your gravitational acceleration towards the earth depends only your distance to it. If you consider general relativity? It's... complicated.