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?
Does that sort of thing have to be considered when planning the orbits of probes etc?
Is Earth traveling fast enough, from the viewpoint of Alice floating near the sun, to have a gravity "tail" or "wake" trailing after it? (Alice near the sun thing is my attempt at a mostly static observer) And of course due to relativity, if Alice was orbiting retrograde to the big heavy object, she'd observe even more effect?
I think I need about 6 more cups of tea before I can think about this!
> 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.
Force is the derivative of momentum. If you apply a gravitational force for a short time, the derivative is the same but the change of momentum is tiny. If you apply it for a longer time, the change is bigger.
(Forgive the layman's attempt at understanding)
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?
Does that sort of thing have to be considered when planning the orbits of probes etc?
Is Earth traveling fast enough, from the viewpoint of Alice floating near the sun, to have a gravity "tail" or "wake" trailing after it? (Alice near the sun thing is my attempt at a mostly static observer) And of course due to relativity, if Alice was orbiting retrograde to the big heavy object, she'd observe even more effect?
I think I need about 6 more cups of tea before I can think about this!