Suppose, through some fantastical mechanism, all macroscopic (i.e. reasonably massive) objects in the universe were instantly made at rest. In other words, the relative velocity between every two of these objects is set to 0. Subsequent to that instant, Physics resumes business as usual. What happens next?
Intuitively, it seems like everything would start falling directly toward the nearest largest mass (so earth falls directly toward the sun, sun falls directly toward galactic core, etc.) but I'm wondering if there is enough perturbation due to interaction with bodies of similar masses that things would actually just stabilize into a similar type of arrangement as before.
Some additional clarification in answer to comment:
The intention is that all reasonably massive objects would be instantaneously measured at 0 velocity relative to an observer at any point in the universe (there's a bit of hand-waving involved when you get down to smaller scales, as I don't want all matter to suddenly be at 0K due to thermal kinetic energy being lost.) So, no matter where you are in the universe at that instant, everything will appear to have instantaneously stopped moving (within the limits of the time it takes for the light to arrive notifying you of this event; things would still appear to have been moving when you look into the past prior to the event.) I think there would be a noticeable discontinuity in the observed motion for past events, though. Perhaps there is a more fundamental problem with the idea here?