Can Jupiter gravitationally eject a pebble in orbit? A smaller mass?

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syfry
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TL;DR
Is there a ratio between the mass of a planet to an orbiting object that would prevent the orbit from being gravitationally ejected?

For example Jupiter might eject a large enough moon, but can it eject an orbiting pebble?
Is there a limit to the smallness for a larger mass to eject? Can a planet eject a grain in orbit, or even a lone atom in orbit?
 
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What do you mean by the term "eject"? What was the previous orbit of the object? Where did the object come from? Unless it was already in an unstable orbit due to initial conditions, where did the extra energy come from to disturb the stable orbit and cause it to become unstable? Links?
 
berkeman said:
What do you mean by the term "eject"? What was the previous orbit of the object? Where did the object come from? Unless it was already in an unstable orbit due to initial conditions, where did the extra energy come from to disturb the stable orbit and cause it to become unstable? Links?
Ah. good questions! They informed me about the mechanisms: an unstable orbit from outside energy.

Where does the energy come from? Probably a third body, which is the usual cause of unstable orbits.

So now that we have a cause, can an orbiting pebble be ejected?

An example is Saturn: it has 63 confirmed moons, and, many bits in Saturn's rings are pebble sized.

With so many things orbiting, we should expect unstable orbits somewhere in that soup. Can Saturn eject one of its orbiting pebbles?