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If an astronaut went on a spacewalk (say from the ISS), tethered him/herself to a relatively massive object in orbit around the earth (say the ISS), and threw a small object in the direction opposite to the massive object's orbit ('backwards'), would that be enough to de-orbit that small object?

Or would the small object only go on a new different orbit?

What if the astronaut throws the object towards the earth instead?

The small object would be the size of a baseball/tennis ball, of any material.

Please do not take initial atmospheric drag into account.
The question might be better phrased as - would the object de-orbit substantially faster/earlier than the massive object?

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