Question regarding Possible Orbits

This feels like a basic question, but it's late and I'm tired:
Is there a way to set up an axis and relative location to a massive body in order use the same amount of force in exactly opposite directions to send two objects with the same mass around the same massive body such that object A makes a close loop around the massive body, resulting in a short distance traveled back to its source area, where object B takes a long path around the same massive body and returns to its starting area?

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