I'm having a ... "discussion" on another forum about capture and ejection of bodies. My opponents believe that, for one example, the sun can capture an object that has entered the SS from outside its g-well (i.e. on a hyperbolic trajectory) - without requiring a third body to steal its energy. I've tried every angle I can think of, including showing them the conservation of energy, even while being converted from gravitational potential energy to kinetic energy and back again. Of course I can't find anything online that describes how something can't be done; I can only find examples of how it does happen (involving said third body) - which always leaves room for "ya but"s. An article would be way better than my own simple assertions. Ideally, I'd like to find a reputable article that describes why hyperbolic orbits don't spontaneously turn into elliptical orbits.(and vice versa). (And of course, heavy of exposition, light on maths).