Capture in a 2-body system (not)

[DaveC426913]

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).

 

[Orodruin]

Have you tried just solving the equations of motion? Or given the phase diagram for the radial coordinate?

 

[Filip Larsen]

Showing it using conservation laws really should be all it takes. The concepts, models and calculations are all simple and really do establish that capture in the given situation is just as impossible as other situations that breaks conservation of energy. If the other part in your discussion is not willing to accept this argument, then he must be having issues with some of the assumptions, like the gravitational energy model or the concept or validity of conservation of energy, and perhaps you can identify which and try address this?

In my experience it is rather difficult to have productive discussion about physical concepts with people who seem to be in denial about something very basic like the validity of conservation of energy, so until that principle and its obvious consequences are accepted I tend to stay away from such discussions. Granted, people not trained in this may still claim they know and accept all the basic principles of physics and then still go invent some magical exceptions to these basic principles when it comes to the situation they want to discuss. And this is then where it seems proper to do like you did with your post and call out for a good teacher to please provide some magic words that would undo the other magic. In any case, sorry if all I just said is bleeding obvious and good luck with your discussion