How do Pluto and Charon manage to break out of Neptune's orbit and break into their own?

Question

How do Pluto and Charon manage to break out of Neptune's orbit and break into their own?

Answer 1

Pluto, with Charon have a 3:2 resonance orbit around the Sun with Neptune.  Neptune does 3 orbits, Pluto does 2.  And Neptune's gravity kicks Pluto to keep them in this resonance over the life of the solar system.  It's a stable arrangement.  Chances are, Pluto did not start out in this arrangement, but was captured in some sense by Neptune at some point.

Answer 2

They don't.

Neptune and Pluto's orbit never intersect in 3D, they only do so on 2D projections. In reality, Neptune and Pluto are in resonance, so both planets can't change their orbit relative to each other. Because Pluto orbit's in a different plane relative to the sun as Neptune, they stay apart from each other.