Short answers, pulled from the story.
The invariable plane passes directly through the barycenter and stands perpendicular to the angular momentum vector of that system. It represents a weighted average of every planetary orbital and rotational plane combined.
Pierre-Simon Laplace derived the concept during his extensive astronomical work published between 1829 and 1839. He originally released five volumes of French text before English translations appeared four years later.
Jupiter contributes 60.3% of the total angular momentum within our Solar System. Saturn follows with 24.5%, Neptune adds 7.9%, and Uranus provides 5.3%.
When all four giant planets align in a single line on the far side, the Sun shifts to 2.17 astronomical units away from that balance point. This movement demonstrates how the massive outer planets pull the central star into complex orbits.
The plane remains nearly constant for almost all practical purposes because Newtonian dynamics allows scientists to ignore even tinier effects when working with standard models. Tidal friction transfers small amounts of momentum from axial rotations to orbital revolutions over time while passing stars apply minor gravitational nudges that accumulate over vast timescales.