I learned that there is a quirk to this because the positions of the planets in the solar system has not one thing- nada, to do with the mass or the attraction of any of the planets.
Aside from relativistic corrections to Newton - sub-part-per-million corrections even in the most extreme cases - you are horribly incorrect. Spacecraft navigation through the solar system is all about multiple-body gravitation effects. There are some remarkably elegant and efficient drift paths. They are among the very few things NASA does very well.
"Gravitation" is the proper word. "Gravity" is gravitation plus centripetal force on the spinning Earth.
Everything orbits barycenters. Discrete analysis all comes out in the general wash. Consider lunar laser ranging and the (never observed) Nordvedt effect,
http://arXiv.org/abs/gr-qc/0411113 <
http://www.npl.washington.edu/eotwash/pdf/prl83-3585.pdf>
http://arXiv.org/abs/gr-qc/0301024 Phys. Rev. Lett. 93 261101 (2004)
Nordtvedt Effect
