And, thusly, the Lagrange points would be 120 degrees in front of and behind the larger one too no matter which one was in front of the other.
I don’t know where the “thusly” comes from, but I didn’t read that the Lagrange points were 120 degrees in front of and behind the larger one. I read they were in front of and behind the smaller one. Whatever.. I’m just glad there aren’t three.
The size of the Lagrange points are determined by the mass of the solar body and the mass of the planet involved.
The IAU therefore resolves that planets and other bodies in our Solar System, except satellites, be defined into three distinct categories in the following way:
(1) A "planet" is a celestial body that: (a) is in orbit around the Sun, (b) has sufficient mass for its self-gravity to overcome rigid body forces so that it assumes a hydrostatic equilibrium (nearly round) shape, and (c) has cleared the neighborhood around its orbit.
(2) A "dwarf planet" is a celestial body that: (a) is in orbit around the Sun, (b) has sufficient mass for its self-gravity to overcome rigid body forces so that it assumes a hydrostatic equilibrium (nearly round) shape, (c) has not cleared the neighbourhood around its orbit, and (d) is not a satellite.
(3) All other objects except satellites orbiting the Sun shall be referred to collectively as "Small Solar System Bodies".
At best, an object in a Lagrange point could be a 'dwarf planet'. Anything larger would have sufficient gravity of its own to perturb the orbit of the planet in whose Lagrange point it occupies.
Garde la Foi, mes amis! Nous nous sommes les sauveurs de la République! Maintenant et Toujours!
(Keep the Faith, my friends! We are the saviors of the Republic! Now and Forever!)
LonePalm, le Républicain du verre cassé (The Broken Glass Republican)