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What is the largest single-object mass that would allow two objects of equal mass to have a stable orbit, one each, in Earth's L4 and L5 Lagrange points?

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What is the largest single-object mass that would allow two objects of equal mass to have a stable orbit, one each, in Earth's L4 and L5 Lagrange points?

This is an interesting question, but the answer won't be so interesting.

The five Lagrange points are mathematical concepts, only valid when the two primary objects (in this case Sun and Earth) are the only masses considered, and they are in circular orbits around their center of mass. The problems here include:

  1. Earth's orbit isn't circular
  2. There's that big 'ole Moon right next to it that has a wiggly tugging effect
  3. There's Jupiter and the other gas giants, and Venus that all add perturbing gravitational effects
  4. A question about "largest mass" can't be asked about a proper Lagrange point to begin with. Those spots are "reserved" for massless, mathematical test objects.

All that being said...

Even though massive objects put near the real world Sun-Earth L4/L5-like regions would need some propulsive station-keeping ability to remain there for years or decades, it might be that having equal masses each can somehow add some stability to the now four-body problem, thereby making the required station-keeping maneuvers less expensive in terms of propellants, or allow them to at least "hang out nearby" those regions longer before drifting out into heliocentric orbits (as they will eventually all do.

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