The three-body problem isn't unsolvable, we're asking the wrong question

The three-body problem is famous for being "unsolvable." Three bodies interacting gravitationally produce chaotic trajectories with no closed-form solution. Poincaré proved this in 1890 and it's mathematically correct.

But here's what's overlooked: the trajectories are chaotic, but the outcome isn't.

Almost every three-body encounter ends the same way: a tight binary plus one ejected body. The lightest body gets ejected most often. The heavier pair forms the binary. This has been confirmed in millions of N-body simulations (Valtonen & Karttunen 2006, Stone & Leigh 2019), but there's no widely accepted theoretical explanation for WHY this outcome dominates.

I've been working on an information-theoretic framework that treats gravity as a boundary compression cost on quantum state space. Applied to the three-body problem, it gives a clean answer:

Each possible outcome (which body escapes, which two form the binary) has a "cost", the boundary compression energy of that configuration. The deepest energy well belongs to the heaviest binary, because two heavy bodies bound together have the lowest boundary cost. Deeper well = larger basin of attraction in phase space = higher probability.

This gives escape probabilities P(body i escapes) ∝ m_j × m_k, where j and k are the bodies that stay. For masses 1:2:5, this predicts:

• Lightest escapes: 59%
• Middle escapes: 29%
• Heaviest escapes: 12%

This matches the known empirical inverse-mass scaling exactly (P ∝ 1/m_i), because m_j × m_k ∝ 1/m_i for fixed total mass.

But the more interesting insight is the structure of the interaction. Every three-body encounter follows four phases:

1. Approach - three bodies fall together (gravitational energy dominates)
2. Chaos - trajectories scramble (information is lost, entropy increases)
3. Binary formation - two bodies lock into orbit (structure crystallizes)
4. Ejection - third body escapes (system relaxes)

This same four-phase cycle appears in cosmology (Big Bang → thermalization → structure formation → expansion) at a scale 10⁶⁰ times larger. It also appears in star formation from molecular clouds: collapse → turbulent fragmentation → protostar formation → stellar wind clearing.

Applying the same basin-volume argument to turbulent fragmentation gives a prediction for the stellar initial mass function: dN/dm ∝ m^(−α) with α = D_fractal/2 + 1, where D_fractal is the fractal dimension of the turbulent density field. For supersonic turbulence (D ≈ 2.7), this gives α = 2.35 — the Salpeter slope, measured since 1955 but never derived from first principles.

The framework also gives an information-theoretic second law for three-body scattering: the information destroyed during the chaotic phase is bounded by the change in gravitational energy divided by the effective temperature of the interaction.

The chaos isn't the physics. The chaos is the system searching for its minimum. Once it finds it, the outcome is determined.

Full derivations: