An approximate formula for the absorptivity of the three-body problem

The absorptivity is the only piece of Kol's flux theory for the three-body problem that still has to be measured by simulation. Since it is fixed in the first passage, we decompose this passage into two rules: a mass rule, which decides between flying by and exchanging partners, and an energy rule, which decides whether the outgoing body stays bound to the pair. In 42,415 first passages in the plane with zero total angular momentum, the chance of staying bound falls with the binding of the pair and, in exchanges, with the mass gain of the new pair, according to logistic laws that explain up to 72% of the variation in mass combinations not used in the fit. The resulting formula, with eight constants fitted only on a mass grid, reproduces the measured absorptivity in seven channels outside this grid with R² of 0.72 to 0.77, on average over eccentricity, and, multiplied by the flux, predicts the escape chances with a mean error of 1.7 percentage points, against 4.2 for the volume theory and 2.5 for the flux without absorptivity. The dependence on eccentricity, strong in some channels, is captured only in part by the speed of the pair at apoapsis, and the distribution of the final eccentricity still requires the measured absorptivity.