  Free time minimizers of the action (called"semi-static" solutions by Ma\~ne)
play a central role in the theory of weak KAM solutions to the Hamilton-Jacobi
equation (see Fathi). We prove that any solution to Newton's three-body problem
which is asymptotic to Lagrange's parabolic homothetic solution is eventually a
free time minimizer. Conversely, we prove that every free time minimizer tends
to Lagrange's solution, provided the mass ratios lie in a certain large open
set of mass ratios. We were inspired by the work of Da Luz-Maderna who had
shown that every free time minimizer for the N-body problem is parabolic, and
therefore must be asymptotic to the set of central configurations. We exclude
being asymptotic to Euler's central configurations by a second variation
argument. Central configurations correspond to rest points for the McGehee
blown-up dynamics. The large open set of mass ratios are those for which the
linearized dynamics at each Euler rest point has a complex eigenvalue.
