  We show that the introduction of two worldline parameters defines a different
approach to computations in the effective field theory approach to the two-body
problem in General Relativity and present some preliminary evidence for a
reduction in computational complexity. These parameters obey a polynomial
equation whose perturbative expansion recovers an infinite series of diagrams.
Futhermore, we show that our equations define an effective two-body horizon for
interacting particles in General Relativity; in the circular orbit case, it
corresponds to the smallest conceivable separation up to which the orbit can
remain circular. We expect our results to simplify higher-order computations in
the two-body problem, as well as to give insights on the nonperturbative
properties of interacting binaries.
