Abstract
Three body resonances (TBRs) between a massless particle with an arbitrary orbit and two planets P_1 and P_2 in circular coplanar orbits occur when the critical angle σ=k_0λ_{0} +k_{1}λ_{1}+k_{2}λ_{2} - (k_{0}+k_{1}+k_{2})ϖ_{0} being k_{i} integers is oscillating over time. The approximate localization in semimajor axis of the TBRs taking arbitrary pairs of planets is very simple, specially if we ignore the secular motion of the perihelion and nodes of the perturbing planets. When these slow secular motions are taken into account each of the nominal three body resonances split in a family of resonances all them very near the nominal one. The challenge is to obtain the width, strength or whatever that give us the dynamical relevance of these TBRs. We propose an algorithm to numerically estimate the strength of arbitrary TBRs between two planets in circular coplanar orbits and a massless particle in an arbitrary orbit. This algorithm allowed us to obtain an atlas of the TBRs in the Solar System showing where are located and how strong are thousands of TBRs involving all the planets from 0 to 1000 au. Relevant results for the population of asteroids and transneptunian objects will be presented.
