Using the most recent proper-motion determination of the old, Solar-metallicity, Galactic open cluster M 67, in orbital computations in a non-axisymmetric model of the Milky Way, including a bar and 3D spiral arms, we explore the possibility that the Sun once belonged to this cluster. We have performed Monte Carlo numerical simulations to generate the present-day orbital conditions of the Sun and M 67, and all the parameters in the Galactic model. We compute 3.5 times 10^5 pairs of orbits Sun-M 67 looking for close encounters in the past with a minimum distance approach within the tidal radius of M 67. In these encounters we find that the relative velocity between the Sun and M 67 is larger than 20 km/s. If the Sun had been ejected from M 67 with this high velocity by means of a three-body encounter, this interaction would destroy an initial circumstellar disk around the Sun, or disperse its already formed planets. We also find a very low probability, much less than 10^-7, that the Sun was ejected from M 67 by an encounter of this cluster with a giant molecular cloud. This study also excludes the possibility that the Sun and M 67 were born in the same molecular cloud. Our dynamical results convincingly demonstrate that M67 could not have been the birth cluster of our Solar System.
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