  Astronomical calculations reveal the solar system's dynamical evolution,
including its chaoticity, and represent the backbone of cyclostratigraphy and
astrochronology. An absolute, fully calibrated astronomical time scale has
hitherto been hampered beyond $\sim$50 Ma, because orbital calculations
disagree before that age. Here we present geologic data and a new astronomical
solution (ZB18a), showing exceptional agreement from $\sim$58 to 53 Ma. We
provide a new absolute astrochronology up to 58 Ma and a new Paleocene-Eocene
boundary age (56.01 $\pm$ 0.05 Ma). We show that the Paleocene-Eocene Thermal
Maximum (PETM) onset occurred near a 405-kyr eccentricity maximum, suggesting
an orbital trigger. We also provide an independent PETM duration (170 $\pm$ 30
kyr) from onset to recovery inflection. Our astronomical solution requires a
chaotic resonance transition at $\sim$50 Ma in the solar system's fundamental
frequencies.
