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Abstract Astronomical (or Milanković) forcing of the Earth system is key to understanding rhythmic climate change on time scales ≳10⁴ y. Paleoceanographic and paleoclimatological applications concerned with past astronomical forcing rely on astronomical calculations (solutions), which represent the backbone of cyclostratigraphy and astrochronology. Here we present state‐of‐the‐art astronomical solutions over the past 3.5 Gyr. Our goal is to provide tuning targets and templates for interpreting deep‐time cyclostratigraphic records and designing external forcing functions in climate models. Our approach yields internally consistent orbital and precession‐tilt solutions, including fundamental solar system frequencies, orbital eccentricity and inclination, lunar distance, luni‐solar precession rate, Earth's obliquity, and climatic precession. Contrary to expectations, we find that the long eccentricity cycle (LEC) (previously assumed stable and labeled “metronome,” recent period ∼405 kyr), can become unstable on long time scales. Our results reveal episodes during which the LEC is very weak or absent and Earth's orbital eccentricity and climate‐forcing spectrum are unrecognizable compared to the recent past. For the ratio of eccentricity‐to‐inclination amplitude modulation (recent individual periods of ~2.4 and ~1.2 Myr, frequently observable in paleorecords) we find a wide distribution around the recent 2:1 ratio, that is, the system is not restricted to a 2:1 or 1:1 resonance state. Our computations show that Earth's obliquity was lower and its amplitude (variation around the mean) significantly reduced in the past. We therefore predict weaker climate forcing at obliquity frequencies in deep time and a trend toward reduced obliquity power with age in stratigraphic records. For deep‐time stratigraphic and modeling applications, the orbital parameters of our 3.5‐Gyr integrations are made available at 400‐year resolution. 

Abstract The dynamical evolution of the solar system is chaotic with a Lyapunov time of only ∼5 Myr for the inner planets. Due to the chaos it is fundamentally impossible to accurately predict the solar system’s orbital evolution beyond ∼50 Myr based on present astronomical observations. We have recently developed a method to overcome the problem by using the geologic record to constrain astronomical solutions in the past. Our resulting optimal astronomical solution (called ZB18a) shows exceptional agreement with the geologic record to ∼58 Ma (Myr ago) and a characteristic resonance transition around 50 Ma. Here we show that ZB18a and integration of Earth’s and Mars’ spin vector based on ZB18a yield reduced variations in Earth’s and Mars’ orbital inclination and Earth’s obliquity (axial tilt) from ∼58 to ∼48 Ma—the latter being consistent with paleoclimate records. The changes in the obliquities have important implications for the climate histories of Earth and Mars. We provide a detailed analysis of solar system frequencies (gandsmodes) and show that the shifts in the variation in Earth’s and Mars’ orbital inclination and obliquity around 48 Ma are associated with the resonance transition and caused by changes in the contributions to the superposition ofsmodes, plusg–smode interactions in the inner solar system. Theg–smode interactions and the resonance transition (consistent with geologic data) are unequivocal manifestations of chaos. Dynamical chaos in the solar system hence not only affects its orbital properties but also the long-term evolution of planetary climate through eccentricity and the link between inclination and axial tilt.