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Abstract Astronomical solutions form the backbone of accurate dating for geology and paleoclimate studies. Beyond 50 Ma, however, the chaos inherent in the solar system makes it impossible to calculate a unique astronomical solution. Geological data have been used to constrain the chaos in order to arrive at an astronomically calibrated time scale up to the end‐Cretaceous. Here, we adopt and extend this approach into the latest Cretaceous, by re‐analyzing the Zumaia and Sopelana composite proxy records from the Maastrichtian. We find that the filtered total light reflectance () record is most compatible with the astronomical solution ZB20a. However, the results are sensitive to parameter choices in our algorithm, which we describe in detail. Nevertheless, we present evidence in favor of using solution ZB20a for cyclostratigraphic applications during the latest Cretaceous. Intervals with very long eccentricity nodes (VLNs) (low amplitude in the short eccentricity cycle) in the astronomical solutions that coincide with large amplitudes in the short eccentricity‐related peaks in the filtered proxy record rule out alternatives. 

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. 

The late Paleocene and early Eocene (LPEE) are characterized by long-term (million years, Myr) global warming and by transient, abrupt (kiloyears, kyr) warming events, termed hyperthermals. Although both have been attributed to greenhouse (CO₂) forcing, the longer-term trend in climate was likely influenced by additional forcing factors (i.e., tectonics) and the extent to which warming was driven by atmospheric CO₂remains unclear. Here, we use a suite of new and existing observations from planktic foraminifera collected at Pacific Ocean Drilling Program Sites 1209 and 1210 and inversion of a multiproxy Bayesian hierarchical model to quantify sea surface temperature (SST) and atmospheric CO₂over a 6-Myr interval. Our reconstructions span the initiation of long-term LPEE warming (~58 Ma), and the two largest Paleogene hyperthermals, the Paleocene–Eocene Thermal Maximum (PETM, ~56 Ma) and Eocene Thermal Maximum 2 (ETM-2, ~54 Ma). Our results show strong coupling between CO₂and temperature over the long- (LPEE) and short-term (PETM and ETM-2) but differing Pacific climate sensitivities over the two timescales. Combined CO₂and carbon isotope trends imply the carbon source driving CO₂increase was likely methanogenic, organic, or mixed for the PETM and organic for ETM-2, whereas a source with higher δ¹³C values (e.g., volcanic degassing) is associated with the long-term LPEE. Reconstructed emissions for the PETM (5,800 Gt C) and ETM-2 (3,800 Gt C) are comparable in mass to future emission scenarios, reinforcing the value of these events as analogs of anthropogenic change.