Chaotic diffusion of the fundamental frequencies in the Solar System

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 ~50 million years before the present (Ma) because orbital calculations disagree before that age. Here, we present geologic data and a new astronomical solution (ZB18a) showing exceptional agreement from ~58 to 53 Ma. We provide a new absolute astrochronology up to 58 Ma and a new Paleocene–Eocene boundary age (56.01 ± 0.05 Ma). We show that the Paleocene–Eocene Thermal Maximum (PETM) onset occurred near a 405-thousand-year (kyr) eccentricity maximum, suggesting an orbital trigger. We also provide an independent PETM duration (170 ± 30 kyr) from onset to recovery inflection. Our astronomical solution requires a chaotic resonance transition at ~50 Ma in the Solar System’s fundamental frequencies.

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The Chaotic Motion of the Solar System

International Astronomical Union Colloquium ◽

10.1017/s025292110006588x ◽

1993 ◽

Vol 132 ◽

pp. 21-21

Author(s):

J. Laskar

Keyword(s):

Lyapunov Exponent ◽

Solar System ◽

Initial Conditions ◽

Maximum Lyapunov Exponent ◽

Secular Resonance ◽

Critical Argument ◽

Outer Planets ◽

Fundamental Frequencies ◽

Chaotic Nature ◽

Evolution With Time

AbstractIn a previous paper (Laskar, Nature, 338, 237-238), the chaotic nature of the solar system excluding Pluto was established by the numerical computation of the maximum Lyapunov exponent of its secular system over 200 Myr. In the present an explanation is given for the exponential divergence of the orbits: it is due to the transition from libration to circulation of the critical argument of the secular resonance 2(g4−g3)−(s4−s3) related to the motions of perihelions and nodes of the Birth and Mars. An other important secular resonance is identified: (g1−g5)−(s1−s2). Its critical argument stays in libration over 200 Myr with a period of about 10 Myr and amplitude from 85° to 135°. The main features of the solutions of the inner planets are now identified when taking these resonances into account. Estimates of the size of the chaotic regions are determined by a new numerical method using the evolution with time of the fundamental frequencies. The size of the chaotic regions in the inner solar system are large and correspond to variations of about 0.2 arcsec/year in the fundamental frequencies. The chaotic nature of the inner solar system can thus be considered as robust against small variations of the initial conditions or of the model. The chaotic regions related to the outer planets frequencies are very thin except for g6 which present variations sufficiently large to be significant over the age of the solar system.

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Geologic constraints on the chaotic diffusion of the solar system

Geology ◽

10.1130/g20750.1 ◽

2004 ◽

Vol 32 (11) ◽

pp. 929 ◽

Cited By ~ 57

Author(s):

Heiko Pälike ◽

Jacques Laskar ◽

Nicholas J. Shackleton

Keyword(s):

Solar System ◽

Chaotic Diffusion

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Astronomical calibration of the Ypresian timescale: implications for seafloor spreading rates and the chaotic behavior of the solar system?

Climate of the Past ◽

10.5194/cp-13-1129-2017 ◽

2017 ◽

Vol 13 (9) ◽

pp. 1129-1152 ◽

Cited By ~ 47

Author(s):

Thomas Westerhold ◽

Ursula Röhl ◽

Thomas Frederichs ◽

Claudia Agnini ◽

Isabella Raffi ◽

...

Keyword(s):

Stable Isotope ◽

Solar System ◽

Chaotic Behavior ◽

Major Change ◽

Early Eocene ◽

Chaotic Diffusion ◽

Planetary Orbits ◽

Hyperthermal Events ◽

Age Model ◽

Spreading Rates

Abstract. To fully understand the global climate dynamics of the warm early Eocene with its reoccurring hyperthermal events, an accurate high-fidelity age model is required. The Ypresian stage (56–47.8 Ma) covers a key interval within the Eocene as it ranges from the warmest marine temperatures in the early Eocene to the long-term cooling trends in the middle Eocene. Despite the recent development of detailed marine isotope records spanning portions of the Ypresian stage, key records to establish a complete astronomically calibrated age model for the Ypresian are still missing. Here we present new high-resolution X-ray fluorescence (XRF) core scanning iron intensity, bulk stable isotope, calcareous nannofossil, and magnetostratigraphic data generated on core material from ODP Sites 1258 (Leg 207, Demerara Rise), 1262, 1263, 1265, and 1267 (Leg 208, Walvis Ridge) recovered in the equatorial and South Atlantic Ocean. By combining new data with published records, a 405 kyr eccentricity cyclostratigraphic framework was established, revealing a 300–400 kyr long condensed interval for magnetochron C22n in the Leg 208 succession. Because the amplitudes are dominated by eccentricity, the XRF data help to identify the most suitable orbital solution for astronomical tuning of the Ypresian. Our new records fit best with the La2010b numerical solution for eccentricity, which was used as a target curve for compiling the Ypresian astronomical timescale (YATS). The consistent positions of the very long eccentricity minima in the geological data and the La2010b solution suggest that the macroscopic feature displaying the chaotic diffusion of the planetary orbits, the transition from libration to circulation in the combination of angles in the precession motion of the orbits of Earth and Mars, occurred ∼  52 Ma. This adds to the geological evidence for the chaotic behavior of the solar system. Additionally, the new astrochronology and revised magnetostratigraphy provide robust ages and durations for Chrons C21n to C24n (47–54 Ma), revealing a major change in spreading rates in the interval from 51.0 to 52.5 Ma. This major change in spreading rates is synchronous with a global reorganization of the plate–mantle system and the chaotic diffusion of the planetary orbits. The newly provided YATS also includes new absolute ages for biostratigraphic events, magnetic polarity reversals, and early Eocene hyperthermal events. Our new bio- and magnetostratigraphically calibrated stable isotope compilation may act as a reference for further paleoclimate studies of the Ypresian, which is of special interest because of the outgoing warming and increasingly cooling phase. Finally, our approach of integrating the complex comprehensive data sets unearths some challenges and uncertainties but also validates the high potential of chemostratigraphy, magnetostratigraphy, and biostratigraphy in unprecedented detail being most significant for an accurate chronostratigraphy.

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Proterozoic Milankovitch cycles and the history of the solar system

Proceedings of the National Academy of Sciences ◽

10.1073/pnas.1717689115 ◽

2018 ◽

Vol 115 (25) ◽

pp. 6363-6368 ◽

Cited By ~ 22

Author(s):

Stephen R. Meyers ◽

Alberto Malinverno

Keyword(s):

Solar System ◽

Milankovitch Cycles ◽

Earth System ◽

System Behavior ◽

Early Solar System ◽

Tidal Dissipation ◽

Fundamental Frequencies ◽

Solar System Dynamics ◽

Geologic Record ◽

Precession Constant

The geologic record of Milankovitch climate cycles provides a rich conceptual and temporal framework for evaluating Earth system evolution, bestowing a sharp lens through which to view our planet’s history. However, the utility of these cycles for constraining the early Earth system is hindered by seemingly insurmountable uncertainties in our knowledge of solar system behavior (including Earth–Moon history), and poor temporal control for validation of cycle periods (e.g., from radioisotopic dates). Here we address these problems using a Bayesian inversion approach to quantitatively link astronomical theory with geologic observation, allowing a reconstruction of Proterozoic astronomical cycles, fundamental frequencies of the solar system, the precession constant, and the underlying geologic timescale, directly from stratigraphic data. Application of the approach to 1.4-billion-year-old rhythmites indicates a precession constant of 85.79 ± 2.72 arcsec/year (2σ), an Earth–Moon distance of 340,900 ± 2,600 km (2σ), and length of day of 18.68 ± 0.25 hours (2σ), with dominant climatic precession cycles of ∼14 ky and eccentricity cycles of ∼131 ky. The results confirm reduced tidal dissipation in the Proterozoic. A complementary analysis of Eocene rhythmites (∼55 Ma) illustrates how the approach offers a means to map out ancient solar system behavior and Earth–Moon history using the geologic archive. The method also provides robust quantitative uncertainties on the eccentricity and climatic precession periods, and derived astronomical timescales. As a consequence, the temporal resolution of ancient Earth system processes is enhanced, and our knowledge of early solar system dynamics is greatly improved.

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Mapping Solar System chaos with the Geological Orrery

Proceedings of the National Academy of Sciences ◽

10.1073/pnas.1813901116 ◽

2019 ◽

Vol 116 (22) ◽

pp. 10664-10673 ◽

Cited By ~ 11

Author(s):

Paul E. Olsen ◽

Jacques Laskar ◽

Dennis V. Kent ◽

Sean T. Kinney ◽

David J. Reynolds ◽

...

Keyword(s):

Solar System ◽

Late Triassic ◽

Proof Of Concept ◽

Fundamental Frequencies ◽

Early Mesozoic ◽

Planetary Orbits ◽

Age Model ◽

Low Probability ◽

Chaotic Nature ◽

Newark Basin

The Geological Orrery is a network of geological records of orbitally paced climate designed to address the inherent limitations of solutions for planetary orbits beyond 60 million years ago due to the chaotic nature of Solar System motion. We use results from two scientific coring experiments in Early Mesozoic continental strata: the Newark Basin Coring Project and the Colorado Plateau Coring Project. We precisely and accurately resolve the secular fundamental frequencies of precession of perihelion of the inner planets and Jupiter for the Late Triassic and Early Jurassic epochs (223–199 million years ago) using the lacustrine record of orbital pacing tuned only to one frequency (1/405,000 years) as a geological interferometer. Excepting Jupiter’s, these frequencies differ significantly from present values as determined using three independent techniques yielding practically the same results. Estimates for the precession of perihelion of the inner planets are robust, reflecting a zircon U–Pb-based age model and internal checks based on the overdetermined origins of the geologically measured frequencies. Furthermore, although not indicative of a correct solution, one numerical solution closely matches the Geological Orrery, with a very low probability of being due to chance. To determine the secular fundamental frequencies of the precession of the nodes of the planets and the important secular resonances with the precession of perihelion, a contemporaneous high-latitude geological archive recording obliquity pacing of climate is needed. These results form a proof of concept of the Geological Orrery and lay out an empirical framework to map the chaotic evolution of the Solar System.

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Strong inclination pacing of climate in Late Triassic low latitudes revealed by the Earth-Saturn tilt cycle

10.5194/egusphere-egu21-6638 ◽

2021 ◽

Author(s):

Miranda Margulis-Ohnuma ◽

Jessica Whiteside ◽

Paul Olsen

Keyword(s):

Solar System ◽

Large Mass ◽

Late Triassic ◽

Orbital Eccentricity ◽

Specific Sequence ◽

Orbital Inclination ◽

Fundamental Frequencies ◽

The Earth ◽

Natural Gamma ◽

Lake Deposits

<p>Gravitational interactions among masses in the solar system are recorded in Earth&#8217;s paleoclimate history because variations in the geometry of Earth&#8217;s orbit and axial orientation modulate solar insolation. However, astronomical models prior to ca. 60 Ma are unreliable due to the unpredictable nature of orbital chaos in the solar system, and therefore such models must be constrained using geological data. Here, we use natural gamma radioactivity and other environmental proxies from paleo-tropical Late Triassic lake deposits of the Newark Rift Basin of eastern North America, previously shown to be paced by variations in axial precession and orbital eccentricity and stratigraphically constrained by U-Pb dating, to explore hitherto undescribed strong variations in orbital inclination in the 201&#8211;206 Ma interval (lacustrine, upper Passaic Formation), where lake level variations are particularly muted. We identify the Earth-Saturn 173 kyr orbital inclination cycle and use it to tune the sequence because it exhibits high theoretical stability and metronomic behavior due to the very large mass of Saturn. We tune separately to long-eccentricity as well, with similar effect. Slight, complimentary offsets in the other inclination and eccentricity periods revealed by the Earth-Saturn (s3-s6) and Venus-Jupiter (g2-g5) tunings are apparent that may be due to chaotic variations of the secular fundamental frequencies in the nodal and perihelion orbital precessions of Earth and Venus, respectively. The surprising strength of the inclination cycles in this specific sequence suggest an additional modulating effect of the Earth System on expression of the components of orbital pacing of climate, as well a mechanism to more fully constrain the secular fundamental frequencies of the solar system beyond the ca. 60 Myr limit of predictability that chaos imposes on astronomical solutions.</p>

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Chaotic diffusion in the Solar System

Icarus ◽

10.1016/j.icarus.2008.02.017 ◽

2008 ◽

Vol 196 (1) ◽

pp. 1-15 ◽

Cited By ~ 86

Author(s):

J LASKAR

Keyword(s):

Solar System ◽

Chaotic Diffusion

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Triassic–Jurassic climate in continental high-latitude Asia was dominated by obliquity-paced variations (Junggar Basin, Ürümqi, China)

Proceedings of the National Academy of Sciences ◽

10.1073/pnas.1501137112 ◽

2015 ◽

Vol 112 (12) ◽

pp. 3624-3629 ◽

Cited By ~ 38

Author(s):

Jingeng Sha ◽

Paul E. Olsen ◽

Yanhong Pan ◽

Daoyi Xu ◽

Yaqiang Wang ◽

...

Keyword(s):

Solar System ◽

High Latitude ◽

Junggar Basin ◽

Reliable Data ◽

Low Latitude ◽

Orbital Resonance ◽

The Earth ◽

Chaotic Diffusion ◽

Age Model ◽

Continental Climate

Empirical constraints on orbital gravitational solutions for the Solar System can be derived from the Earth’s geological record of past climates. Lithologically based paleoclimate data from the thick, coal-bearing, fluvial-lacustrine sequences of the Junggar Basin of Northwestern China (paleolatitude ∼60°) show that climate variability of the warm and glacier-free high latitudes of the latest Triassic–Early Jurassic (∼198–202 Ma) Pangea was strongly paced by obliquity-dominated (∼40 ky) orbital cyclicity, based on an age model using the 405-ky cycle of eccentricity. In contrast, coeval low-latitude continental climate was much more strongly paced by climatic precession, with virtually no hint of obliquity. Although this previously unknown obliquity dominance at high latitude is not necessarily unexpected in a high CO2 world, these data deviate substantially from published orbital solutions in period and amplitude for eccentricity cycles greater than 405 ky, consistent with chaotic diffusion of the Solar System. In contrast, there are indications that the Earth–Mars orbital resonance was in today’s 2-to-1 ratio of eccentricity to inclination. These empirical data underscore the need for temporally comprehensive, highly reliable data, as well as new gravitational solutions fitting those data.

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Astronomical Calibration of the Ypresian Time Scale: Implications for Seafloor Spreading Rates and the Chaotic Behaviour of the Solar System?

10.5194/cp-2017-15 ◽

2017 ◽

Cited By ~ 1

Author(s):

Thomas Westerhold ◽

Ursula Röhl ◽

Thomas Frederichs ◽

Claudia Agnini ◽

Isabella Raffi ◽

...

Keyword(s):

Stable Isotope ◽

Solar System ◽

Time Scale ◽

Major Change ◽

Early Eocene ◽

Chaotic Diffusion ◽

Planetary Orbits ◽

Hyperthermal Events ◽

Age Model ◽

Spreading Rates

Abstract. To fully understand the global climate dynamics of the warm early Eocene with its reoccurring hyperthermal events, an accurate high-fidelity age model is required. The Ypresian Stage (56–47.8 Ma) covers a key interval within the Eocene as it ranges from the warmest marine temperatures in the early Eocene to the long-term cooling trends in the middle Eocene. Despite the recent development of detailed marine isotope records spanning portions of the Ypresian Stage, key records to establish a complete astronomically calibrated age model for the Ypresian are still missing. Here we present new high-resolution X-ray fluorescence (XRF) core scanning Iron intensity, bulk stable isotope, calcareous nannofossil, and magnetostratigraphic data generated on core material from ODP Sites 1258 (Leg 207, Demerara Rise), 1262, 1263, 1265 and 1267 (Leg 208, Walvis Ridge) recovered in the Equatorial and South Atlantic Ocean. By combining new data with published records a 405-kyr eccentricity cyclostratigraphic framework was established, revealing a 300–400 kyr long condensed interval for Magnetochron C22n in the Leg 208 succession. Because the amplitudes are dominated by eccentricity, the XRF data help to identify the most suitable orbital solution for astronomical tuning of the Ypresian. Our new records fit best with the La2010b numerical solution for eccentricity, which was used as a target curve for compiling the Ypresian Astronomical Time Scale (YATS). The consistent positions of the very long eccentricity minima in the geological data and the La2010b solution suggest that the macroscopic feature displaying the chaotic diffusion of the planetary orbits, the transition from libration to circulation in the combination of angles in the precession motion of the orbits of Earth and Mars, occurred ~ 52 Ma ago. This is the first geological evidence for the chaotic behaviour of the solar system. Additionally, the new astrochronology and revised magnetostratigraphy provide robust ages and durations for Chrons C21n to C24n (47–54 Ma) revealing a major change in spreading rates in the interval from 51.0–52.5 Ma. Significantly, this major change in spreading rates is synchronous with a global reorganization of the plate-mantle system and the chaotic diffusion of the planetary orbits. Therefore, we hypothesize that changes in the gravitational interaction of the sun and the planets may have affected the dynamic mantle flow of the Earth triggering plate motion reorganisations ~ 52 Ma ago. Finally, the newly provided YATS also includes new absolute ages for bio- and magnetostratigraphic events/reversals and early Eocene hyperthermal events. Our new biomagnetostratigraphically calibrated stable isotope compilation may act as a reference for further paleoclimate studies of the Ypresian which is of special interest because of the outgoing warming and increasingly cooling phase.

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