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Astrochronology Intro
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This page introduces the use of astronomy (and in particular long-term Solar System Dynamics) as a support tool for geology, stratigraphy, paleoclimate research.

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Introduction


The Earth's mean orbital parameters (relative to the Sun) influence the Earth's climate via variations in incident solar radiation or "insolation".


Hence, paleoclimate research can take advantage of astronomical results obtained from mathematical models of long term solar system dynamics, that focus on the evolutions of (slowly changing) mean orbital parameters over geological timescales (millions of years), and on their consequences on insolation. In particular, geological data (such as sediment core data) may be time-calibrated via correlation with the relatively accurate ("clockwork") time series derived from these astronomical models.


While employing the same computation techniques (numerical integration), these long term solar system dynamics models contrast to the more familiar ephemeris models (discussed on my astro » ephemerides page), that focus on the calculation on historic timescales (decades, centuries or at most a few thousand years) of accurate positions of the celestial bodies, i.e. including (rapidly changing) longitude or anomaly. Such calculation of position is prohibitive on long time scales, and unnecessary for the modelling of climate effects.


Note that there are still several difficulties and unresolved questions on this astronomical forcing of the Earth's climate.


Introductory web pages

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Theoretical Background Material


Nonlinear differential equations and stability

The study of long term solar system dynamics requires insight in the theory of nonlinear dynamics and stability (Poincaré, Liapounov, state space and phase plane, trajectories, limit cycles, separatrices).


Below are books with sections discussing the fundamentals of this theory (in my possession since my MScEE student time, though the relevant material was not covered at MScEE level). Similar, more recent, and more elaborate discussions may be found from a number of sources, and likely also online on the web.


Selected bibliography

  • Elementary Differential Equations and Boundary Value Problems, 2nd edition, William E. Boyce and Richard C. DiPrima
    Wiley International Edition, 1969, ISBN 0-471-09332-7
    Relevant section: Ch. 9, Nonlinear Differential Equations and Stability.
     
  • Control Systems Theory, Olle I. Elgerd
    McGraw-Hill International Student Edition, 1967
    Relevant section: Ch. 8, Nonlinear Control Systems.


Long term solar system dynamics: general theory

Plenty of relevant online material is found by googling on appropriate combinations of keywords, e.g.
  perturbation resonance "solar system"


Selected online texts

  • Orbital Resonances and Chaos in the Solar System (Renu Malhotra, 1998): [e] www.lpl.arizona.edu/faculty/malhotra_preprints/rio97.pdf
    Lecture (27-page paper) published in Solar System Formation and Evolution, ASP Conference Series, Vol 149, 1998.
    Abstract: Long term solar system dynamics is a tale of orbital resonance phenomena. Orbital resonances can be the source of both instability and long term stability. This lecture provides an overview, with simple models that elucidate our understanding of orbital resonance phenomena.
     
  • Evolution of the Solar System, NASA publication SP-345: [e] history.nasa.gov/SP-345/sp345.htm
    A 27-chapter text on the evolution of the solar system up to now since its formation.
    (This text is mentioned here as a general reference; only a few sections are relevant to the topic of this page).
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Computation of Insolation


The various mathematical models

([e] Source)


  • Milankovitch 1941
  • Vernekar 1972
  • Berger 1978
  • Berger 1988
  • Laskar 1990
  • Quinn et al. 1991
  • Laskar et al. 1993
  • Varadi et al. 2003
  • Laskar et al. 2004 (see La2004 section hereunder)

The earlier models (before 1980), along with the history of the evolution of the theories and biographical information about the originators, are discussed in:


  • Ice Ages: Solving the Mystery (J. Imbrie and K. Palmer Imbrie): [e] (long url)
    Harvard University Press; Reprint edition (April, 1986). Available from Amazon.


Computation and simulation tools

  • Astronomical Solutions for Earth Paleoclimates: [e] www.imcce.fr/Equipes/ASD/insola/earth/earth.html
    First-hand material from Laskar. Provides full Fortran programs for (1) solutions La2004 from -50Myr to +20Myr, (2) solutions La93 from -20Myr to +10Myr.
     
  • Chronos - Cyclostratigraphy Online Database and Research Center: [e] www.jhu.edu/~eps/chronoscyclostrat/
    Chronos plans to build a public-access browser-based toolbox for various models (Milankovitch 1941, Berger 1978, Laskar 1990, Laskar 2004).


Installing and running the la2004 insolation tool

The page mentioned under "Astronomical Solutions for Earth Paleoclimates" has pregenerated tables with the necessary data (a time series, from -51 Myr to +21 Myr, of eccentricity, obliquity and longitude of perihelion for the orbit of the Earth) and an application program for computing insolation from these tables, for any latitude on Earth. This is available in Fortran source form and also as precompiled packages. Hereunder are instructions for the installation and use of the precompiled Windows package, for Win2000 or later platforms.


  • Make an la2004 subdirectory somewhere on your PC
  • Open www.imcce.fr/Equipes/ASD/insola/earth/binaries/index.html
  • Click the .zip for Windows 2000 and later
  • Select "save", to the la2004 directory you created
  • Unzip the downloaded file (from Windows Explorer, doubleclick la2004_x86_win.zip)
  • Run the unzipped executable (doubleclick insola.exe). This is an executable that opens in a DOS window.
  • Follow the instructions from the program.
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The La2004 Model


Announcements

(Same or almost-same announcement text from various sources)




Paper

(The actual 25-page paper from Astronomy and Astrophysics)




Clarification of terms used in the paper

  • Symplectic integration (from wikipedia): [e] en.wikipedia.org/wiki/Symplectic_integrater
    Symplectic integration is a technique that is energy-conservative. This avoids the problem of erratic gradual energy loss throughout the numerous integration steps, that would cause the simulated bodies to spiral towards the Sun.
     
  • Poisson bracket (from mathworld, Wolfram Research): [e] mathworld.wolfram.com/PoissonBracket.html
     
  • Main secular frequencies gi and si
    (Explanation to the paper's Table 3)
    The indices 1 through 9 refer to the planets Mercury through Pluto. The frequencies apply to precession of the orientation of the orbits (relative to the fixed stars): gi for precession of the perihelion, si for precession of the node (i.e. precession of the orbit normal). In general, these frequencies slowly change over time; table 3 gives the initial values (epoch xxx).


Other papers by Laskar

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Geological Paleoclimate Applications: examples


With thanks to Thierry Moorkens, for suggesting the topic. Thierry is researching Rupelian (see [e] Paleogene timetable) clay sediment layers in the Rupel river area, Belgium.

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