Released on October 25th, 2004
"A long-term numerical solution for the insolation quantities of the Earth",
by Laskar et al.
A team led by Jacques Laskar from the Institut de Mécanique Céleste et de Calcul des Ephémérides (IMCCE) and the Paris Observatory has released new computational results for the long-term evolution of the orbital and rotational motion of the Earth. Following Milankovitch’s theory of the paleoclimate that describes how major climatic changes on Earth are affected by astronomical events, these results have been employed to provide a new calibration of the sedimentary records over the 0 – 23.03 Myr geological period (the so-called Neogene period). Thus, Laskar et al.’s work has contributed to the definition of the new Geological Time Scale that has been adopted by the International Commission of Stratigraphy (ICS) and the International Union of Geological Sciences (IUGS). It is the first time that astronomical computations have been used to establish the ICS geological chronology over a full geological period.
Due to gravitational planetary perturbations, the orbit of the Earth slowly changes over time, as does the orientation of the planet's spin axis. These changes induce variations of the solar radiation received on the Earth's surface that are responsible for some of the large climatic changes of the past.
The major effects of astronomical phenomena on the Earth’s climate were first described by the Serbian mathematician Milankovitch in his theory of the paleoclimate (1941). In 1976, Milankovitch’s theory was validated in the landmark work of Hays, Imbrie and Shackleton, who measured the change in continental ice volume over time through the variation of the isotopic ratio of oxygen in marine sediments. The succession of the Ice Ages that occurred during the Pleistocene epoch (between 10 000 yrs and 1.8 million yrs (Myr) ago) has been shown to be related to the periodic changes of the Earth’s orbit and rotational parameters. Since then, the Milankovitch theory has been confirmed: the variation of the Earth’s orbital parameters regulates some of the major changes in the Earth’s climate.
Therefore, the computation of the evolving planetary orbits is of major interest to those who try to understand the past and future of the Earth’s climate. Such computations, provided by astronomers, were used by Milankovitch to establish his theory. Indeed, he used the orbital computations made in 1856 by Le Verrier, former director of the Paris Observatory and famed for the discovery of Neptune in 1846. Since then, the Paris Observatory’s teams have continued to be involved in the computation of the variations of planetary orbits over an extended time span.
In addition to providing tools for the understanding of the Earth's major climatic changes, computations of planetary orbits make it possible to refine the geological time scale used by geologists. A fundamental step to understanding the Earth’s past chronology is the establishment of a complete, precise time scale for geological records.
The Geologic Time Scale depends on two aspects of the dating of the records. First, the sedimentary records that are collected worldwide must be linked together through significant events, such as the appearance/disappearance of living species or the paleomagnetic reversals. The sedimentary records can then be associated to a relative timescale.
The next step is to date the records on an absolute scale (i.e. to determine their age in Myr). One technique is to use radiogenic dating which is based on the radioactive decay of elements within a sample. This technique is widely applied to date the oldest geological records (more than about 100 Myr old). However, the use of astronomical computations is much more precise for determining the age of younger sedimentary records. The principle of the astronomical dating technique is as follows. The past orbital parameters of the Earth are computed and used to calculate the variation in time of the solar energy input on the Earth (the so-called insolation). Next, the cycles of the varying insolation are matched to the cycles of the paleoclimate inferred from sedimentary archives. The sedimentary records can then be dated in an absolute way.
After Milankovitch first used Le Verrier’s computational results to establish his theory of paleoclimate cycles, teams from the Paris Observatory have been involved in the contribution of astronomy to paleoclimatic studies. For several decades, paleoclimatologists have used computational results obtained by the Paris Observatory’s astronomers to calibrate the geological time scale. Ten years ago, Jacques Laskar and his colleagues computed the evolution of the Earth’s orbit for the last 10 Myr. Since then, the collection of geological data has been much improved and more complete astronomical computations were required.
This need has now been fulfilled since the new computational results obtained by Jacques Laskar and his team  precisely reproduce the Earth’s past and future orbits for a period of 40 – 50 Myr. For the first time, astronomical computations of the Earth’s past orbit have been used to calibrate a whole geological period, the so-called Neogene geological period, that began 23.03 Myr ago. The new computation contributes to one of the major improvements of the newly published Geological Time Scale (GTS 2004) adopted for the Neogene period by the Union of Geological Sciences. This new time scale results from a collaborative effort among sedimentologists around the world to obtain full coverage of the Earth's history for the last 3.8 billion years (Gyr). Thanks to the adoption of these astronomical results for the calibration of the Neogene period, the new GTS 2004 makes it possible for paleoclimatologists to be more precise in dating the geological events that occurred during this geological period.
In fact, the past and future orbits of the Earth have been computed for the period between –250 and +250 Myr. However, one of the major problems with such computations is that over a long time span, planetary orbits have chaotic behaviour, as was shown by Jacques Laskar in 1989; the error in the computation of planetary orbits is multiplied by 10 every 10 Myr. Thus, the Earth’s past orbit cannot be computed precisely (and used to calibrate paleoclimate data) beyond 100 Myr ago. However, extended computations beyond 100 Myr ago can still provide useful information.
In particular, the team studied the variation of the eccentricity of the Earth’s orbit over a 250 Myr period. It was already known that the eccentricity of the Earth’s orbit has a modulation with a period of 405 000 years. Shorter cycles (periods of 20 000 and 40 000 years) also exist and are used to calibrate the Neogene period, as described above. But, as their periods change in time due to chaos, these short cycles can no longer be used to calibrate the older geological periods. The period of the cycle of 405 000 yrs is much more stable in time as it results from the gravitational perturbations of Jupiter and Saturn. Some Jurassic and Triassic sediments show evidence of such a cycle of 405 000 yrs. In their present work, the astronomers better characterized this modulation of the eccentricity and proposed using this 405 000 yrs-cycle to calibrate the geological time scale dating back to the beginning of the Mesozoic era (250 Myr ago). This would lead to an improvement of about 10 times the accuracy of the geological time scale for this geological period.
Finally, Jacques Laskar gives evidence of a significant variation of the Earth’s obliquity (the angle between the Earth's equator and orbit) in the near future. Due to tidal dissipation in the Earth-Moon system, the Earth's rotation is slowing down, and the Moon is receding at about 3.82 cm/yr. This induces a slow change in the obliquity. The team shows that this small effect induces a slow increase in the obliquity of about 2 degrees per billion years; but in the near future, as the Earth’s precession
rate will cross a resonance, the obliquity will decrease about 0.4 degrees within a few millions of years, with some possible impact on the climate. The evolution of the Earth’s obliquity from -250 to +250 Myr is shown on the figure below.
Evolution of the obliquity of the Earth in degrees, from -250 to +250 Myr. The pink zone is the actual obliquity, while the black curve is the averaged value of the obliquity over 0.5 Myr time intervals.
Surprisingly, the crossing of the resonance, yielding to the fast decrease of the obliquity, is the only strong change that occurred between -250 Myr and + 250 Myr. Indeed, the fast decrease of the obliquity that will occur in the near future is related to the increase in the Earth-Moon distance and is not a cyclic occurrence. However, additional effects that would affect the past evolution of the Earth’s dynamical shape (such as the increase of ice volume at the poles during an Ice Age or the mantle convection) might yield to the same resonance crossing. The team therefore looked for similar events that might have already occurred in the past, but found no evidence of such past events. Finally, unless new results concerning the past evolution of the dynamical shape of the Earth show that the crossing of this resonance could have occurred in the past, we should consider that the proximity of this resonance is pure chance.
Thanks to these new astronomical computations, the new Geological Time Scale has been much improved for the Neogene period (the past 23 Myr) so that it is now dated with an accuracy of about 40 000 years. The next step to improve the Geological Time Scale is to provide an astronomical calibration of the Paleogene period that covers the past 23-65.5 Myr. This will require both an extension of collections of geological data and a greater refinement of the computational modeling of the Earth’s past orbit.
 The team consists of J. Laskar, P. Robutel, F. Joutel, M. Gastineau (Observatoire de Paris/IMCCE, France), A.C.M. Correia (IMCCE/Observatoire de Paris, France; Universidade de Aveiro, Portugal), and B. Levrard (Observatoire de Paris/IMCCE, France).
A long-term numerical solution for the insolation quantities of the Earth
by J. Laskar, P. Robutel, F. Joutel, M. Gastineau, A.C.M. Correia, and B. Levrard.
Published in Astronomy & Astrophysics (DOI number: 10.1051/0004-6361:20041335)
Dr. Jacques Laskar
IMCCE/Observatoire de Paris
77 Avenue Denfert-Rochereau
75014 Paris, France
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Dr. Jennifer Martin
Journal Astronomy & Astrophysics
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