Poincars Geology: Deep Time Solutions to Chaotic Evolution of the Solar System by Use of the Drill

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Poincarés Geology Deep Time Solutions to
Chaotic Evolution of the Solar System by Use of
the Drill
Paul E. Olsen DOSECC Workshop, June 4, 2009
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Jules Henri Poincaré (1854 - 1912)
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The n-body problem The problem of finding, given
the initial positions, masses, and velocities of
n bodies, their subsequent motions as determined
by classical mechanics. Poincaré discovered
Newtons clockwork Solar System did not exist.
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Sussman and Wisdom, 1988, 1992 Pluto and all 8
planets orbits are chaotic Laskar, 1989 Inner
planets orbits more chaotic than thought Laskar,
1989, 1990 Accuracy of numerical solutions for
paleoclimate limited to 10s of m.y. Spin axis
of Venus flips Batygin Laughlin, 2008 Mercury
falls into the Sun at 1.261 Gyr Mercury and
Venus collide in 862 Myr Mars get ejected from
the Solar System at 822 Myr
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Main Sources of Uncertainty in the Numerical
Orbital Solutions (from Laskar 1999, 2004,
2008) Time of validity of the numerical
solutions TV Uncertainty on the masses and
initial conditions 38 m.y. Contribution of the
main Galilean satellites 35 m.y. Uncertainty in
the EarthMoon system evolution 40 m.y. Effect of
the main asteroids 32 m.y. Mass loss of the
Sun 50 m.y. Uncertainty of 2 x 10-7 on the
J2 of the Sun 26 m.y. g4-g3 resonance
30 m.y.
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But celestial mechanical interactions leave a
record on the Earth in the sedimentary record of
climate. A Geology for Poincaré
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Pliocene, Eraclea Minoa, Sicily
www.geo.vu.nl/users/kuik/
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Miocene, Calatayud Basin, Spain
www.searchanddiscovery.net
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• 2 Approaches
• Use geological record to determine values of
  celestial mechanical constants (fundamental
  frequencies) and resolve state of Earth - Mars
  resonance.
• Use geological record to reject possible
  numerical solutions of Solar System behavior.
• Both absolutely require continental drilling

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Approach 1 Use geological record to determine
values of celestial mechanical constants
(fundamental frequencies) and resolve state of
Earth - Mars resonance. Use the geological
record as an interferometer.
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Late Triassic, Lockatong Formation, Eureka, PA
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Depth Ranks
5 4 3.5 3 2
1.5 1 0.5 0
Examples of Cores
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Fundamental frequencies of the 8 planets derived
from numerical solutions eccentricty
inclination g1 Mercury s1 g2
Venus s2 g3 Earth s3 g4 Mars s4 g5
Jupiter s5 g6 Saturn s6 g7 Uranus s7 g
8 Neptune s8
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• k P (yr)
• 1 g2 - g5 405,091
• g4 - g5 94,932
• g4 - g2 123,945
• 4 g3 - g5 98,857
• 5 g3 - g2 130,781
• g4 - g3 2,373,298
• g1 - g5 977,600
• 8 g4 - g1 105,150
• g2 - g5 g6 - g7 486,248
• g2 - g1 688,038
• 11 g6 - g5 100,805
• 12 g2 g4 - 2g5 76,909
• 13 g6 - g2 134,300
• 14 2g3 - g4 - g5 103,158
• 15 2g4 - g2 - g3 118,077
• 16 g1 - g3 109,936
• 17 g7 - g2 127,123

Fundamental Frequencies of the Planets g1,
Mercury g2, Venus g3, Earth g4, Mars g5,
Jupiter g6, Saturn g7, Uranus g8, Neptune
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Power Spectrum of Depth Ranks
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Tuned depth rank and color
Compared to astronomical expectations
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Period (yr)
Power
Frequency (ky)
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Determining Triassic Fundamental Frequencies
Fundamental Planetary Frequency Neogene Neog
ene Triassic Triassic Lyapunov Frequency Period
Frequency Period Time g2-g5 2.46914E-06 40
5000 2.46914E-06 405000 g4-g3 4.25000E-07 235294
1 5.68182E-07 1760000 g1-g5 1.04000E-06 961538 1
.08932E-06 918000 g2-g1 1.43500E-06 696864 1.356
85E-06 737000 g2 g4 - g3 -
g5 2.88752E-06 346318 2.97619E-06 336000 g2g4-2
g5 1.30024E-05 76909 1.29870E-05 77000 g1
4.31800E-06 231589 4.36801E-06 228937 1.37E06 g2
5.75374E-06 173800 5.75374E-06 173800
7.22E06 g3 1.34000E-05 74627 1.32225E-05 75629 4
.82E06 g4 1.38200E-05 72359 1.37907E-05 72513 4.
50E06 g5 3.27869E-06 305000 3.27869E-06 305000
8.37E06
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Courtesy of J. Laskar
Period of g4-g3 (m.y.)
Period of s4-s3 (m.y. )
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Is it Testable?
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Courtesy of J. Laskar
Period of g4-g3 (m.y.)
Period of s4-s3 (m.y. )
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Getting at the g3-g4 Resonance One could even
dream that if the succession of the transitions
from the 12 to the 11 resonance were found and
dated over an interval of 200 Ma that this could
be the ultimate test for the gravitational model.
J. Laskar, 1999
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Vollmer et al., 2008
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Vollmer et al., 2008
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Approach 2 Use the geological record to reject
possible solutions of Solar System behavior.
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Laskar, 2004
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Pälike, Laskar, Shackleton, 2004
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Conclusions

• Existing records insufficient to provide long
  enough records to precisely determine g4-g3 or
  s4-s3.
• Cannot robustly exclude huge numbers of possible
  solutions without composite record spanning at
  least 200 Ma.
• Need pairs of low and high latitude records to
  see both precession and obliquity separately.
• Need to find the best places for long continuous
  records - drilling is essential.
• Local forcing good (!) integrated records bad!

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What will it take ?
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One million dollars! ahem! I mean One BILLION
dollars!
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What will it take ?

• Need about 170 m.y. of core.
• Need at least 25 m.y. in each continuous record.
• Need at least 25 overlap in times between
  sections.
• Thats 9 coring projects x 2 for high and low
  latitudes.
• At 5 M per project, thats at least 90 M.

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Where do we go?
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Eocene, Green River Formation, Wyoming
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Early Cretaceous Yixian Formation, Liaoning, China
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What would we get?

• Complete description of the orbital dynamics of
  the Solar System.
• Ability to produce insolation target curves for
  any arbitrary time allowing lt 20 ky stratigraphic
  precision
• Improvements in precision of 104 to 1010) in
  celestial mechanical measurements (Laskar, 2008).
• Tuning of radiometric decay constants.
• Precise determination of the J2 value of the Sun.
• Constraints on the Velikovsky-ish behavior of the
  inner planets.
• Solar-System-wide tests of General Relativity.

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We cannot solve the n-body problem for the Solar
System and resultant chaotic behavior
analytically as Poincaré showed. But we can tell
which possible numerical solutions are not
possible and which are possible and completely
describe the gravitational behavior of the main
bodies of the Solar System - By using
continental coring.
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