• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to project page

1994 Fiscal Year Final Research Report Summary

Numerical Simulation of Dynamical Evolution of the Solar System over 5 Billion Years

Research Project

Project/Area Number 04640277
Research Category

Grant-in-Aid for General Scientific Research (C)

Allocation TypeSingle-year Grants
Research Field Astronomy
Research InstitutionNational Astronomical Observatory

Principal Investigator

KINOSHITA Hiroshi  National Astronomical Observatory, Professor, 位置天文・天体力学研究系, 教授 (00012857)

Co-Investigator(Kenkyū-buntansha) TANIKAWA Kiyotaka  National Astronomical Observatory, Associate Professor, 理論天文学研究系, 助教授 (80125210)
NAKAI Hiroshi  National Astronomical Observatory, Research Associate, 位置天文・天体力学研究系, 助手 (60155653)
YOSHIDA Haruo  National Astronomical Observatory, Associate Professor, 位置天文・天体力学研究系, 助教授 (70220663)
Project Period (FY) 1992 – 1994
KeywordsPlanetary System / Chaos / Pluto / Resonance / Orbital Stability / Numerical Simulation
Research Abstract

Planetary motions are said to be chaotic in the sense that the maximum Lyapunov exponent is positive.So far the longest integration up to now, over 845 million years (42 Pluto's Lyapunov times) , does not show any indication of a gross instability in the motion of Pluto.We carried out the numerical integration of Pluto over the age of the solar system (5.5 billion years both towards the past and the future) . This integration also did not give any indication of chaotic evolution of Pluto.The divergences of Keplerian elements of a nearby trajectory at first grow limearly with the time and then start to increase exponentially.The exponential divergences stop at about 420 million years and saturate.The exponential divergneces are suppressed by the following three resoncnaces that Pluto has :
1) Pulto is in the 3 : 2 mean motion resonance with Neptune.
2) The argument of perihelion librates around 90 degrees and its period is 3.8 Myr.The dominant periodic variations of the eccentricity and the inclination are synchronized with the libration of the argument of perihelion.
3) Moreover the longitude of Pluto's node referred to the longitude of Neptune's node circulates and the period of this circulation is equal to the period of the libration of the argument of Perihelion (a secondary resonance) .
In order to investigate how Pluto evolves to the present stable state of three resonance lockings, we have to take account of a non-conservative mechanism in the earlsy stage of the solar system.

  • Research Products

    (16 results)

All Other

All Publications (16 results)

  • [Publications] H. Kinoshita, H. Nakai: "Long-Term Behavior of the Motion of Pluto over 5. 5 Billion Years" The Small Bodies in the Solar System and Their Interactions with Planets, ed. by Rickman, Kluwer. in press (1995)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] H. Nakai, H. Kinoshita: "Stability of the Orbit of Pluto" Proceedings of the Twenty-Sixth Symposium on Celestial Mechanics. 133-138 (1994)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] H. Nakai, H. Kinoshita & H. Yoshida: "Dependency on Computer's Arithmetic Precision in Calculation of Lyapunov Characteristic Exponent" Proceedings of the Twenty-Fifth Symposium on Celestial Mechanics. 1-10 (1992)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] H. Yoshida: "Recent Progress in the Theory and Application of Symplectic Integrators" Celestial Mechanics and Dynamical Astronomy. 56. 27-43 (1993)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] H. Kinoshita: "Motion of the Orbital Plane of a Satellite due to a Secular Change of the Obliquity of its Mother Planet" Celestial Mechanics and Dynamical Astronomy. 57. 359-368 (1993)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] K. Tanikawa, Y. Yamaguchi: "Stable and Unstable Manifolds in a Zone of Instability" Journal of Mathematical Physics. 35. 2408-2412 (1994)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] H.Nakai and H.Kinoshita: "Stability of the Orbit of Pluto" Proceedings of the Twenty-Sixth Symposium on Celestial Mechanics. 133-138 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H.Nakai, H.Kinoshita and H.Yoshida: "Dependency on Computer's Arithmetic Precision in Calculation of Lyapunov Charcteristic Exponent" Proceedings of the Twenty-Fifth Symposium on Celestial Mechanics. 1-10 (1992)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H.Yoshida: "Recent Progress in the Theory and Application of Symplectic Integrators" Celestial Mechanics and Dynamical Astronomy. 56. 27-43 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H.Kinoshita: "Analytical Expansions of Torque-Free Motions for Short and Long Axis Modes" Celestial Mechanics and Dynamical Astronomy. 53. 365-375 (1992)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H.Kinoshita: "Motion of the Orbital Plane of a Satellite due to a Secular Change of the Obliquity of its Mother Planet" Celestial Mechanics and Dynamical Astronomy. 57. 359-368 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] K.Tanikawa and Y.Yamaguchi: "Stable and Unstable Manifolds in a Zone of Instability" Journal of Mathematical Physics. 35. 2408-2412 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H.Kinoshita and H.Nakai: Long-Term Behaivior of the Motion of Pluto over 5.5 Billion Years : The Small Bodies in the Solar System and Their Interactions with Planets, ed.by Rick-man.Kluwer(in press), (1995)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H.Kinoshita and H.Nakai: New Methods for Long-Time Numerical Integration of Planetary Orbits : Chaos, Resonance, and Collective Dynamical Phenomena in the Solar System, ed.by S.Ferraz-Me1lo. Kluwer, 395-406 (1992)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H.Yoshida: Non-Integrability Criterion of Hamiltonian Systems Based on Ziglin's Theorem and its Relation tothe Singular Point Analysis : Hamiltonian Mechanics, ed.by j.Seimenis. Plenum Press, 1-12 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] K.Tanikawa and Y.Yamaguchi: Toward the Understanding of Chaos : Towards the Harnessing of Chaos, ed M.Yamaguchi. Elsevier, 409-412 (1994)

    • Description
      「研究成果報告書概要(欧文)」より

URL: 

Published: 1996-04-15  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi