Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-23T17:24:14.684Z Has data issue: false hasContentIssue false
  • English
  • Français

The motion of Pluto over the age of the solar system

Published online by Cambridge University Press:  25 May 2016

Hiroshi Kinoshita  and
Hiroshi Nakai
Hiroshi Kinoshita
Affiliation:
National Astronomical Observatory 2-21-1 Osawa, Mitaka, Tokyo, Japan E-mail(internet): [email protected]
Hiroshi Nakai
Affiliation:
National Astronomical Observatory 2-21-1 Osawa, Mitaka, Tokyo, Japan E-mail(internet): [email protected]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Pluto's motion is chaotic in the sense that the maximum Lyapunov exponent is positive and the Lyapunov time (the inverse of the Lyapunov exponent) is about 20 million years (Myr). We have carried out the numerical integration of Pluto over the age of the solar system (5.7 billion years towards the past and 5.5 billion years towards the future), which is about 280 times of the Lyapunov time. Our integration does not show any indication of gross instability in the motion of Pluto. The time evolution of Keplerian elements of a nearby trajectory of Pluto at first grow linearly with the time and then start to increase exponentially. These exponential divergences stop at about 420 Myr and saturate. The exponential divergences are suppressed by the following three resonances that Pluto has:

  1. (1) Pluto is in the 3:2 mean motion resonance with Neptune and the libration period of the critical argument is about 20000 years.

  2. (2) The argument of perihelion librates around 90 degrees and its period is 3.8 Myr.

  3. (3) The motion of the Pluto's orbital plane referred to the Neptune's orbital plane is synchronized with the libration of the argument of perihelion (a secondary resonance). The libration period associated with the second resonance is 34.5 Myr.

We briefly discuss the motions of Kuiper belt objects in a 3:2 mean motion resonance with Neptune and several possible scenarios how Pluto evolves to the present stable state.

Type
Part II - Planets and Moon: Theory and Ephemerides
Information
Symposium - International Astronomical Union , Volume 172: Dynamics, Ephemerides and Astrometry of the Solar System , 1996 , pp. 61 - 70
Copyright
Copyright © Kluwer 1996 

References

Brouwer, D. and van Woerkom, A. J. J. (1950) The Secular Perturbations of the Orbital Elements of the Principal Planets, Astron. Papers Am. Ephemeris. 13(Pt. 2), pp. 85–107.Google Scholar
Cohen, C. J. and Hubbard, E. C. (1965) Libration of the Close Approaches of Pluto to Neptune, Astron. J. 70, pp. 10–13.Google Scholar
Colombo, G. and Franklin, F. A. (1970) On the Evolution of the Solar System and the Pluto-Neptune Case, in Periodic Orbits, Stability and Resonances Giacaglia, (ed.), Reidel Pub. Comp., pp. 328–331.Google Scholar
Dormand, J. R. and Woolfson, M. M. (1980) The Origin of Pluto, Mon. Not. R. astr. Soc. 193, pp. 171–174.Google Scholar
Harrington, R. S. and van Flandern, T. C. (1979) The Satellites of Neptune and the Origin of Pluto, Icarus. 39, pp. 131–136.Google Scholar
Kinoshita, H. and Nakai, H. (1984) Motions of the Perihelion of Neptune and Pluto, Celestial Mechanics. 34, pp. 203–217.Google Scholar
Kinoshita, H., Yoshida, H., and Nakai, H. (1991) Symplectic Integrators and Applications to Dynamical Astronomy, Celestial Mechanics. 50, pp. (59–71).Google Scholar
Kinoshita, H. and Nakai, H. (1995) Long-Term Behavior of the Motion of Pluto over 5. 5 Billion Years, in The Small Bodies in the Solar System and their Interactions with Planets Rickman, (ed.), Kluwer, in press.Google Scholar
Kozai, Y. (1962) Secular perturbation of asteroids with high inclination and eccentricity, Astron. J. 67, pp. 591–598.Google Scholar
Laskar, J. (1988) Secular Evolution of the Solar System over 10 Million Years, Astron. Astrophys. 198, pp. 341–362.Google Scholar
Laskar, J. (1989) A numerical experiment on the chaotic behavior of the solar system, Nature. 338, pp. 237–238.Google Scholar
Laskar, J., Quinn, T. R., and Tremaine, S. (1992) Confirmation of Resonant Structure in the Solar System, Icarus. 95, pp. 148–152.Google Scholar
Levison, H. F. and Stern, S. A. (1995) Possible Origin and Early Dynamical Evolution of the Pluto-Charon Binary, Icarus. 116, pp. 315–339.Google Scholar
Lyttleton, R. A. (1936) On the Possible Results of an Encounter of Pluto with the Neptunian System, Mon. Not. Roy. Astron. Soc. 97, pp. 108–115.Google Scholar
Malhotra, R. (1993) The Origin of Pluto's Peculiar Orbit, Nature. 365, pp. 819–821.Google Scholar
Malhotra, R. (1995) The Origin of Pluto's Orbit: Implications for the Solar System beyond Neptune, Astron. J. 110, pp. 420–429.Google Scholar
Milani, A., Nobili, A. M. and Carpino, M. (1989) Dynamics of Pluto, Icarus. 82, pp. 200–217.Google Scholar
Morbidelli, A. and Moons, M. (1993) Secular Resonances in Mean Motion Commensurabilities: The 2/1 and 3/2 Cases, Icarus. 102, pp. 316–332.Google Scholar
Moons, M. and Morbidelli, A. (1995) Secular Resonances in Mean Motion Commensurabilities: The 4/1, 3/1, 5/2, and 7/3 Cases, Icarus. 114, pp. 33–50.Google Scholar
Nacozy, P. E. and Diehl, R. D. (1972) On the Long-Term Motion of Pluto, Celestial Mechanics. 8, pp. 445–454.Google Scholar
Nacozy, P. E. and Diehl, R. D. (1978) A Discussion of the Solution for the Motion of Pluto, Celestial Mechanics. 17, pp. 405–421.Google Scholar
Nakai, H., Kinoshita, H., and Yoshida, H. (1992) Dependence on computer's arithmetic precision in calculation of Lyapunov characteristic exponent, in Proceedings of 25 the Symposium on Celestial Mechanics Kinoshita, H. and Nakai, H. (eds.), pp. 1–10.Google Scholar
Nobili, A. M., Milani, A. and Carpino, M. (1989) Fundamental frequencies and small divisors in the orbits of the outer planets, Astron. Astrophys. 210, pp. 313–336.Google Scholar
Olsson-Steel, D. I. (1988) Results of Close Encounters between Pluto and Neptune, Astron. Astrophys. 195, pp. 327–330.Google Scholar
Quinlan, D. and Tremaine, S. (1990) Symmetric multistep methods for the numerical integration of planetary orbits, Astron. J. 100, pp. 1694–1700.Google Scholar
Sussman, G. J. and Wisdom, J. (1988) Numerical evidence that the motion of Pluto is chaotic, Science. 241, pp. 433–437.Google Scholar
Sussman, G. J. and Wisdom, J. (1992), Chaotic evolution of the solar system, Science. 257, pp. 56–62.CrossRefGoogle ScholarPubMed
Williams, J. G. and Benson, G. S. (1971) Resonances in the Neptune-Pluto system, Astron. J. 76, pp. 167–177.Google Scholar
Wisdom, J. (1992) Long term evolution of the solar system, in Chaos, Resonance and Collective Dynamical Phenomena in the Solar System Ferraz-Mello, S. (ed.), Kluwer, pp. 17–24.Google Scholar
Yoshikawa, M. (1989) A Survey on the Motion of Asteroids in Commensurabilities with Jupiter, Astron. Astrophys. 213, pp. 436–458.Google Scholar
Yoshikawa, M. (1990) Motions of Asteroids at the Kirkwood Gaps. I. On the 3:1 resonance with Jupiter, Icarus. 87, pp. 78–102.Google Scholar
Yoshikawa, M. (1990) Motions of Asteroids at the Kirkwood Gaps. II. On the 5:2, 7:3, and 2:1 resonance with Jupiter, Icarus. 92, pp. 94–117.Google Scholar