Successive Refinements in Long-Term Integrations of Planetary Orbits

@article{Varadi2003SuccessiveRI,
  title={Successive Refinements in Long-Term Integrations of Planetary Orbits},
  author={F. Varadi and Bruce Runnegar and Michael Ghil},
  journal={The Astrophysical Journal},
  year={2003},
  volume={592},
  pages={620-630}
}
We report on accurate, long-term numerical simulations of the orbits of the major planets in our solar system. The equations of motion are directly integrated by a Stormer multistep scheme, which is optimized to reduce round-off errors. The physical models are successively refined to include corrections due to general relativity and the finite size of the lunar orbit. In one case, the Earth-Moon system is resolved as two separate bodies, and the results are compared with those based on… 

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References

SHOWING 1-10 OF 101 REFERENCES
The limits of Earth orbital calculations for geological time-scale use
  • J. Laskar
  • Physics
    Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
  • 1999
The orbital motion of the planets in the Solar System is chaotic. As a result, initially close orbits diverge exponentially with a characteristic Lyapunov time of 5 Ma. This sensitivity to initial
Dynamical Evolution of Planetesimals in the Outer Solar System: I. The Jupiter/Saturn Zone
Abstract We report on numerical simulations designed to understand the distribution of small bodies in the Solar System and the winnowing of planetesimals accreted from the early solar nebula. The
Dynamical Evolution of Planetesimals in the Outer Solar System II. The Saturn/Uranus and Uranus/Neptune Zones
Abstract We report on numerical simulations exploring the dynamical stability of planetesimals in the gaps between the outer Solar System planets. We search for stable niches in the Saturn/Uranus and
Confirmation of resonant structure in the solar system
Abstract Using a semianalytical secular theory, Laskar (1989, Nature 338, 237–238) computed the orbits of the planets over 200 million years and found that their motion, and especially the motion of
The chaotic motion of the solar system: A numerical estimate of the size of the chaotic zones
Abstract In a previous paper (J. Laskar, Nature 338, (237–238)), the chaotic nature of the Solar System excluding Pluto was established by the numerical computation of the maximum Lyapunov exponent
A Three Million Year Integration of the Earth's Orbit
The equations of motion of the nine planets and the Earth's spin axis are integrated for 3.05 million years into the past. The equations include the dominant relativistic corrections and corrections
Numerical Simulations of the Orbits of the Galilean Satellites
Long-term numerical simulations of the orbits of the Galilean satellites are carried out using a realistic physical model. The free libration of the Laplace angle, which plays a central role in the
Long-Term Planetary Integration With Individual Time Steps
We describe an algorithm for long-term planetary orbit integrations, including the dominant post-Newtonian effects, that employs individual timesteps for each planet. The algorithm is symplectic and
The origin of chaos in the outer solar system
TLDR
The theory shows that the chaos among the jovian planets results from the overlap of the components of a mean motion resonance among Jupiter, Saturn, and Uranus, and provides rough estimates of the Lyapunov time and the dynamical lifetime of Uranus.
The Combined Effects of Cold-Nebula Drag and Mean-Motion Resonances
Abstract A model for Epstein drag forces in the Solar System's primordial dust cloud is proposed; this model is consistent with the asteroid belt forming in a cold nebula. Small bodies are assumed to
...
1
2
3
4
5
...