Successive Refinements in Long-Term Integrations of Planetary Orbits

  title={Successive Refinements in Long-Term Integrations of Planetary Orbits},
  author={F. Varadi and Bruce Runnegar and Michael Ghil},
  journal={The Astrophysical Journal},
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… 

Figures and Tables from this paper

Due to the chaotic nature of the solar system, the question of its dynamic long-term stability can only be answered in a statistical sense, for instance, based on numerical ensemble integrations of
La2010: a new orbital solution for the long-term motion of the Earth
We present here a new solution for the astronomical computation of the orbital motion of the Earth spanning from 0 to −250 Myr. The main improvement with respect to our previous numerical solution
Surfing on the edge: chaos versus near-integrability in the system of Jovian planets
We demonstrate that the system of Sun and Jovian planets, integrated for 200 Myr as an isolated five-body system using many sets of initial conditions all within the uncertainty bounds of their
Dynamic stability of the Solar System: Statistically inconclusive results from ensemble integrations
Due to the chaotic nature of the Solar System, the question of its long-term stability can only be answered in a statistical sense, for instance, based on numerical ensemble integrations of nearby
Long term evolution and chaotic diffusion of the insolation quantities of Mars
As the obliquity of Mars is strongly chaotic, it is not possible to give a solution for its evolution over more than a few million years. Using the most recent data for the rotational state of Mars,
A long-term numerical solution for the insolation quantities of the Earth
We present here a new solution for the astronomical computation of the insolation quantities on Earth spanning from -250 Myr to 250 Myr. This solution has been improved with respect to La93 (Laskar
The interplay of chaos between the terrestrial and giant planets
We report on some simple experiments on the nature of chaos in our planetary system. We make the following interesting observations. First, we look at the system of Sun + four Jovian planets as an
Numerical Solutions for the Orbital Motion of the Solar System over the Past 100 Myr: Limits and New Results
I report results from accurate numerical integrations of Solar System orbits over the past 100Myr with the integrator package HNBody. The simulations used different integrator algorithms, step sizes,
Geologic constraints on the chaotic diffusion of the solar system
The correlation of Earth's orbital parameters with climatic variations has been used to generate astronomically calibrated geologic time scales of high accuracy. However, because of the chaotic
Is the outer Solar System chaotic
One-sentence summary: Current observational uncertainty in the positions of the Jovian planets precludes deciding whether or not the outer Solar System is chaotic. 100 word technical summary: The


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
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