Numerical Solutions for the Orbital Motion of the Solar System over the Past 100 Myr: Limits and New Results

@article{Zeebe2017NumericalSF,
  title={Numerical Solutions for the Orbital Motion of the Solar System over the Past 100 Myr: Limits and New Results},
  author={Richard E. Zeebe},
  journal={The Astronomical Journal},
  year={2017},
  volume={154}
}
  • R. Zeebe
  • Published 14 September 2017
  • Physics, Geology
  • The Astronomical Journal
I report results from accurate numerical integrations of solar system orbits over the past 100 Myr with the integrator package HNBody. The simulations used different integrator algorithms, step sizes, and initial conditions, and included effects from general relativity, different models of the Moon, the Sun’s quadrupole moment, and up to 16 asteroids. I also probed the potential effect of a hypothetical Planet 9, using one set of possible orbital elements. The most expensive integration… 

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References

SHOWING 1-10 OF 39 REFERENCES

On the Dynamical Stability of the Solar System

A long-term numerical integration of the classical Newtonian approximation to the planetary orbital motions of the full solar system (Sun + eight planets), spanning 20 Gyr, was performed. The results

HIGHLY STABLE EVOLUTION OF EARTH'S FUTURE ORBIT DESPITE CHAOTIC BEHAVIOR OF THE SOLAR SYSTEM

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

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

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

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

Successive Refinements in Long-Term Integrations of Planetary Orbits

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 Störmer multistep scheme, which is

Constraints on Planet Nine’s Orbit and Sky Position within a Framework of Mean-motion Resonances

A number of authors have proposed that the statistically significant orbital alignment of the most distant Kuiper Belt Objects (KBOs) is evidence of an as-yet undetected planet in the outer solar

OBSERVATIONAL CONSTRAINTS ON THE ORBIT AND LOCATION OF PLANET NINE IN THE OUTER SOLAR SYSTEM

We use an extensive suite of numerical simulations to constrain the mass and orbit of Planet Nine, the recently proposed perturber in a distant eccentric orbit in the outer solar system. We compare

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

Existence of collisional trajectories of Mercury, Mars and Venus with the Earth

Numerical simulations of the evolution of the Solar System over 5 Gyr, including contributions from the Moon and general relativity find that one per cent of the solutions lead to a large increase in Mercury’s eccentricity—an increase large enough to allow collisions with Venus or the Sun.