# DYNAMIC STABILITY OF THE SOLAR SYSTEM: STATISTICALLY INCONCLUSIVE RESULTS FROM ENSEMBLE INTEGRATIONS

## Abstract

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 orbits. Destabilization of the inner planets, leading to close encounters and/or collisions can be initiated through a large increase in Mercury's eccentricity, with a currently assumed likelihood of ∼1%. However, little is known at present about the robustness of this number. Here I report ensemble integrations of the full equations of motion of the eight planets and Pluto over 5 Gyr, including contributions from general relativity. The results show that different numerical algorithms lead to statistically different results for the evolution of Mercury's eccentricity (e{sub M}). For instance, starting at present initial conditions (e{sub M}≃0.21), Mercury's maximum eccentricity achieved over 5 Gyr is, on average, significantly higher in symplectic ensemble integrations using heliocentric rather than Jacobi coordinates and stricter error control. In contrast, starting at a possible future configuration (e{sub M}≃0.53), Mercury's maximum eccentricity achieved over the subsequent 500 Myr is, on average, significantly lower using heliocentric rather than Jacobi coordinates. For example, the probability for e{sub M} to increase beyond 0.53 over 500 Myr is >90% (Jacobi)more »

- Authors:

- School of Ocean and Earth Science and Technology, University of Hawaii at Manoa, 1000 Pope Road, MSB 629, Honolulu, HI 96822 (United States)

- Publication Date:

- OSTI Identifier:
- 22364774

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Astrophysical Journal; Journal Volume: 798; Journal Issue: 1; Other Information: Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ALGORITHMS; CHAOS THEORY; EQUATIONS OF MOTION; GENERAL RELATIVITY THEORY; MERCURY; ORBITS; PLUTO PLANET; PROBABILISTIC ESTIMATION; PROBABILITY; SATELLITES; SOLAR SYSTEM; SOLAR SYSTEM EVOLUTION; STABILITY

### Citation Formats

```
Zeebe, Richard E., E-mail: zeebe@soest.hawaii.edu.
```*DYNAMIC STABILITY OF THE SOLAR SYSTEM: STATISTICALLY INCONCLUSIVE RESULTS FROM ENSEMBLE INTEGRATIONS*. United States: N. p., 2015.
Web. doi:10.1088/0004-637X/798/1/8.

```
Zeebe, Richard E., E-mail: zeebe@soest.hawaii.edu.
```*DYNAMIC STABILITY OF THE SOLAR SYSTEM: STATISTICALLY INCONCLUSIVE RESULTS FROM ENSEMBLE INTEGRATIONS*. United States. doi:10.1088/0004-637X/798/1/8.

```
Zeebe, Richard E., E-mail: zeebe@soest.hawaii.edu. Thu .
"DYNAMIC STABILITY OF THE SOLAR SYSTEM: STATISTICALLY INCONCLUSIVE RESULTS FROM ENSEMBLE INTEGRATIONS". United States.
doi:10.1088/0004-637X/798/1/8.
```

```
@article{osti_22364774,
```

title = {DYNAMIC STABILITY OF THE SOLAR SYSTEM: STATISTICALLY INCONCLUSIVE RESULTS FROM ENSEMBLE INTEGRATIONS},

author = {Zeebe, Richard E., E-mail: zeebe@soest.hawaii.edu},

abstractNote = {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 orbits. Destabilization of the inner planets, leading to close encounters and/or collisions can be initiated through a large increase in Mercury's eccentricity, with a currently assumed likelihood of ∼1%. However, little is known at present about the robustness of this number. Here I report ensemble integrations of the full equations of motion of the eight planets and Pluto over 5 Gyr, including contributions from general relativity. The results show that different numerical algorithms lead to statistically different results for the evolution of Mercury's eccentricity (e{sub M}). For instance, starting at present initial conditions (e{sub M}≃0.21), Mercury's maximum eccentricity achieved over 5 Gyr is, on average, significantly higher in symplectic ensemble integrations using heliocentric rather than Jacobi coordinates and stricter error control. In contrast, starting at a possible future configuration (e{sub M}≃0.53), Mercury's maximum eccentricity achieved over the subsequent 500 Myr is, on average, significantly lower using heliocentric rather than Jacobi coordinates. For example, the probability for e{sub M} to increase beyond 0.53 over 500 Myr is >90% (Jacobi) versus only 40%-55% (heliocentric). This poses a dilemma because the physical evolution of the real system—and its probabilistic behavior—cannot depend on the coordinate system or the numerical algorithm chosen to describe it. Some tests of the numerical algorithms suggest that symplectic integrators using heliocentric coordinates underestimate the odds for destabilization of Mercury's orbit at high initial e{sub M}.},

doi = {10.1088/0004-637X/798/1/8},

journal = {Astrophysical Journal},

number = 1,

volume = 798,

place = {United States},

year = {Thu Jan 01 00:00:00 EST 2015},

month = {Thu Jan 01 00:00:00 EST 2015}

}