SIMBAD references

We apply a combination of N-body modeling techniques and automated data fitting with Monte Carlo Markov Chain uncertainty analysis of Keplerian orbital models to RV data to determine long-term stability of the planetary system GJ 581. We find that while there are stability concerns with the four-planet model as published by Forveille et al., when uncertainties in the system are accounted for, particularly stellar jitter, the hypothesis that the four-planet model is gravitationally unstable is not statistically significant. Additionally, the system including proposed planet g by Vogt et al. also shows some stability concerns when eccentricities are allowed to float in the orbital fit, yet when uncertainties are included in the analysis, the system including planet g also cannot be proven to be unstable. We present revised reduced χ² values for Keplerian astrocentric orbital fits assuming four-planet and five-planet models for GJ 581 under the condition that best fits must be stable, and we find no distinguishable difference by including planet g in the model. Additionally, we present revised orbital element estimates for each, assuming uncertainties due to stellar jitter under the constraint of the system being gravitationally stable.