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We apply a combination of N-body modeling techniques and automated datafitting with Monte Carlo Markov Chain uncertainty analysis of Keplerian orbitalmodels to radial velocity data to determine long term stability of theplanetary system GJ 581. We find that while there are stability concerns withthe 4-planet model as published by Forveille et al. (2011), when uncertaintiesin the system are accounted for, particularly stellar jitter, the hypothesisthat the 4-planet model is gravitationally unstable is not statisticallysignificant. Additionally, the system including proposed planet g by Vogt etal. (2012) also shows some stability concerns when eccentricities are allowedto float in the orbital fit, yet when uncertainties are included in theanalysis the system including planet g also can not be proven to be unstable.We present revised reduced chi-squared values for Keplerian astrocentricorbital fits assuming 4-planet and 5-planet models for GJ~581 under thecondition that best fits must be stable, and find no distinguishable differenceby including planet g in the model. Additionally we present revised orbitalelement estimates for each assuming uncertainties due to stellar jitter underthe constraint of the system being gravitationally stable.

A Consistent Orbital Stability Analysis for the GJ 581 System