Period Relation for the 2:1 resonance in the GJ876 planetary system

Abstract

The recent radial velocity Keck data for GJ876 in Laughlin et al. (2005) is shown to be in good agreement, apart from a 6 m/s scatter, with a theoretical calculation (Nauenberg, 2002) based on orbital parameters from a fit to the earlier Keck data. The time variation of the periods of the inner and outer planets, which are locked in a near 2:1 resonance, are evaluated, and their mean values, Pi and Po, are shown to satisfy closely the relation Po/Pi=2+Po/P, where P is the period for the retrograde precesion of the common mean periastron of these planets.