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Explanetary system exhibiting Laplace resonance
I came across this recent paper on Arxiv (also published in MNRAS) which nicely confirms some of the work we have been doing in PRP on energy exchange in the solar system via mean motion resonance. Team wassup refer to this well known phenomenon (since the 1700′s) as ‘numerology’. 
An earlier 2010 paper finds a fourth planet in the system as part of the resonant coupling.
Dynamical analysis of the Gliese-876 Laplace resonance
J. G. Marti, C. A. Giuppone, C. Beauge (Submitted on 28 May 2013)
The existence of multiple planetary systems involved in mean motion conmensurabilities has increased significantly since the Kepler mission. Although most correspond to 2-planet resonances, multiple resonances have also been found. The Laplace resonance is a particular case of a three-body resonance where the period ratio between consecutive pairs is n_1/n_2 near to n_2/n_3 near to 2/1. It is not clear how this triple resonance can act in order to stabilize (or not) the systems. The most reliable extrasolar system located in a Laplace resonance is GJ876 because it has two independent confirmations.
However best-fit parameters were obtained without previous knowledge of resonance structure and no exploration of all the possible stable solutions for the system where done. In the present work we explored the different configurations allowed by the Laplace resonance in the GJ876 system by varying the planetary parameters of the third outer planet. We find that in this case the Laplace resonance is a stabilization mechanism in itself, defined by a tiny island of regular motion surrounded by (unstable) highly chaotic orbits. Low eccentric orbits and mutual inclinations from -20 to 20 degrees are compatible with the observations. A definite range of mass ratio must be assumed to maintain orbital stability. Finally we give constraints for argument of pericenters and mean anomalies in order to assure stability for this kind of systems.
Comments:7 pages, 7 figures, accepted in MNRAS
Subjects:Earth and Planetary Astrophysics (astro-ph.EP)DOI:10.1093/mnras/stt765Cite as:arXiv:1305.6768 [astro-ph.EP] (or arXiv:1305.6768v1 [astro-ph.EP] for this version)
Source: http://tallbloke.wordpress.com/2014/02/19/explanetary-system-exhibiting-laplace-resonance/
