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M.H. Lee, S.J. Peale (UCSB)
The evolution of originally more widely separated orbits into the currently observed 2:1 orbital resonance between the two ~ Jupiter mass planets about GJ876 (Marcy et al. 2001) is essentially independent of the means of orbital convergence. The best fit dynamically determined coplanar orbits (Laughlin and Chambers 2001), using both Keck and Lick data and corresponding to \sin{i}\approx 0.77, yield a system with \lambda1-2\lambda2+\varpi1, \lambda1-2\lambda2+\varpi2 and \varpi1-\varpi2 all librating about 0\circ with remarkably small amplitudes, where \lambda1,2 are the mean longitudes of the inner and outer planets respectively and \varpi1,2 are the longitudes of periapse. The eccentricities of the planets are forced by the resonance and are constrained to the particular observed ratio by the requirement that the retrograde secular periapse motions be identical. If the outer planet migrates inward relative to the inner planet from dissipative interactions with the nebula, the system is automatically captured into all the resonant librations for sufficiently small initial eccentricities and evolves to an equilibrium configuration with constant eccentricities as the orbits continue to shrink with constant semimajor axis ratio a1/a2. The equilibrium eccentricities so obtained are independent of the rate of evolution and are remarkably close to the best fit values, although the amplitudes of libration of the resonance variables are somewhat smaller than those in the best fit solution. If the system is evolved by allowing either da1/dt>0 or da2/dt<0 with the cause unspecified, all three resonance variables are again automatically trapped into libration about 0\circ, but now the eccentricities can grow to very large values while the system remains stably librating. The amplitudes of the librations at any time depend on the initial values of the eccentricities, and for particular initial values, the amplitudes match the best fit amplitudes as the current values of the eccentricities are passed. The robustness of the evolution into the resonance whatever means is chosen and the damped nature and extreme stability of the best fit solution means that the system is almost certainly correctly represented by the Laughlin and Chambers best fit solution.