**DDA2001, April2001**

*Session 13. Extra Solar Planets*

Wednesday, 2:30-4:00pm
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## [13.01] Evolution of the GJ876 Planets into the 2:1 Orbital Resonance

*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 \lambda_{1}-2\lambda_{2}+\varpi_{1},
\lambda_{1}-2\lambda_{2}+\varpi_{2} and \varpi_{1}-\varpi_{2} all
librating about 0^{\}circ with remarkably small amplitudes,
where \lambda_{1,2} are the mean longitudes of the inner
and outer planets respectively and \varpi_{1,2} 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 a_{1}/a_{2}. 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 da_{1}/dt>0 or da_{2}/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.

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