The discovery by Marcy et al. (2001) of two planets in 2:1 orbital resonance about the star GJ 876 has been supplemented by a dynamical fit to the data by Laughlin & Chambers (2001) which places the planets in coplanar orbits deep in three resonances at the 2:1 mean-motion commensurability. The selection of this almost singular state by the dynamical fit means that the resonances are almost certainly real, and with the small amplitudes of libration of the resonance variables, indefinitely stable. Several unusual properties of the 2:1 resonances are revealed by the GJ 876 system. The libration of both lowest order mean-motion resonance variables and the secular resonance variable, θ 1 = λ 1 − 2λ 2 + ̟ 1 , θ 2 = λ 1 − 2λ 2 + ̟ 2 , and θ 3 = ̟ 1 − ̟ 2 , about 0 • (where λ 1,2 are the mean longitudes of the inner and outer planet and ̟ 1,2 are the longitudes of periapse) differs from the familiar geometry of the Io-Europa pair, where θ 2 and θ 3 librate about 180 • . By considering the condition that̟ 1 =̟ 2 for stable simultaneous librations of θ 1 and θ 2 , we show that the GJ 876 geometry results because of the large orbital eccentricities e i , whereas the very small eccentricities in the Io-Europa system lead to the latter's geometry. Surprisingly, the GJ 876 configuration, with θ 1 , θ 2 , and θ 3 all librating, remains stable for e 1 up to 0.86 and for amplitude of libration of θ 1 approaching 45 • with the current eccentricities -further supporting the indefinite stability of the existing system.Any process that drives originally widely separated orbits toward each other could result in capture into the observed resonances at the 2:1 commensurability. We find that forced inward migration of the outer planet of the GJ 876 system results in certain capture into the observed resonances if initially e 1 0.06 and e 2 0.03 and the migration rate |ȧ 2 /a 2 | 3 × 10 −2 (a 2 / AU) −3/2 yr −1 . Larger eccentricities lead to likely capture into higher order resonances before the 2:1 commensurability is reached. The planets are sufficiently massive to open gaps in the nebular disk surrounding the young GJ 876 and to clear the disk material between them, and the resulting planet-nebular interaction typically forces the outer planet to migrate inward on the disk viscous time scale, whose inverse is about three orders of magnitude less than the above upper bound on |ȧ 2 /a 2 | for certain capture. If there is no eccentricity damping, eccentricity growth is rapid with continued migration within the resonance, with e i exceeding the observed values after a further reduction in the semi-major axes a i of only 7%. With eccentricity dampingė i /e i = −K|ȧ i /a i |, the eccentricities reach equilibrium values that remain constant for arbitrarily long migration within the resonances. The equilibrium eccentricities are close to the observed eccentricities for K ≈ 100 if there is migration and damping of the outer planet only, but for K ≈ 10 if there is also migration and damping of the inner planet. This result is independent of th...

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[1] The recent determination of the gravity field of Mercury and new Earth-based radar observations of the planet's spin state afford the opportunity to explore Mercury's internal structure. These observations provide estimates of two measures of the radial mass distribution of Mercury: the normalized polar moment of inertia and the fractional polar moment of inertia of the solid portion of the planet overlying the liquid core. Employing Monte Carlo techniques, we calculate several million models of the radial density structure of Mercury consistent with its radius and bulk density and constrained by these moment of inertia parameters. We estimate that the top of the liquid core is at a radius of 2020 AE 30 km, the mean density above this boundary is 3380 AE 200 kg m À3 , and the density below the boundary is 6980 AE 280 kg m À3 . We find that these internal structure parameters are robust across a broad range of compositional models for the core and planet as a whole. Geochemical observations of Mercury's surface by MESSENGER indicate a chemically reducing environment that would favor the partitioning of silicon or both silicon and sulfur into the metallic core during core-mantle differentiation. For a core composed of Fe-S-Si materials, the thermodynamic properties at elevated pressures and temperatures suggest that an FeS-rich layer could form at the top of the core and that a portion of it may be presently solid.

Radio tracking of the MESSENGER spacecraft has provided a model of Mercury's gravity field. In the northern hemisphere, several large gravity anomalies, including candidate mass concentrations (mascons), exceed 100 milli-Galileos (mgal). Mercury's northern hemisphere crust is thicker at low latitudes and thinner in the polar region and shows evidence for thinning beneath some impact basins. The low-degree gravity field, combined with planetary spin parameters, yields the moment of inertia C/MR(2) = 0.353 ± 0.017, where M and R are Mercury's mass and radius, and a ratio of the moment of inertia of Mercury's solid outer shell to that of the planet of C(m)/C = 0.452 ± 0.035. A model for Mercury's radial density distribution consistent with these results includes a solid silicate crust and mantle overlying a solid iron-sulfide layer and an iron-rich liquid outer core and perhaps a solid inner core.

The dissipation of tidal energy in Jupiter's satellite Io is likely to have melted a major fraction of the mass. Consequences of a largely molten interior may be evident in pictures of Io's surface returned by Voyager I.