A pre-Caloris synchronous rotation for Mercury

The planet Mercury is locked in a spin-orbit resonance where it rotates three times about its spin axis for every two orbits about the Sun. The current explanation for this unique state assumes that the initial rotation of this planet was prograde and rapid, and that tidal torques decelerated the planetary spin to this resonance. When core-mantle boundary friction is accounted for, capture into the 3/2 resonance occurs with a 26% probability, but the most probable outcome is capture into one of the higher-order resonances. Here we show that if the initial rotation of Mercury were retrograde, this planet would be captured into synchronous rotation with a 68% probability. Strong spatial variations of the impact cratering rate would have existed at this time, and these are shown to be consistent with the distribution of pre-Calorian impact basins observed by Mariner 10 and MESSENGER. Escape from this highly stable resonance is made possible by the momentum imparted by large basin-forming impact events, and capture into the 3/2 resonance occurs subsequently under favourable conditions.Comment: Nature Geosci., 201

A seven-planet resonant chain in TRAPPIST-1

The TRAPPIST-1 system is the first transiting planet system found orbiting an ultra-cool dwarf star1. At least seven planets similar to Earth in radius were previously found to transit this host star2. Subsequently, TRAPPIST-1 was observed as part of the K2 mission and, with these new data, we report the measurement of an 18.77 d orbital period for the outermost transiting planet, TRAPPIST-1h, which was unconstrained until now. This value matches our theoretical expectations based on Laplace relations3 and places TRAPPIST-1h as the seventh member of a complex chain, with three-body resonances linking every member. We find that TRAPPIST-1h has a radius of 0.727 R⊕ and an equilibrium temperature of 169 K. We have also measured the rotational period of the star at 3.3 d and detected a number of flares consistent with a low-activity, middle-aged, late M dwarf

Dynamics and origin of the 2:1 orbital resonances of the GJ 876 planets

The discovery by Marcy and coworkers 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, 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,θ1 = λ1 - 2λ2 + ω̄1, θ2 = λ1 - 2λ2 + ω̄2, and θ3 = ω̄1- ω̄2 about 0° (where λ1,2 are the mean longitudes of the inner and outer planet and ω̄1,2 are the longitudes of periapse) differs from the familiar geometry of the Io-Europa pair, where θ2 and θ3 librate about 180°. By considering the condition that ω̄1 = ω̄2 for stable simultaneous librations of θ1 and θ2, we show that the GJ 876 geometry results from the large orbital eccentricities ei, whereas the very small eccentricities in the Io-Europa system lead to the latter's geometry. Surprisingly, the GJ 876 configuration, with θ 1, θ2, and θ3 all librating, remains stable for e1 up to 0.86 and for amplitude of libration of θ1 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 e1 ≲ 0.06 and e2 ≲ 0.03 and the migration rate | ȧ 2/a2 ≲ 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 timescale, whose inverse is about 3 orders of magnitude less than the above upper bound on | ȧ2/a 2 | for certain capture. If there is no eccentricity damping, eccentricity growth is rapid with continued migration within the resonance, with ei exceeding the observed values after a further reduction in the semimajor axes ai of only 7%. With eccentricity damping ėi/ei= - K | ȧi/ai, 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 the magnitude or functional form of the migration rate ȧi, as long as ė i/ei = - K | ȧi/ai . Although existing analytic estimates of the effects of planet-nebula interaction are consistent with this form of eccentricity damping for certain disk parameter values, it is as yet unclear that such interaction can produce the large value of K required to obtain the observed eccentricities. The alternative eccentricity damping by tidal dissipation within the star or the planets is completely negligible, so the observed dynamical properties of the GJ 876 system may require an unlikely fine-tuning of the time of resonance capture to be near the end of the nebula lifetime.link_to_subscribed_fulltex

Erratum: Secular evolution of hierarchical planetary systems (The Astrophysical Journal (2003) 592 (1201))

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Consequences of a solid inner core on Mercury's spin configuration

The pressure torque by a liquid core that drove Mercury to the nominal Cassini state of rotation is dominated by the torque from the solid inner core. The gravitational torque exerted on Mercury's mantle from an asymmetric solid inner core increases the equilibrium obliquity of the mantle spin axis. Since the observed obliquity of the mantle must be compatible with the presence of a solid inner core, the moment of inertia inferred from the occupancy of the Cassini state must be reduced to compensate the torque from the inner core and bring Mercury's spin axis to the observed position. The unknown size and shape of the inner core means that the moment of inertia is more uncertain than previously inferred