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 mi Hi-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 CIMR² = 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 CJC = 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 curious case of Mercury's internal structure Hauck II, Steven A.; Margot, Jean-Luc; Solomon, Sean C. ...
Journal of geophysical research. Planets,
06/2013, Volume:
118, Issue:
6
Journal Article
Peer reviewed
Open access
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 ± 30 km, the mean density above this boundary is 3380 ± 200 kg m−3, and the density below the boundary is 6980 ± 280 kg m−3. 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.
Key PointsNew MESSENGER and Earth‐based radar data provide Mercury's moments of inertiaMercury's core‐mantle boundary is 420 +/‐ 30 km below the planet's surfaceThe core may be compositionally segregated
Tidal Evolution of Close-in Planets Matsumura, Soko; Peale, Stanton J; Rasio, Frederic A
Astrophysical journal/The Astrophysical journal,
12/2010, Volume:
725, Issue:
2
Journal Article
Peer reviewed
Open access
Recent discoveries of several transiting planets with clearly non-zero eccentricities and some large obliquities started changing the simple picture of close-in planets having circular and ...well-aligned orbits. The two major scenarios that form such close-in planets are planet migration in a disk and planet-planet interactions combined with tidal dissipation. The former scenario can naturally produce a circular and low-obliquity orbit, while the latter implicitly assumes an initially highly eccentric and possibly high-obliquity orbit, which are then circularized and aligned via tidal dissipation. Most of these close-in planets experience orbital decay all the way to the Roche limit as previous studies showed. We investigate the tidal evolution of transiting planets on eccentric orbits, and find that there are two characteristic evolution paths for them, depending on the relative efficiency of tidal dissipation inside the star and the planet. Our study shows that each of these paths may correspond to migration and scattering scenarios. We further point out that the current observations may be consistent with the scattering scenario, where the circularization of an initially eccentric orbit occurs before the orbital decay primarily due to tidal dissipation in the planet, while the alignment of the stellar spin and orbit normal occurs on a similar timescale to the orbital decay largely due to dissipation in the star. We also find that even when the stellar spin-orbit misalignment is observed to be small at present, some systems could have had a highly misaligned orbit in the past, if their evolution is dominated by tidal dissipation in the star. Finally, we also re-examine the recent claim by Levrard et al. that all orbital and spin parameters, including eccentricity and stellar obliquity, evolve on a similar timescale to orbital decay. This counterintuitive result turns out to have been caused by a typo in their numerical code. Solving the correct set of tidal equations, we find that the eccentricity behaves as expected, with orbits usually circularizing rapidly compared to the orbital decay rate.
Laser altimetry by the MESSENGER spacecraft has yielded a topographic model of the northern hemisphere of Mercury. The dynamic range of elevations is considerably smaller than those of Mars or the ...Moon. The most prominent feature is an extensive lowland at high northern latitudes that hosts the volcanic northern plains. Within this lowland is a broad topographic rise that experienced uplift after plains emplacement. The interior of the 1500-km-diameter Caloris impact basin has been modified so that part of the basin floor now stands higher than the rim. The elevated portion of the floor of Caloris appears to be part of a quasi-linear rise that extends for approximately half the planetary circumference at mid-latitudes. Collectively, these features imply that long-wavelength changes to Mercury's topography occurred after the earliest phases of the planet's geological history.
Earth‐based radar observations of the spin state of Mercury at 35 epochs between 2002 and 2012 reveal that its spin axis is tilted by (2.04 ± 0.08) arc min with respect to the orbit normal. The ...direction of the tilt suggests that Mercury is in or near a Cassini state. Observed rotation rate variations clearly exhibit an 88‐day libration pattern which is due to solar gravitational torques acting on the asymmetrically shaped planet. The amplitude of the forced libration, (38.5 ± 1.6) arc sec, corresponds to a longitudinal displacement of ∼450 m at the equator. Combining these measurements of the spin properties with second‐degree gravitational harmonics (Smith et al., 2012) provides an estimate of the polar moment of inertia of MercuryC/MR2 = 0.346 ± 0.014, where M and R are Mercury's mass and radius. The fraction of the moment that corresponds to the outer librating shell, which can be used to estimate the size of the core, is Cm/C = 0.431 ± 0.025.
Key Points
Mercury's obliquity is (2.04 +/‐ 0.08) arcminutes
Mercury exhibits a longitude libration of amplitude (37.8 +/‐ 1.4) arcseconds
Mercury's moment of inertia is 0.346 +/‐ 0.014
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.
We have coregistered laser altimeter profiles from 3 years of MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) orbital observations with stereo digital terrain models to ...infer the rotation parameters for the planet Mercury. In particular, we provide the first observations of Mercury's librations from orbit. We have also confirmed available estimates for the orientation of the spin axis and the mean rotation rate of the planet. We find a large libration amplitude of 38.9 ± 1.3 arc sec and an obliquity of the spin axis of 2.029 ± 0.085 arc min, results confirming that Mercury possesses a liquid outer core. The mean rotation rate is observed to be (6.13851804 ± 9.4 × 10−7)°/d (a spin period of 58.6460768 days ± 0.78 s), significantly higher than the expected resonant rotation rate. As a possible explanation we suggest that Mercury is undergoing long‐period librational motion, related to planetary perturbations of its orbit.
Key Points
The libration amplitude, rotation rate, and pole orientation of Mercury have been measured
The non‐resonant rotation rate is interpreted in terms of a long‐period libration
Implications for Mercury's moment of inertia and interior structure are discussed
The low-degree shape of Mercury Perry, Mark E.; Neumann, Gregory A.; Phillips, Roger J. ...
Geophysical research letters,
16 September 2015, Volume:
42, Issue:
17
Journal Article
Peer reviewed
Open access
The shape of Mercury, particularly when combined with its geoid, provides clues to the planet's internal structure, thermal evolution, and rotational history. Elevation measurements of the northern ...hemisphere acquired by the Mercury Laser Altimeter on the MErcury Surface, Space ENvironment, GEochemistry, and Ranging spacecraft, combined with 378 occultations of radio signals from the spacecraft in the planet's southern hemisphere, reveal the low‐degree shape of Mercury. Mercury's mean radius is 2439.36 ± 0.02 km, and there is a 0.14 km offset between the planet's centers of mass and figure. Mercury is oblate, with a polar radius 1.65 km less than the mean equatorial radius. The difference between the semimajor and semiminor equatorial axes is 1.25 km, with the long axis oriented 15° west of Mercury's dynamically defined principal axis. Mercury's geoid is also oblate and elongated, but it deviates from a sphere by a factor of 10 less than Mercury's shape, implying compensation of elevation variations on a global scale.
Key Points
Mercury's shape and geoid are highly correlated and show mass compensation on a global scale
Mercury is not in hydrostatic equilibrium and has an excess of spectral power density in degree 2
Mercury's average radius is 2439.4 km; the offset between the centers of mass and figure is 0.14 km
•Rotation and orientation of Mercury’s mantle and core are evolved in the orbit frame.•Torques on mantle and core include gravitational, tidal, and core–mantle interaction.•The latter include ...viscous, magnetic, topographic and pressure torques.•The dissipative core–mantle torques cause mantle spin to deviate from the Cassini state.•Pressure torque causes dissipation to drive the mantle spin firmly to Cassini state.
The rotational evolution of Mercury’s mantle plus crust and its core under conservative and dissipative torques is important for understanding the planet’s spin state. Dissipation results from tidal torques and viscous, magnetic, and topographic torques contributed by interactions between the liquid core and solid mantle. For a spherically symmetric core–mantle boundary (CMB), the system goes to an equilibrium state wherein the spin axes of the mantle and core are fixed in the frame precessing with the orbit, and in which the mantle and core are differentially rotating. This equilibrium exhibits a mantle spin axis that is offset from the Cassini state by larger amounts for weaker core–mantle coupling for all three dissipative core–mantle coupling mechanisms, and the spin axis of the core is separated farther from that of the mantle, leading to larger differential rotation. Relatively strong core–mantle coupling is necessary to bring the mantle spin axis to a position within the uncertainty in its observed position, which is close to the Cassini state defined for a completely solid Mercury. Strong core–mantle coupling means that Mercury’s response is closer to that of a solid planet. Measured or inferred values of parameters in all three core–mantle coupling mechanisms for a spherically symmetric CMB appear not to accomplish this requirement. For a hydrostatic ellipsoidal CMB, pressure coupling dominates the dissipative effects on the mantle and core positions, and dissipation with pressure coupling brings the mantle spin solidly to the Cassini state. The core spin goes to a position displaced from that of the mantle by about 3.55arcmin nearly in the plane containing the Cassini state. The core spin lags the precessing plane containing the Cassini state by an increasing angle as the core viscosity is increased. With the maximum viscosity considered of ν∼15.0cm2/s if the coupling is by the circulation through an Ekman boundary layer or ν∼8.75×105cm2/s for purely viscous coupling, the core spin lags the precessing Cassini plane by 23arcsec, whereas the mantle spin lags by only 0.055arcsec. Larger, non-hydrostatic values of the CMB ellipticity also result in the mantle spin at the Cassini state, but the core spin is moved closer to the mantle spin. Current measurement uncertainties preclude using the mantle offset to constrain the internal core viscosity.
•We investigate the tidal evolution of Pluto–Charon from an initially eccentric orbit under two different tidal models.•The ratio of dissipation in Charon to that in Pluto controls the behavior of ...the orbital eccentricity.•A judicious choice of this ratio leads to a nearly constant eccentricity throughout most of the tidal evolution.•Charon on an initially eccentric orbit does not achieve synchronous rotation quickly after its formation.•The capture into spin–orbit resonances due to non-zero C22 can profoundly affect the tidal evolution of the system.
Both Pluto and its satellite Charon have rotation rates synchronous with their orbital mean motion. This is the theoretical end point of tidal evolution where transfer of angular momentum has ceased. Here we follow Pluto’s tidal evolution from an initial state having the current total angular momentum of the system but with Charon in an eccentric orbit with semimajor axis a≈4RP (where RP is the radius of Pluto), consistent with its impact origin. Two tidal models are used, where the tidal dissipation function Q∝1/frequency and Q=constant, where details of the evolution are strongly model dependent. The inclusion of the gravitational harmonic coefficient C22 of both bodies in the analysis allows smooth, self consistent evolution to the dual synchronous state, whereas its omission frustrates successful evolution in some cases. The zonal harmonic J2 can also be included, but does not cause a significant effect on the overall evolution. The ratio of dissipation in Charon to that in Pluto controls the behavior of the orbital eccentricity, where a judicious choice leads to a nearly constant eccentricity until the final approach to dual synchronous rotation. The tidal models are complete in the sense that every nuance of tidal evolution is realized while conserving total angular momentum—including temporary capture into spin–orbit resonances as Charon’s spin decreases and damped librations about the same.
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