Latitudinal librations of Mercury with a fluid core

In the framework of the space missions to Mercury, an accurate model of rotation is needed. Librations around the 3:2 spin-orbit resonance as well as latitudinal librations have to be predicted with the best possible accuracy. In this paper, we use a Hamiltonian analysis and numerical integrations to study the librations of Mercury, both in longitude and latitude. Due to the proximity of the period of the free libration in longitude to the orbital period of Jupiter, the 88-day and 11.86-year contributions dominate Mercury’s libration in longitude (with the Hermean parameters chosen). The amplitude of the libration in latitude is much smaller (under 1 arcsec) and should not be detected by the space missions. Nevertheless, we point out that this amplitude could be much larger (up to several tens of arcsec) if the free period related to the libration in latitude approaches the period of the Jupiter-Saturn Great Inequality (883 years). Given the large uncertainties on the planetary parameters, this new resonant forcing on Mercury’s libration in latitude should be borne in mind.     

The equatorial shape and gravity field of Mercury from MESSENGER flybys 1 and 2

On 14 January and 6 October 2008 the MESSENGER spacecraft passed within 200 km of the surface of Mercury. These flybys by MESSENGER provided the first observations of Mercury from a spacecraft since the Mariner 10 flybys in 1974 and 1975. Data from the Mercury Laser Altimeter (MLA) provided new information on the equatorial shape of Mercury, and Doppler tracking of the spacecraft through the flybys provided new data on the planet’s gravity field. The MLA passes were on opposite hemispheres of the planet and span collectively ∼40% of the equatorial circumference. The mean elevation of topography observed during flyby 1, in the longitude range 0-90°E, is greater than that seen during flyby 2 in the longitude range 180-270°E, indicating an offset between centers of mass and figure having a magnitude and phase in general agreement with topography determined by Earth-based radar. Both MLA profiles are characterized by slopes of ∼0.015° downward to the east, which is consistent with a long-wavelength equatorial shape defined by a best-fitting ellipse. The Doppler tracking data show sensitivity to the gravitational structure of Mercury. The equatorial ellipticity of the gravitational field, C_2,2, is well determined and correlates with the equatorial shape. The S_2,2 coefficient is ∼0, as would be expected if Mercury’s coordinate system, defined by its rotational state, is aligned along its principal axes of inertia. The recovered value of the polar flattening of the gravitational potential, J₂, is considerably lower in magnitude than the value obtained from Mariner 10 tracking, a result that is problematic for internal structure models. This parameter is not as well constrained as the equatorial ellipticity because the flyby trajectories were nearly in the planet’s equatorial plane. The residuals from the Doppler tracking data suggest the possibility of mascons on Mercury, but flyby observations are of insufficient resolution for confident recovery. For a range of assumptions on degree of compensation and crustal and mantle densities, the allowable crustal thickness is consistent with the upper limit of about 100 km estimated from the inferred depth of faulting beneath a prominent lobate scarp, an assumed ductile flow law for crustal material, and the condition that temperature at the base of the crust does not exceed the solidus temperature. The MESSENGER value of C_2,2 has allowed an improved estimate of the ratio of the polar moment of inertia of the mantle and crust to the full polar moment (C_m/C), a refinement that strengthens the conclusion that Mercury has at present a fluid outer core.     

Analytical model of the long-period forced longitude librations of Mercury

The shaking of Mercury’s orbit by the planets forces librations in longitude in addition to those at harmonics of the orbital period that have been used to detect Mercury’s molten core. We extend the analytical formulation of Peale et al. (Peale, S.J., Margot, J.L., Yseboodt, M. [2009]. Icarus 199, 1-8) in order to provide a convenient means of determining the amplitudes and phases of the forced librations without resorting to numerical calculations. We derive an explicit relation between the amplitude of each forced libration and the moment of inertia parameter (B-A)/C_m. Far from resonance with the free libration period, the libration amplitudes are directly proportional to (B-A)/C_m. Librations with periods close to the free libration period of ∼12 years may have measurable (∼arcsec) amplitudes. If the free libration period is sufficiently close to Jupiter’s orbital period of 11.86 years, the amplitude of the forced libration at Jupiter’s period could exceed the 35 arcsec amplitude of the 88-day forced libration. We also show that the planetary perturbations of the mean anomaly and the longitude of pericenter of Mercury’s orbit completely determine the libration amplitudes.While these signatures do not affect spin rate at a detectable level (as currently measured by Earth-based radar), they have a much larger impact on rotational phase (affecting imaging, altimetry, and gravity sensors). Therefore, it may be important to consider planetary perturbations when interpreting future spacecraft observations of the librations.     

Highly reducing conditions during core formation on Mercury: Implications for internal structure and the origin of a magnetic field

The high average density and low surface FeO content of the planet Mercury are shown to be consistent with very low oxygen fugacity during core segregation, in the range 3-6 log units below the iron-wüstite buffer. These low oxygen fugacities, and associated high metal content, are characteristic of high-iron enstatite (EH) and Bencubbinite (CB) chondrites, raising the possibility that such materials may have been important building blocks for this planet. With this idea in mind we have explored the internal structure of a Mercury sized planet of EH or CB bulk composition. Phase equilibria in the silicate mantle have been modeled using the thermodynamic calculator p-MELTS, and these simulations suggest that orthopyroxene will be the dominant mantle phase for both EH and CB compositions, with crystalline SiO₂ being an important minor phase at all pressures. Simulations for both compositions predict a plagioclase-bearing “crust” at low pressure, significant clinopyroxene also being calculated for the CB bulk composition. Concerning the core, comparison with recent high pressure and high temperature experiments relevant to the formation of enstatite meteorites, suggest that the core of Mercury may contain several wt.% silicon, in addition to sulfur. In light of the pressure of the core-mantle boundary on Mercury (∼7 GPa) and the pressure at which the immiscibility gap in the system Fe-S-Si closes (∼15 GPa) we suggest that Mercury’s core may have a complex shell structure comprising: (i) an outer layer of Fe-S liquid, poor in Si; (ii) a middle layer of Fe-Si liquid, poor in S; and (iii) an inner core of solid metal. The distribution of heat-producing elements between mantle and core, and within a layered core have been quantified. Available data for Th and K suggest that these elements will not enter the core in significant amounts. On the other hand, for the case of U both recently published metal/silicate partitioning data, as well as observations of U distribution in enstatite chondrites, suggest that this element behaves as a chalcophile element at low oxygen fugacity. Using these new data we predict that U will be concentrated in the outer layer of the mercurian core. Heat from the decay of U could thus act to maintain this part of Mercury’s core molten, potentially contributing to the origin of Mercury’s magnetic field. This result contrasts with the Earth where the radioactive decay of U represents a negligible contribution to core heating.     

The interior structure of Mercury and its core sulfur content

Depth-dependent interior structure models of Mercury are calculated for several plausible chemical compositions of the core and of the mantle. For those models, we compute the associated libration amplitude, obliquity, tidal deformation, and tidal changes in the external potential. In particular we study the relation between the interior structure parameters for five different mantle mineralogies and two different temperature profiles together with two extreme crust density values. We investigate the influence of the core light element concentration, temperature, and melting law on core state and inner and outer core size. We show that a sulfur concentration above 10 wt% is unlikely if the temperature at the core-mantle boundary is above 1850 K and the silicate shell at least 240 km thick. The interior models can only have an inner core if the sulfur weight fraction is below 5 wt% for core-mantle boundary temperature in the 1850-2200 K range. Within our modeling hypotheses, we show that with the expected precision on the moment of inertia the core size can be estimated to a precision of about 50 km and the core sulfur concentration with an error of about 2 wt%. This uncertainty can only be reduced when more information on the mantle mineralogy of Mercury becomes available. However, we show that the uncertainty on the core size estimation can be greatly reduced, to about 25 km, if tidal surface displacements and tidal variations in the external potential are considered.     

Mercury radar speckle dynamics

Current data reveal that Mercury is a dynamic system with a core which has not yet solidified completely and is at least partially decoupled from the mantle. Radar speckle displacement experiments have demonstrated that the accuracy in spin-dynamics determination for Earth-like planets can approach 10⁻⁵. The extended analysis of space-time correlation properties of radar echoes shows that the behavior of speckles does not prevent estimation of Mercury’s instantaneous spin-vector components to accuracy of a few parts in 10⁷. This limit can be reached with more powerful radar facilities and leads to constraining the interior in more detail from effects of spin dynamics, e.g., from observation of the core-mantle interplay through high precision monitoring of the 88-day spin-variation of Mercury’s crust.     

Orbital effects on Mercury’s escaping sodium exosphere

We present results from coronagraphic imaging of Mercury’s sodium tail over a 7° field of view. Several sets of observations made at the McDonald Observatory since May 2007 show a tail of neutral sodium atoms stretching more than 1000 Mercury radii (R_m) in length, or a full degree of sky. However, no tail was observed extending beyond 120 R_m during the January 2008 MESSENGER fly-by period, or during a similar orbital phase of Mercury in July 2008. Large changes in Mercury’s heliocentric radial velocity cause Doppler shifts about the Fraunhofer absorption features; the resultant change in solar flux and radiation pressure is the primary cause of the observed variation in tail brightness. Smaller fluctuations in brightness may exist due to changing source rates at the surface, but we have no explicit evidence for such changes in this data set. The effects of radiation pressure on Mercury’s escaping atmosphere are investigated using seven observations spanning different orbital phases. Total escape rates of atmospheric sodium are estimated to be between 5 and 13 × 10²³ atoms/s and show a correlation to radiation pressure. Candidate sources of Mercury’s sodium exosphere include desorption by UV sunlight, thermal desorption, solar wind channeled along Mercury’s magnetic field lines, and micro-meteor impacts. Wide-angle observations of the full extent of Mercury’s sodium tail offer opportunities to enhance our understanding of the time histories of these source rates.     

Librations of the Galilean satellites: The influence of global internal liquid layers

The four Galilean satellites are thought to harbor one or even two global internal liquid layers beneath their surface layer. The iron core of Io and Ganymede is most likely (partially) liquid and also the core of Europa may be liquid. Furthermore, there are strong indications for the existence of a subsurface ocean in Europa, Ganymede, and Callisto. Here, we investigate whether libration observations can be used to prove the existence of these liquid layers and to constrain the thickness of the overlying solid layers. For Io, the presence of a small liquid core increases the libration of the mantle by a few percent with respect to an entirely solid Io and mantle libration observations could be used to determine the mantle thickness with a precision of several tens of kilometers given that the libration amplitude can be measured with a precision of 1 m. For Europa, Ganymede, and Callisto, the presence of a water ocean close to the surface increases by at least an order of magnitude the ice shell libration amplitude with respect to an entirely solid satellite. The shell libration depends essentially on the shell thickness and to a minor extent on the density difference between the ocean and the ice shell. The possible presence of a liquid core inside Europa and Ganymede has no noticeable influence on their shell libration. For a precision of several meters on the libration measurements, in agreement with the expected accuracy with the NASA/ESA EJSM orbiter mission to Europa and Ganymede, an error on the shell thickness of a few tens kilometers is expected. Therefore, libration measurements can be used to detect liquid layers such as Io’s core or water subsurface oceans in Europa, Ganymede, and Callisto and to constrain the thickness of the overlying solid surface layers.     

Mercury surface composition: Integrating petrologic modeling and remote sensing data to place constraints on FeO abundance

A significant opaque component in Mercury’s crust is inferred based on albedo and spectral observations. Previous workers have favored iron-titanium bearing oxide minerals as the spectrally neutral opaque. A consequence of this hypothesis is that Mercury’s surface would have a high FeO content. An array of remote sensing techniques have not provided definitive constraints on the FeO content of Mercury’s surface. However, spectral observations have not detected a diagnostic 1 μm absorption band and have thus limited the FeO in coexisting silicates to <2 wt.% FeO. In this paper, we assess equilibrium among oxide and silicate minerals to constrain the distribution of iron between opaque oxides and silicates under a variety of environmental conditions. Equilibrium modeling is favored here because the geologic process that produced Mercury’s low-albedo intermediate terrain must have occurred globally, which favors a common widespread igneous process. Based on our modeling, we find that iron-rich ilmenite cannot occur with silicates that do not display a 1 μm absorption feature unless plagioclase abundances are high. However, such high plagioclase abundances are precluded by Mercury’s low albedo. Incorporating equilibrium crystallization modeling with spectral and albedo constraints we find the iron abundance of Mercury’s intermediate terrain is ?10 wt.% FeO. This intermediate iron composition matches constraints provided by visible albedo and total neutron absorption observed by MESSENGER. In fact, the total neutron absorption of mixtures of oxide, plagioclase, olivine and pyroxene for the oxide abundances estimated for Mercury, favor Mg-rich members of the ilmenite-geikielite solid-solution series. This work offers compositional constraints for Fe, Ti, and Mg that will be testable by various MESSENGER instrument data sets after it begins its orbital mission.     

Whole-disk spectrophotometric properties of Mercury: Synthesis of MESSENGER and ground-based observations

Disk-integrated and disk-resolved measurements of Mercury’s surface obtained by both the Mercury Dual Imaging System (MDIS) and the Mercury Atmospheric and Surface Composition Spectrometer (MASCS) onboard the MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) spacecraft were analyzed and compared with previous ground-based observations of Mercury at 11 wavelengths. The spectra show no definitive absorption features and display a red spectral slope (increasing reflectance with increasing wavelength) typical of space-weathered rocky surfaces. The MDIS spectra show evidence of phase reddening, which is not observed in the MASCS spectra. The MDIS spectra are commensurate with ground-based observations to within 10%, whereas the MASCS spectra display greater discrepancies with ground-based observations at near-infrared wavelengths. The derived photometric calibrations provide corrections within 10% for observations taken at phase angles less than ∼100°. The derived photometric properties are indicative of a more compact regolith than that of the lunar surface or of average S-type asteroids. The photometric roughness of the surface is also much smoother than the Moon’s. The calculated geometric albedo (reflectance at zero phase) is higher than lunar values. The lower reflectance of immature units on Mercury compared with immature units on the Moon, in conjunction with the higher geometric albedo, is indicative of more complicated grain structures within Mercury’s regolith.     

Effects of a physical librations of the moon caused by a liquid core,and determination of the fourth mode of a free libration

An analytical theory of lunar physical librations based on its two-layer model consisting of a non-spherical solid mantle and ellipsoidal liquid core is developed. The Moon moves on a high-precision orbit in the gravitational field of the Earth and other celestial bodies. The defined fourth mode of a free libration is caused by the influence of the liquid core, with a long period of 205.7 yr, with amplitude S = 0″0395 and with an initial phase Π₀ = ?134° (for the initial epoch 2000.0). Estimates of dynamic (meridional) oblatenesses of a liquid core of the Moon have been estimated: ?_D = 4.42 × 10^?4, μ_D = 2.83 × 10^?4 (?_D + μ_D = 7.24 × 10^?4). These results have been obtained as a result of comparison of the developed analytical theory of physical librations of the Moon with the empirical theory of librations of the Moon constructed on the basis of laser observations.     

A procedure for determining the nature of Mercury's core

Abstract— We review the assertion that the precise measurement of the second degree gravitational harmonic coefficients, the obliquity, and the amplitude of the physical libration in longitude, C₂₀, C₂₂, θ, and φ₀, for Mercury are sufficient to determine whether or not Mercury has a molten core (Peale, 1976). The conditions for detecting the signature of the molten core are that such a core not follow the 88‐day physical libration of the mantle induced by periodic solar torques, but that it does follow the 250 000‐year precession of the spin axis that tracks the orbit precession within a Cassini spin state. These conditions are easily satisfied if the coupling between the liquid core and solid mantle is viscous in nature. The alternative coupling mechanisms of pressure forces on irregularities in the core‐mantle boundary (CMB), gravitational torques between an axially asymmetric mantle and an assumed axially asymmetric solid inner core, and magnetic coupling between the conducting molten core and a conducting layer in the mantle at the CMB are shown for a reasonable range of assumptions not to frustrate the first condition while making the second condition more secure. Simulations have shown that the combination of spacecraft tracking and laser altimetry during the planned MESSENGER (MErcury Surface, Space ENvironment, GEochemistry, Ranging) orbiter mission to Mercury will determine C₂₀, C₂₂, and θ to better than 1% and φ₀ to better than 8%—sufficient precision to distinguish a molten core and constrain its size. The possible determination of the latter two parameters to 1% or less with Earth‐based radar experiments and MESSENGER determination of C₂₀ and C₂₂ to 0.1% would lead to a maximum uncertainty in the ratio of the moment of inertia of the mantle to that of the whole planet, C_m/C, of ?2% with comparable precision in characterizing the extent of the molten core.     

Long-period forcing of Mercury's libration in longitude

Planetary perturbations of Mercury's orbit lead to forced librations in longitude in addition to the 88-day forced libration induced by Mercury's orbital motion. The forced librations are a combination of many periods, but 5.93 and 5.66 years dominate. These two periods result from the perturbations by Jupiter and Venus respectively, and they lead to a 125-year modulation of the libration amplitude corresponding to the beat frequency. Other periods are also identified with Jupiter and Venus perturbations as well as with those of the Earth, and these and other periods in the perturbations cause several arc second fluctuations in the libration extremes. The maxima of these extremes are about 30″ above and the minima about 7″ above the superposed ∼^60″, 88-day libration during the 125-year modulation. Knowledge of the nature of the long-period forced librations is important for the interpretation of the details of Mercury's rotation state to be obtained from radar and spacecraft observations. We show that the measurement of the 88-day libration amplitude for the purposes of determining Mercury's core properties is not compromised by the additional librations, because of the latter's small amplitude and long period. If the free libration in longitude has an amplitude that is large compared with that of the forced libration, its ∼10-year period will dominate the libration spectrum with the 88-day forced libration and the long-period librations from the orbital perturbations superposed. If the free libration has an amplitude that is comparable to those of the long-period forced libration, it will be revealed by erratic amplitude, period and phase on the likely time span of a series of observations. However, a significant free libration component is not expected because of relatively rapid damping.     

The librations, shape, and icy shell of Europa

Europa, the smallest of the Galilean satellites, has a young icy surface and most likely contains an internal ocean. The primary objective of possible future missions to Europa is the unambiguous detection and characterization of a subsurface ocean. The thickness of the overlying icy shell provides important information on the thermal evolution of the satellite and on the interaction between the ocean and the surface, the latter being fundamental for astrobiology. However, the thickness is not well known, and estimates range from several hundred of meters to some ten of kilometers. Here, we investigate the use of libration (rotation variation) observations to study the interior structure of Europa and in particular its icy shell. A dynamical libration model is developed, which includes gravitational coupling between the icy shell and the heavy solid interior. The amplitude of the main libration signal at 3.55 days (the orbital period) is shown to depend on Europa's shape and structure. Models of the interior structure of Europa are constructed and the equatorial flattening of the internal layers, which are key parameters for the libration, are calculated by assuming that Europa is in hydrostatic equilibrium. Europa's flattened shape is assumed to be due to rotation and permanent tides, and we extend the classical Radau equation for rotationally flattened bodies to include also tidal deformation. We show that the presence of an ocean increases the amplitude of libration by about 10%, depending mainly on the thickness of the icy shell. Therefore, libration observations offer possibility of detection of a subsurface ocean in Europa and estimation of the thickness of its overlying icy shell.     

The free precession and libration of Mercury

An analysis based on the direct torque equations including tidal dissipation and a viscous core-mantle coupling is used to determine the damping time scales of O(¹⁰⁵) years for free precession of the spin about the Cassini state and free libration in longitude for Mercury. The core-mantle coupling dominates the damping over the tides by one to two orders of magnitude for the plausible parameters chosen. The short damping times compared with the age of the Solar System means we must find recent or on-going excitation mechanisms if such free motions are found by the current radar experiments or the future measurement by the MESSENGER and BepiColombo spacecraft that will orbit Mercury. We also show that the average precession rate is increased by about 30% over that obtained from the traditional precession constant because of a spin-orbit resonance induced contribution by the C₂₂ term in the expansion of the gravitational field. The C₂₂ contribution also causes the path of the spin during the precession to be slightly elliptical with a variation in the precession rate that is a maximum when the obliquity is a minimum. An observable free precession will compromise the determination of obliquity of the Cassini state and hence of C/MMR² for Mercury, but a detected free libration will not compromise the determination of the forced libration amplitude and thus the verification of a liquid core.     

Identification and measurement of neutron-absorbing elements on Mercury’s surface

MESSENGER Neutron Spectrometer (NS) observations of cosmic-ray-generated thermal neutrons provide the first direct measurements of Mercury’s surface elemental composition. Specifically, we show that Mercury’s surface is enriched in neutron-absorbing elements and has a measured macroscopic neutron-absorption cross section of 45-81 × 10⁻⁴ cm²/g, a range similar to the neutron absorption of lunar basalts from Mare Crisium. The expected neutron-absorbing elements are Fe and Ti, with possible trace amounts of Gd and Sm. Fe and Ti, in particular, are important for understanding Mercury’s formation and how its surface may have changed over time through magmatic processes. With neutron Doppler filtering - a neutron energy separation technique based on spacecraft velocity - we demonstrate that Mercury’s surface composition cannot be matched by prior models, which have characteristically low abundances of Fe, Ti, Gd, and Sm. While neutron spectroscopy alone cannot separate the relative contributions of individual neutron-absorbing elements, these results provide strong new constraints on the nature of Mercury’s surface materials. For example, if all the measured neutron absorption were due to the presence of an Fe-Ti oxide and that oxide were ilmenite, then Mercury’s surface would have an ilmenite content of 7-18 wt.%. This result is in general agreement with the inference from color imaging and visible-near-infrared spectroscopy that Mercury’s overall low reflectance is consistent with a surface composition that is enriched in Fe-Ti oxides. The incorporation of substantial Fe and Ti in oxides would imply that the oxygen fugacity of basalts on Mercury is at the upper range of oxygen fugacities inferred for basalts on the Moon.     

Constraints on Europa’s rotational dynamics from modeling of tidally-driven fractures

Cycloids, arcuate features observed on Europa’s surface, have been interpreted as tensile cracks that form in response to diurnal tidal stress caused by Europa’s orbital eccentricity. Stress from non-synchronous rotation may also contribute to tidal stress, and its influence on cycloid shapes has been investigated as well. Obliquity, fast precession, and physical libration would contribute to tidal stress but have often been neglected because they were expected to be negligibly small. However, more sophisticated analyses that include the influence of Jupiter’s other large satellites and the state of Europa’s interior indicate that perhaps these rotational parameters are large enough to alter the tidal stress field and the formation of tidally-driven fractures. We test tidal models that include obliquity, fast precession, stress due to non-synchronous rotation, and physical libration by comparing how well each model reproduces observed cycloids. To do this, we have designed and implemented an automated parameter-searching algorithm that relies on a quantitative measure of fit quality, which we use to identify the best fits to observed cycloids. We then apply statistical techniques to determine the tidal model best supported by the data. By incorporating obliquity, fits to observed southern hemisphere cycloids improve, and we can reproduce equatorial and equator-crossing cycloids. Furthermore, we find that obliquity plus physical libration is the tidal model best supported by the data. With this model, the obliquities range from 0.32° to 1.35°. The libration amplitudes are 0.72–2.44°, and the libration phases are −6.04° to 17.72° with one outlier at 84.5°. The variability in obliquity is expected if Europa’s ice shell is mechanically decoupled from the interior, and the libration amplitudes are plausible in the presence of a subsurface ocean. Indeed, the presence of a decoupling ocean may result in feedbacks that cause all of these rotational parameters to become time-variable.     

Mercury’s magnetospheric magnetic field after the first two MESSENGER flybys

The “paraboloid” model of Mercury’s magnetospheric magnetic field is used to determine the best-fit magnetospheric current system and internal dipole parameters from magnetic field measurements taken during the first and second MESSENGER flybys of Mercury on 14 January and 6 October 2008. Together with magnetic field measurements taken during the Mariner 10 flybys on 29 March 1974 and 16 March 1975, there exist three low-latitude traversals separated in longitude and one high-latitude encounter. From our model formulation and fitting procedure a Mercury dipole moment of 196 nT ·  (where R_M is Mercury’s radius) was determined. The dipole is offset from Mercury’s center by 405 km in the northward direction. The dipole inclination to Mercury’s rotation axis is relatively small, ∼4°, with an eastern longitude of 193° for the dipole northern pole. Our model is based on the a priori assumption that the dipole position and the moment orientation and strength do not change in time. The root mean square (rms) deviation between the Mariner 10 and MESSENGER magnetic field measurements and the predictions of our model for all four flybys is 10.7 nT. For each magnetic field component the rms residual is ∼6 nT or about 1.5% of the maximum measured magnetic field, ∼400 nT. This level of agreement is possible only because the magnetospheric current system parameters have been determined separately for each flyby. The magnetospheric stand-off distance, the distance from the planet’s center to the inner edge of the tail current sheet, the tail lobe magnetic flux, and the displacement of the tail current sheet relative to the Mercury solar-magnetospheric equatorial plane have been determined independently for each flyby. The magnetic flux in the tail lobes varied from 3.8 to 5.9 MWb; the subsolar magnetopause stand-off distance from 1.28 to 1.43 R_M; and the distance to the inner edge of the current sheet from 1.23 to 1.32 R_M. The differences in the current systems between the first and second MESSENGER flybys are attributed to the effects of strong magnetic reconnection driven by southward interplanetary magnetic field during the latter flyby.