On the figure of the planet Mercury

The figure of Mercury is estimated in terms of an isostatic form of equilibrium which tends to be controlled by the situation near perihelion passage at the 32 resonance spin rate. The ratios of the principal moments of inertia for Mercury are: (1)(C–A)/C7×10^–5; (2)(C–B)/C5×10^–5 and (3)(B–A)/C2×10^–5. The thermal effect on Mercury's figure during solidification forces Mercury's rotation to be trapped in the 32 resonance lock as its spin rate is being slowed by tidal effects. It is shown that the process of trapping of Mercury has been naturally affected by the instantaneous solidification of Mercury into a shape with two thermal bulges, and that the two permanent thermal bulges stabilize the planet's rotation.     

A note on the instantaneous rotational velocity of Mercury

The fluctuation in the angular velocity of the present rotation of Mercury is investigated. The instantaneous rotational rate in terms of orbital mean motion at different positions along Mercury's orbit is given. At aphelion the rotational velocity decreases substantially because the solar gravitational torque on the two thermal bulges on Mercury's surface tends to retard the rotation of Mercury before aphelion passage. It is found that the difference between the rotational periods derived from the motions at perihelion and aphelion is 4.68 min and that the maximum rate of rotation occurs atf=/4 andf=7/4, wheref is the true anomaly.     

Analysis of solar radiation pressure induced coupled liberations of a gravity stabilized axisymmetric satellite

A planar, fixed-orbit model of the rotation of the planet Mercury is analyzed. The model includes only the solar torques on the planet's permanent asymmetry and its solar tidal bulge. For this model, it is shown that the zero of the averaged tidal torque corresponds to an asymptotically stable periodic solution of the second kind which, for two tidal torque representations, is close to the asymptotically stable equilibrium point corresponding to an exact 32 spin-orbit resonance. A conjecture that the current rotation state of Mercury is due to transfer from capture by the zero of the averaged tidal torque to 32 resonance capture with changes in the eccentricity of the planet's orbit is discussed briefly.     

Physical Properties of the Hermean Surface (A Review)

Two new missions to Mercury are planned in the next few years (according to the NASA Messenger project in 2004 and the ESA BepiColomboproject in 2009). Many aspects of the study of Mercury concerning the origin of the planet, its interior structure, the formation and composition of the regolith, the surface cratering processes, the magnetosphere, the very tenuous atmosphere (exosphere) of Mercury, the orbital and rotational dynamics, and the thermal history of the planet's surface and interior are intensely developing at present. The presence of rocks on Mercury's surface, such as anorthosites (consisting mainly of calcium plagioclase) and feldspars, was reliably established in the course of such investigations. There are obvious signatures of old lava outflows and the heterogeneous composition of the crust depleted in FeO (less than 3%) and enriched with feldspar, with the possible presence of low-iron pyroxenes and alkali basalts. The sole spectral feature in the near infrared, observed at some longitudes, is a possible pyroxene absorption band at 0.95 m, which can be used to investigate the abundance and distribution of FeO in the regolith. Mercury represents a geologically intriguing planetary object. Its exosphere contains Na and K, the origin of which is undoubtedly related to the nature of Mercury's surface. The physical properties of Mercury's regolith, its structure, the grain sizes, the refractive index, and even the characteristic sizes of block material, lend themselves, in principle, to investigation by remote sensing methods. It is possible that deposits of buried water ice and/or elemental sulfur are present in the polar regions of the planet. The results of the study of the structure, physical properties, and composition of Mercury's regolith can be used to single out fundamental features in the origin of Mercury's surface. Thermal infrared spectra are also indicative of the presence of feldspars, pyroxenes, and igneous nepheline-bearing alkali syenites. The wavelengths of the thermal emissivity maxima indicate intermediate or slightly mafic rocks with a pronounced heterogeneous composition. The iron absorption bands give evidence for the presence of FeO in the Hermean crust and mantle. To some extent, the physical properties of the crustal layers may be associated with the odd magnetic field of the planet. The resulting Hermean magnetic field may be produced, at least partly, by randomly oriented paleomagnetic fields of individual large magnetized blocks of the planet's crust.     

Librations and obliquity of Mercury from the BepiColombo radio-science and camera experiments

A major goal of the BepiColombo mission to Mercury is the determination of the structure and state of Mercury's interior. Here the BepiColombo rotation experiment has been simulated in order to assess the ability to attain the mission goals and to help lay out a series of constraints on the experiment's possible progress. In the rotation experiment pairs of images of identical surface regions taken at different epochs are used to retrieve information on Mercury's rotation and orientation. The idea is that from observations of the same patch of Mercury's surface at two different solar longitudes of Mercury the orientation of Mercury can be determined, and therefore also the obliquity and rotation variations with respect to the uniform rotation.The estimation of the libration amplitude and obliquity through pattern matching of observed surface landmarks is challenging. The main problem arises from the difficulty to observe the same landmark on the planetary surface repeatedly over the MPO mission lifetime, due to the combination of Mercury's 3:2 spin-orbit resonance, the absence of a drift of the MPO polar orbital plane and the need to combine data from different instruments with their own measurement restrictions.By assuming that Mercury occupies a Cassini state and that the spacecraft operates nominally we show that under worst case assumptions the annual libration amplitude and obliquity can be measured with a precision of, respectively, 1.4 arcseconds (as) and 1.0 as over the nominal BepiColombo MPO lifetime with about 25 landmarks for rather stringent illumination restrictions. The outcome of the experiment cannot be easily improved by simply relaxing the observational constraints, or increasing the data volume.     

Possible dynamical evolution of the rotation of Venus since formation

The past evolution of the rotation of Venus has been studied by a numerical integration method using the hypothesis that only solar tidal torques and core-mantle coupling have been active since formation. It is found quite conceivable that Venus had originally a rotation similar to the other planets and has evolved in 4.5×10⁹ years from a rapid and direct rotation (12-hour spin period and nearly zero obliquity) to the present slow retrograde one.While the solid tidal torque may be quite efficient in despinning the planet, a thermally driven atmospheric tidal torque has the capability to drive the obliquity from 0° towards 180° and to stabilize the spin axis in the latter position. The effect of a liquid core is discussed and it is shown that core-mantle friction hastens the latter part of the evolution and makes even stronger the state of equilibrium at 180°. The model assumes a nearly stable balance between solid and atmospheric tides at the current rotation rate interpreting the present 243 day spin period as being very close to the limiting value.A large family of solutions allowing for the evolution, in a few billions years, of a rapid prograde rotation to the present state have been found. Noticeably different histories of evolution are observed when the initial conditions and the values of the physical parameters are slightly modified, but generally the principal trend is maintained.The proposed evolutionary explanation of the current rotation of Venus has led us to place constraints on the solid bodyQ and on the magnitude of the atmospheric tidal torque. While the constraints seem rather severe in the absence of core-mantle friction (aQ15 at the annual frequency is required, and a dominant diurnal thermal response in the atmosphere is needed), for a large range of values of the core's viscosity, the liquid core effect allows us to relax somewhat these constraints: a solid bodyQ of the order 40 can then be allowed. ThisQ value implies that a semi-diurnal ground pressure oscillation of 2 mb is needed in the atmosphere in order for a stable balance to occur between the solid and atmospheric tides at the current rotation rate. No model of atmospheric tides on Venus has been attempted in this study, however the value of 2 mb agrees well with that predicted by the model given in Dobrovolskis (1978).     

Estimating Mercury's 88-day libration amplitude from orbit

In this paper it is derived that the libration of Mercury can be described by where Φ₀ is the unknown libration amplitude, M is Mercury's mean anomaly and K=−9.483. Φ₀ can be determined by comparing pairs of images of the same landmarks taken by an orbiter at different positions of Mercury. If the angle between the orbit plane of a polar orbiter and Mercury's line of periapsis is between −60° and 60° and if one landmark at the equator is imaged per day with a relative precision of , then the libration amplitude can be determined in two Mercury years (176 days) with an accuracy of or better, which is sufficient to answer the question whether Mercury has a solid or fluid core.     

Determination of the properties of Mercury's magnetic field by the MESSENGER mission

The MESSENGER mission to Mercury, to be launched in 2004, will provide an opportunity to characterize Mercury's internal magnetic field during an orbital phase lasting one Earth year. To test the ability to determine the planetary dipole and higher-order moments from measurements by the spacecraft's fluxgate magnetometer, we simulate the observations along the spacecraft trajectory and recover the internal field characteristics from the simulated observations. The magnetic field inside Mercury's magnetosphere is assumed to consist of an intrinsic multipole component and an external contribution due to magnetospheric current systems described by a modified Tsyganenko 96 model. Under the axis-centered-dipole approximation without correction for the external field the moment strength is overestimated by ∼4% for a simulated dipole moment of , and the error depends strongly on the magnitude of the simulated moment, rising as the moment decreases. Correcting for the external field contributions can reduce the error in the dipole term to a lower limit of ∼1-2% without a solar wind monitor. Dipole and quadrupole terms, although highly correlated, are then distinguishable at the level equivalent to an error in the position of an offset dipole of a few tens of kilometers. Knowledge of the external magnetic field is therefore the primary limiting factor in extracting reliable knowledge of the structure of Mercury's magnetic field from the MESSENGER observations.     

New orbital elements for Moon and planets

The results of a simultaneous solution for the orbital elements of Moon and planets are given and their derivation is discussed. A modern Cowell integrator is used for orbit computations, and least-squares fits are made to some 40000 optical observations taken since 1913. The model includes relativistic terms, the leading zonal harmonics of Earth and Moon, the precession of the lunar equator, and the tidal couple between Earth and Moon. The tidal term in the Moon's mean longitude is found to be –19±4 per century squared. The solution also yields an extrapolation of the atomic time scale back to 1912.5. At that time, the difference between atomic and ephemeris time is about 6±2 s. Lunar declinations observed by the Washington transit circles, after receiving limb corrections and thus with respect to the center of Watts' reference sphere, are smaller than computed values by 0.33±0.01. It is found that solar oblateness cannot quite be determined with optical data covering about 50 yr, butJ ₂ is unlikely to be much larger than 10^–5. The advance of Mercury's perihelion is verified to within our resolution of 2 per century to match that predicted by Einstein.The solution presented here is believed to be the only simultaneous improvement of the orbits of Moon and planets. This simultaneity is found to be an essential feature in separating the Moon's mean motion, the lunar tidal deceleration, and the corrections to the Earth rotation rate. It is now possible to refer all astronomical events of the past 60 yr to a time with uniform rate, namely the atomic clock system. Considering the long baseline, this model should facilitate the prediction of fast variables, such as the lunar longitude, with considerably increased confidence. The planetary orbital elements compete with efforts of similar scope and accuracy at the Massachusetts Institute of Technology and the Jet Propulsion Laboratory.     

Mercury's sodium exosphere

Mercury's neutral sodium exosphere is simulated using a comprehensive 3D Monte Carlo model following sodium atoms ejected from Mercury's surface by thermal desorption, photon stimulated desorption, micro-meteoroid vaporization and solar wind sputtering. The evolution of the sodium surface density with respect to Mercury's rotation and its motion around the Sun is taken into account by considering enrichment processes due to surface trapping of neutrals and ions and depletion of the sodium available for ejection from the surfaces of grains. The change in the sodium exosphere is calculated during one Mercury year taking into account the variations in the solar radiation pressure, the photo-ionization frequency, the solar wind density, the photon and meteoroid flux intensities, and the surface temperature. Line-of-sight column densities at different phase angles, the supply rate of new sodium, average neutral and ion losses over a Mercury year, surface density distribution and the importance of the different processes of ejection are discussed in this paper. The sodium surface density distribution is found to become significantly nonuniform from day to night sides, from low to high latitudes and from morning to afternoon because of rapid depletion of sodium atoms in the surfaces of grains mainly driven by thermal depletion. The shape of the exosphere, as it would be seen from the Earth, changes drastically with respect to Mercury's heliocentric position. High latitude column density maxima are related to maxima in the sodium surface concentration at high latitudes in Mercury's surface and are not necessarily due to solar wind sputtering. The ratio between the sodium column density on the morning side of Mercury's exosphere and the sodium column density on the afternoon side is consistent with the conclusions of Sprague et al. (1997, Icarus 129, 506-527). The model, which has no fitting parameters, shows surprisingly good agreement with recent observations of Potter et al. (2002, Meteor. Planet. Sci. 8, 3357-3374) successfully explaining their velocity and column density profiles vs. heliocentric distance. Comparison with this data allows us to constrain the supply rate of new sodium atoms to the surface. We also discuss the possible origins of the strong high latitude emissions (Potter and Morgan, 1990, Science 248, 835-838; 1997a, Adv. Space Res. 19, 1571-1576; 1997b, Planet. Space Sci. 45, 95-100; Sprague et al., 1998, Icarus 135, 60-68) and the strong variations of the total content of the sodium exosphere on short (Potter et al., 1999, Planet. Space Sci. 47, 1441-1449) and long time scales (Sprague et al., 1997, Icarus 129, 506-527).     

On the oscillations in Mercury's obliquity

Mercury's capture into the 3:2 spin–orbit resonance can be explained as a result of its chaotic orbital dynamics. One major objective of MESSENGER and BepiColombo spatial missions is to accurately measure Mercury's rotation and its obliquity in order to obtain constraints on internal structure of the planet. Analytical approaches at the first-order level using the Cassini state assumptions give the obliquity constant or quasi-constant. Which is the obliquity's dynamical behavior deriving from a complete spin–orbit motion of Mercury simultaneously integrated with planetary interactions? We have used our SONYR model (acronym of Spin–Orbit N-bodY Relativistic model) integrating the spin–orbit N-body problem applied to the Solar System (Sun and planets). For lack of current accurate observations or ephemerides of Mercury's rotation, and therefore for lack of valid initial conditions for a numerical integration, we have built an original method for finding the libration center of the spin–orbit system and, as a consequence, for avoiding arbitrary amplitudes in librations of the spin–orbit motion as well as in Mercury's obliquity. The method has been carried out in two cases: (1) the spin–orbit motion of Mercury in the 2-body problem case (Sun–Mercury) where an uniform precession of the Keplerian orbital plane is kinematically added at a fixed inclination (S_2K case), (2) the spin–orbit motion of Mercury in the N-body problem case (Sun and planets) (S_n case). We find that the remaining amplitude of the oscillations in the S_n case is one order of magnitude larger than in the S_2K case, namely 4 versus 0.4 arcseconds (peak-to-peak). The mean obliquity is also larger, namely 1.98 versus 1.80 arcminutes, for a difference of 10.8 arcseconds. These theoretical results are in a good agreement with recent radar observations but it is not excluded that it should be possible to push farther the convergence process by drawing nearer still more precisely to the libration center. We note that the dynamically driven spin precession, which occurs when the planetary interactions are included, is more complex than the purely kinematic case. Nevertheless, in such a N-body problem, we find that the 3:2 spin–orbit resonance is really combined to a synchronism where the spin and orbit poles on average precess at the same rate while the orbit inclination and the spin axis orientation on average decrease at the same rate. As a consequence and whether it would turn out that there exists an irreducible minimum of the oscillation amplitude, quasi-periodic oscillations found in Mercury's obliquity should be to geometrically understood as librations related to these synchronisms that both follow a Cassini state. Whatever the open question on the minimal amplitude in the obliquity's oscillations and in spite of the planetary interactions indirectly acting by the solar torque on Mercury's rotation, Mercury remains therefore in a stable equilibrium state that proceeds from a 2-body Cassini state.     

Simultaneous determination of global topography, tidal Love number and libration amplitude of Mercury by laser altimetry

Solar tidal forces generate elevation changes of Mercury's surface of the order 1 m within one Hermean year, and solar torques on the non-symmetric permanent mass distribution of the planet cause an uneven rotation of Mercury's surface with a libration amplitude of the order of 40 arcsec. Knowledge of the precise reaction of the planet to tidal forcing, expressed by the Love numbers h₂ and k₂, as well as accurate knowledge of the amplitude of forced libration Φ_lib, puts constraints on the internal structure, for example the state and the size of the core. The MESSENGER and BepiColombo missions to Mercury carry laser altimeters, whose primary goal is to accurately map the topography. Here we investigate if the Love number h₂ and the amplitude of forced libration can be determined together with the static topography of the planet from a global altimetry record. We do this by creating synthetic altimeter data for the nominal orbit of BepiColombo over the nominal mission duration of approximately four Mercury years and inverting them for the static and time-dependent parts of the topography. We assume purely Gaussian noise. We find that it is possible to extract both parameters h₂ and Φ_lib with an accuracy of approximately 10%, while the static topography coefficients of a spherical harmonic expansion can be determined simultaneously with an accuracy at the centimetre level. Extraction of the static topography to higher harmonic degrees improves the precision of the measurement of h₂ and Φ_lib. The simulation results demonstrate that it seems feasible to test current models on Mercury's interior with sufficient precision using BepiColombo Laser Altimeter data.     

The interplanetary magnetic field environment at Mercury's orbit

Mercury is exposed to the most dynamic heliospheric space environment of any planet in the solar system. The magnetosphere is particularly sensitive to variations in the interplanetary magnetic field (IMF), which control the intensity and geometry of the magnetospheric current systems that are the dominant source of uncertainty in determinations of the internal planetary magnetic field structure. The Magnetometer on the MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) spacecraft has made extensive magnetic field observations in the inner heliosphere over the heliocentric distances of Mercury's orbit, between 0.31 and 0.47 AU. In this paper, Magnetometer data from MESSENGER, obtained at rates of 2 and 20 vector samples per second, are used together with previous observations in the inner heliosphere by Helios and at Earth by the Advanced Composition Explorer, to study the characteristics of IMF variability at Mercury's orbit. Although the average IMF geometry and magnitude depend on heliocentric distance as predicted by Parker, the variability is large, comparable to the total field magnitude. Using models for the external current systems we evaluate the impact of the variability on the field near the planet and find that the large IMF fluctuations should produce variations of the magnetospheric field of up to 30% of the dipole field at 200 km altitude, corresponding to the planned periapsis of MESSENGER's orbit at Mercury. The IMF fluctuations in the frequency range are consistent with turbulence, whereas evidence for dissipation was observed for . The transition between the turbulent and dissipative regimes is indicated by a break in the power spectrum, and the frequency of this break point is proportional to the IMF magnitude.     

On the rotation of rigid Venus

According to A.A. Khentov Venus' rotation is in the quasi-stationary state as a result of the balance interaction of the solar tidal torque with the aerodynamical torque of the rotating Venus' atmosphere. In case of the nonconservative forces are negligible and the solar attraction is the stabilizing factor, the rotation of the rigid Venus may be assumed as the first approximation. The theory of the rotation of the rigid Venus in the coordinates,, had been constructed. It have been found that Venus rotates almost uniformly and the libration harmonics are negligible.     

On the variations in the insolation at Mercury resulting from oscillations of the orbital eccentricity

This paper describes variations in the insolation on Mercury resulting from fluctuations of the orbital eccentricity (0.11≤e≤0.24) of the planet. Equations for the instantaneous and the daily insolation are briefly discussed and several numerical examples are given illustrating the sensitivity of the solar radiation to changes ine. Special attention is paid to the behavior of the solar radiation distribution curves near sunrise and sunset which at the warm pole of Mercury (longitudes ±90°) occur as the planet goes through perihelion. It has been found that for eccentricities larger than about 0.194 there exists two permanent thermal bulges on opposite sides of the Mercurian surface that alternately point to the Sun at every perihelion passage. The critical value ofe past which the Sun shortly sets after perihelion is near 0.213.     

Properties of the Hermean Regolith: II. Disk-Resolved Multicolor Photometry and Color Variations of the “Unknown” Hemisphere

Multicolor photometric observations of the “unknown” hemisphere of Mercury have been performed with the Swedish Vacuum Solar Telescope on La Palma at maximal elongations from the Sun in 1997 and 1998. A set of six interference filters with central wavelengths from 450 to 940 nm were used. Multicolor photometry of Mercury was performed on disk-resolved images of the unknown hemisphere (longitudes 160°-340°) with a highest resolution of ∼200 km (J. Warell and S. Limaye 2001, Planet. Space Sci.49, 1531-1552).Disk-integrated spectrophotometry shows that (1) the spectrum of Mercury displays a linear slope from 650 to 940 nm, indicating that the average mercurian regolith is considerably more mature than relatively immature pure anorthosite regions on the Moon; (2) there is negative evidence for the presence of the putative 1-μm absorption feature near 940 nm due to the presence of ferrous iron (Fe²⁺) in pyroxenes; and (3) no effect of phase reddening of the integrated disk is observed between phase angles of 63° and 84°.For the first time, disk-resolved spectrophotometry of Mercury's surface has been obtained, from which it is inferred that (4) the scattering properties of Mercury's regolith are more homogeneous than for the Moon and that there is no clear relation between reflectance and chemical properties at spatial scales of ∼300 km on the unknown hemisphere and (5) there exists an inverse relation of spectral slope with emission angle which is larger for Mercury than for the Moon, indicating that the average mercurian regolith is more backscattering and that this effect increases with wavelength.Finally, from filter ratio images of Mercury's disk it is found that (6) no color variations larger that 2% with respect to the surroundings are detected at a spatial resolution of ∼300 km.     

Mercury's integral phase curve: Phase reddening and wavelength dependence of photometric quantities

We present results of a five-filter photometric study of Mercury's integral phase curve in the Johnson-Cousins UBVRI system, performed with the 0.90-m Westerlund Telescope in Uppsala, Sweden. CCD observations were made of the integrated disk for the phase angle range 22-152°, and the study is the first to cover the extended visible spectrum of Mercury. The observations are analyzed with Hapke's semi-empirical radiative transfer-based light-scattering model and photometric quantities are derived. A statistically significant phase reddening effect of is determined for Mercury based on color index observations, which is similar to that of the Moon. Phase coefficients fit to integral absolute magnitude data and Hapke models in combination with color index data provide a phase reddening effect of which does however not provide statistically significant evidence for its presence. Phase coefficients indicate that phase reddening may be decreasing in magnitude with wavelength. As for the case with the Moon, the value of the phase integral increases with wavelength, but at an eight times higher rate. This value is consistent with the difference in the rate of change in the spectral slope-emission angle relation for the two bodies. We attribute these differences with Mercury's redder spectral slope and an increase with wavelength of the backscattering lobe amplitude in the double Henyey-Greenstein particle phase function formulation. The normal albedo of integral Mercury at 1064 nm, pertinent to the return pulse energy of the BepiColombo laser altimeter (BELA), is estimated to 0.23±0.06 with a range of 0.13-0.33 for 99% of the surface.     

The dynamical flattenings of Mercury and Venus

The method which is used to calculate the dynamical flattenings % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% Gaamisaiabg2da9iaacIcacaWGdbGaeyOeI0YaaSaaaeaacaaIXaaa% baGaaGOmaaaacaGGOaGaamyqaiabgUcaRiaadkeacaGGPaGaaiykai% aac+cacaWGdbaaaa!4717!\[H = (C - \frac{1}{2}(A + B))/C\] of the Earth and Moon meets with difficulties when it applies to Mercury and Venus. In this paper, after the calculation of the dimensionless moment of inertiaC/MR ² by solving the Emden equation, the effectiveness of the method deriving dynamical flattening from the observed value of the Mercury's obliquity is analysed based on the resonance rotation theory. Some suggestions are made for the future space explorations. Finally, the ranges of dynamical flattening and of the obliquity of Venus are calculated.     

Consequences of the tidal slowing of Mercury

Mercury, currently rotating very slowly, probably rotated faster in the past. If Mercury's rotation period had been near 8 hours initially, similar to that of most solar system bodies today, it would have been flattened by a few percent. As Mercury was slowed by solar tides, craters which were circular when they were emplaced would have been distorted by the same few percent. Substantial surface stresses, well above the fracture stress, would have been produced unless stress relief occurred; these stresses should have produced tensional fractures near the poles and two intersecting sets of shear planes in equatorial regions. Satellite orbits about the slowly spinning Mercury have been shown to collapse onto its surface: the impact craters resulting from these hypothetical lost satellites should be elongated along the orbit paths, which probably lie near the equator. However, none of these features has been found on the Mariner 10 images. They may be obscured by the effects of tidal heating that should cause an overall internal temperature increase of about 100°K although the increase would be substantially more in certain regions. Radial tides, sometimes called push-pull tides, are important at the present time because Mercury's large orbital eccentricity causes the planet to undergo significant tidal flexing each orbital period; the contemporary tidal heating due to this mechanism is estimated at more than 10¹⁶ erg/sec.     

The 0.7-5.3 μm IR spectra of Mercury and the Moon: Evidence for high-Ca clinopyroxene on Mercury

We present infrared spectra of Mercury and the Moon in the wavelength range 0.7-5.3 μm obtained with the SpeX spectrograph at the NASA Infrared Telescope Facility. The spectra were acquired from pole and terminator locations of Mercury's surface and of Mersenius C and the Copernicus central peak on the Moon. Spectra of both bodies were measured in close temporal succession and were reduced in the same manner with identical calibration stars to minimize differences in the reduction process. The Copernicus spectra display the expected absorption features due to mafic minerals in the near infrared and show spectral features in the SiO combination/overtone vibrational band region above 4 μm. The spectra of Mercury from longitude 170° and north and south mid-latitudes display a 1-μm absorption band indicative of high-Ca clinopyroxene, while a spectrum from longitude 260° and northern mid-latitudes does not. The Mercury spectra show a broad feature of low emittance over the full 3-5 μm thermal infrared region, but no narrow features in this spectral range. The longitude 260° spectrum shows excess thermal emission around 5 μm attributable to the existence of a thermal gradient in the insolated dayside regolith. The thermal-IR spectra suggest a significant difference in the compositional and/or structural properties of Mercury and the Moon that may be due to grain size, absorption coefficient, or the magnitude of near-surface thermal gradients. The results indicate that the composition of Mercury's surface is heterogeneous on regional scales, and that the near infrared wavelength range provides more discriminative information on the surface composition than the 2-4 μm region, where the solar reflected and thermally emitted radiation contribute approximately equally to the observed flux of these bodies.