A lunar core and the moon's magnetic field

The suggestion that the Moon's magnetic field is due to adiabatic magnetohydrodynamic convection of a molten core has been made by a number of recent authors. Considerations based on petrology, mass and rotational inertia limit the size of this hypothetical core to a few 100 km at the most. A proposal has been made that this core is either molten iron or iron sulfide. Fortunately, we know the properties of both molten iron and iron-sulfide at lunar core pressures. We can find no way of maintaining circulation in a hypothetical lunar core, as circulation is contingent upon a temperature gradient being greater than the adiabatic gradient, or an internal heat source.     

Size and compositional constraints of Ganymede's metallic core for driving an active dynamo

Ganymede has an intrinsic magnetic field which is generally considered to originate from a self-excited dynamo in the metallic core. Driving of the dynamo depends critically on the satellite's thermal state and internal structure. However, the inferred structure based on gravity data alone has a large uncertainty, and this makes the possibility of dynamo activity unclear; variations in core size and composition significantly change the heat capacity and alter the cooling history of the core. The main objectives of this study is to explore the structural conditions for a currently active dynamo in Ganymede using numerical simulations of the thermal history, and to evaluate under which conditions Ganymede can maintain the dynamo activity at present. We have investigated the satellite's thermal history using various core sizes and compositions satisfying the mean density and moment of inertia of Ganymede, and evaluate the temperature and heat flux at the core-mantle boundary (CMB). Based on the following two conditions, we evaluate the possibility of dynamo activity, thereby reducing the uncertainty of the previously inferred interior structure. The first condition is that the temperature at the CMB must exceed the melting point of a metallic core, and the second is that the heat flux through the CMB must exceed the adiabatic temperature gradient. The mantle temperature starts to increase because of the decay of long-lived radiogenic elements in the rocky mantle. After a few Gyr, radiogenic elements are exhausted and temperature starts to decrease. As the rocky mantle cools, the heat flux at the CMB steadily increases. If the temperature and heat flux at the CMB satisfy these conditions simultaneously, we consider the case as capable of driving a dynamo. Finally, we identify the Dynamo Regime, which is the specific range of internal structures capable of driving the dynamo, based on the results of simulations with various structures. If Ganymede's self-sustained magnetic field were maintained by thermal convection, the satellite's metallic core would be relatively large and, in comparison to other terrestrial-type planetary cores, strongly enriched in sulfur. The dynamo activity and the generation of the magnetic field of Ganymede should start from a much later stage, possibly close to the present.     

Constraints on mantle plumes on Venus: Implications for volatile history

The analysis of Venus’ gravity field and topography suggests the presence of a small number of deep mantle plumes (～9). This study predicts the number of plumes formed at the core–mantle boundary, their characteristics, and the production of partial melt from adiabatic decompression. Numerical simulations are performed using a 3D spherical code that includes large viscosity variations and internal heating. This study investigates the effect of several parameters including the core–mantle boundary temperature, the amount of internal heating, and the mantle viscosity. The smallest number of plumes is achieved when no internal heating is present. However, scaling Earth’s radiogenic heating to Venus suggests a value of ～16 TW. Cases with internal heating produce more realistic lid thickness and partial melting, but produce either too many plumes or no plumes if a high mantle temperature precludes the formation of a hot thermal boundary layer. Mantle viscosity must be reduced to at least 10²⁰ Pa s in order to include significant internal heating and still produce hot plumes. In all cases that predict melting, melting occurs throughout the upper mantle. Only cases with high core temperature (>1700 K) produce dry melting. Over time the upper mantle may have lost significant volatiles. Depending on the water content of the lower mantle, deep plumes may contribute to present-day atmospheric water via volcanic outgassing. Assuming 50 ppm water in mantle, 10 plumes with a buoyancy flux of 500 kg/s continuously erupting for 4 myr will outgas an amount of water on the order of that in the lower atmosphere. A higher level of internal heating than achieved to date, as well as relatively low mantle viscosity, may be required to achieve simulations with ～10 plumes and a thinner lid. Alternatively, if the mantle is heating up due to the stagnant lid, the effect is equivalent to having lower rates of internal heating. A temperature increase of 110 K/byr is equivalent to ?13 TW. This value along with the internal heating of 3 TW used in this study may represent the approximate heat budget of Venus’ mantle.     

Melting in the martian mantle: Shergottite formation and implications for present‐day mantle convection on Mars

Abstract— Radiometric age dating of the shergottite meteorites and cratering studies of lava flows in Tharsis and Elysium both demonstrate that volcanic activity has occurred on Mars in the geologically recent past. This implies that adiabatic decompression melting and upwelling convective flow in the mantle remains important on Mars at present. I present a series of numerical simulations of mantle convection and magma generation on Mars. These models test the effects of the total radioactive heating budget and of the partitioning of radioactivity between crust and mantle on the production of magma. In these models, melting is restricted to the heads of hot mantle plumes that rise from the core‐mantle boundary, consistent with the spatially localized distribution of recent volcanism on Mars. For magma production to occur on present‐day Mars, the minimum average radioactive heating rate in the martian mantle is 1.6 times 10^?12 W/kg, which corresponds to 39% of the Wanke and Dreibus (1994) radioactivity abundance. If the mantle heating rate is lower than this, the mean mantle temperature is low, and the mantle plumes experience large amounts of cooling as they rise from the base of the mantle to the surface and are, thus, unable to melt. Models with mantle radioactive heating rates of 1.8 to 2.1 times 10 ^?12 W/kg can satisfy both the present‐day volcanic resurfacing rate on Mars and the typical melt fraction observed in the shergottites. This corresponds to 43–50% of the Wanke and Dreibus radioactivity remaining in the mantle, which is geochemically reasonable for a 50 km thick crust formed by about 10% partial melting. Plausible changes to either the assumed solidus temperature or to the assumed core‐mantle boundary temperature would require a larger amount of mantle radioactivity to permit present‐day magmatism. These heating rates are slightly higher than inferred for the nakhlite source region and significantly higher than inferred from depleted shergottites such as QUE 94201. The geophysical estimate of mantle radioactivity inferred here is a global average value, while values inferred from the martian meteorites are for particular points in the martian mantle. Evidently, the martian mantle has several isotopically distinct compositions, possibly including a radioactively enriched source that has not yet been sampled by the martian meteorites. The minimum mantle heating rate corresponds to a minimum thermal Rayleigh number of 2 times 10⁶, implying that mantle convection remains moderately vigorous on present‐day Mars. The basic convective pattern on Mars appears to have been stable for most of martian history, which has prevented the mantle flow from destroying the isotopic heterogeneity.     

Possible relations between the rotational axis of the Earth's inner core and the magnetic dipole axis

The geomagnetic field is maintained by amagnetohydrodynamic dynamo process within the liquid outer core. The distribution of the associated electric currents is modified if the outer core is bounded by electrically conducting material. Then, eddy currents and the related magnetic fields are generated within these regions. In particular, the relative rigid rotation of the inner core produces a secondary magnetic field, which is superimposed on the dynamo field. The angle between the dipole axis of the total field and the rotational axis of the inner core is an important quantity needed for the theory of polar motion of the Earth. This angle is investigated for a broad spectrum of angular velocities of the inner core. To simplify the mathematical procedure, we model the dynamo field using an axisymmetric field generated by a system of electric currents within the outer core. The conductivity of the mantle is neglected. We find that the position of the dipole axis depends on the angular velocity of the inner core as well as on the distribution of the current system within the outer core. Coincidence of both axes can be reached if the angular velocity is high enough and if the current system is concentrated within a thin sheet near the outer core-inner core boundary.     

Tides and nutation of the Earth: II. Realistic models of the liquid core

In the first part of this study (Molodensky, 2004; hereinafter, paper I), a survey of the theory of tides and nutation of the Earth was given with the inclusion of the dynamical effects of the elastic mantle and liquid core in the framework of a very simple model of a homogeneous, incompressible core. Here, effects of the inhomogeneity, compressibility, and viscosity of the liquid core are considered, along with those of electromagnetic coupling of the liquid core with the mantle and solid inner core. Errors in the present-day measurements of the amplitudes of forced nutation (of the order of 20 arc s) are well below not only the dynamical effects of the Earths liquid core but also the effects of the inelasticity of the mantle, the dynamical effects of the solid inner core, and the possible effects of electromagnetic coupling between the liquid core, solid inner core, and mantle. This opens up new avenues for astrometric studies of the mechanical properties and electrical conductivity of the mantle and solid inner core at very low frequencies. The modern data on the amplitudes and phases of the Earths forced nutation cannot be interpreted entirely unambiguously, since the following factors remain unknown: (i) the role of the core-mantle electromagnetic coupling compared to the coupling due to core viscosity near the core-mantle boundary and (ii) the frequency dependence of the creep function of the mantle at low frequencies. In large measure, the effects of electromagnetic and viscous coupling can be separated if high-precision data on the tidal variations in the gravitational force at periods of about a day are invoked and allowances are made for the differences between the effects of viscous and electromagnetic coupling on the amplitudes and phases of forced nutation and on the tidal variations in the gravitational force. Here, ranges of possible values of the creep function are constructed for periods from one hour to one day; for these calculations, values consistent with the entire set of data on the forced nutation of the Earth are assumed for the effective dynamical flattening of the liquid core-mantle and liquid core-solid inner core boundaries (these values describe the ellipticity of the boundaries of the inner core, outer core, and mantle, as well as the electromagnetic coupling between the liquid core, mantle, and solid inner core).Translated from Astronomicheskii Vestnik, Vol. 39, No. 1, 2005, pp. 61–80.Original Russian Text Copyright © 2005 by Molodensky.     

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.     

Planck mean efficiency factors for six material candidates as interstellar grains

Planck mean absorption cross-sections have been computed for spherical grains composed of graphite, iron, ice, olivine, amorphous quartz and a lunar silicate. Experimentally determined infrared optical constants have been used for all these materials. Ice mantle particles and planetesimal particles (iron core and olivine mantle) have also been considered with values of outer and inner radii covering a wide range of astrophysical conditions.The results given both graphically and in a tabular form are discussed and compared with those of other authors. The relationships of mantle and core properties are also critically discussed.     

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.     

Implications of an internal dynamo for the thermal history of Mercury

The dynamo explanation of Mercury's magnetic field leads to constraints on the thermal evolution of the planet. A heat-source density at least comparable to the Earth's mantle-wide average must have been retained throughout Mercury's mantle, if the core is still molten, and if Mercury's mantle possesses rheological properties similar to those of the Earth's upper mantle.     

Molecular dynamics estimates for the thermodynamic properties of the Fe–S liquid cores of the Moon,Io, Europa,and Ganymede

A molecular dynamics (MD) simulation is performed for the physical and chemical properties of solid and liquid Fe–S solutions using the embedded atom model (EAM) potential as applied to the internal structure of the Moon, Io, Europa, and Ganymede under the assumption that the satellites' cores can be described by a two-component iron–sulfur system. Calculated results are presented for the thermodynamic parameters including the caloric, thermal, and elastic properties (specific heat, thermal expansion, Grüneisen parameter, density, compression module, velocity of sound, and adiabatic gradient) of the Fe–S solutions at sulfur concentrations of 0–18 at %, temperatures of up to 2500 K, and pressures of up to 14 GPa. The velocity of sound, which increases as pressure rises, is weakly dependent on sulfur concentration and temperature. For the Moon’s outer Fe–S core (~5 GPa/2000 K), which contains 6–16 at % (3.5–10 wt %) sulfur, the density and the velocity of sound are estimated at 6.3–7.0 g/cm³ and 4000 ± 50 m/s, respectively. The MD calculations are compared with the interpretation of the Apollo observations (Weber et al., 2011) to show a good consistency of the velocity of P-waves in the Moon’s liquid core whereas the thermodynamic density of the Fe–S core is not consistent with the seismic models with ρ = 5.1–5.2 g/cm³ (Garcia et al., 2011; Weber et al., 2011). The revision the density values for the core leads to the revision of its size and mass. At sulfur concentrations of 3.5–10 wt %, the density of the Fe–S melt is 20–30% higher that the seismic density of the core. Therefore, the most likely radius of the Moon’s outer core must be less than 330 km (Weber et al., 2011) because, provided that the constraint on the Moon’s mass and moment of inertia is satisfied, an increase in the density of the core must lead to a reduction of its radius. For Jupiter’s Galilean moons Io, Europa, and Ganymede, constraints are obtained on the size, density, and sound velocity of the Fe–S liquid cores. The geophysical and geochemical characteristics of the internal structure of the Moon and Jupiter’s moons are compared. The calculations of the adiabatic gradient at the P–T conditions for the Fe–S cores of the Moon, Io, Europa, and Ganymede suggest the top-down crystallization of the core (Fe-snow scenario).     

The production of Ganymede's magnetic field

One of the great discoveries of NASA's Galileo mission was the presence of an intrinsically produced magnetic field at Ganymede. Generation of the relatively strong (750 nT) field likely requires dynamo action in Ganymede's metallic core, but how such a dynamo has been maintained into the present epoch remains uncertain. Using a one-dimensional, three layer thermal model of Ganymede, we find that magnetic field generation can only occur if the sulfur mass fraction in Ganymede's core is very low (?3%) or very high (?21%), and the silicate mantle can cool rapidly (i.e. it has a viscosity like wet olivine). However, these requirements are not necessarily compatible with cosmochemical and physical models of the satellite. We therefore investigate an alternative scenario for producing Ganymede's magnetic field in which passage through an eccentricity pumping Laplace-like resonance in Ganymede's past enables present day dynamo action in the metallic core. If sufficient tidal dissipation occurs in Ganymede's silicate mantle during resonance passage, silicate temperatures can undergo a runaway which prevents the core from cooling until the resonance passage ends. The rapid silicate and core cooling that follows resonance escape triggers dynamo action via thermal and/or compositional convection. To test the feasibility of this mechanism we couple our thermal model with an orbital evolution model to examine the effects of resonance passage on Ganymede's silicate mantle and metallic core. We find that, contrary to expectations, there are no physically plausible scenarios in which tidal heating in the silicates is sufficient to cause the thermal runaway necessary to prevent core cooling. These findings are robust to variations in the silicate rheology, tidal dissipation factor of Jupiter (QJ), structure of the ice shell, and the inclusion of partial melting in the silicate mantle. Resonance passage therefore appears unlikely to explain Ganymede's magnetic field and we must appeal to the special conditions described above to explain the presence of the field.     

Implications from Galileo Observations on the Interior Structure and Chemistry of the Galilean Satellites

Data from the recent gravity measurements by the Galileo mission are used to construct wide ranges of interior structure and composition models for the Galilean satellites of Jupiter. These models show that mantle densities of Io and Europa are consistent with an olivine-dominated mineralogy with the ratios of Mg to Fe components depending on mantle temperature for Io and on ice shell thickness for Europa. The mantle density and composition depend relatively little on core composition. The size of the core is largely determined by the core's composition with core radius increasing with the concentration of a light component such as sulfur. For Io, the range of possible core sizes is between 38 and 53% of the satellite's radius. For Europa, there is also a substantial effect of the thickness of the ice layer which is varied between 120 and 170 km on the core size. Core sizes are between 10 and 45% of Europa's radius. The core size of Ganymede ranges between one-quarter and one-third of the surface radius depending on its sulfur content and the thickness of the ice shell. A subset of the Ganymede models is consistent with an olivine-dominated mantle mineralogy. The thickness of the silicate mantle above the core varies between 900 and 1100 km. The outermost ice shell is about 900 km in thickness and is further subdivided by pressure-induced phase transitions into ice I, ice III, ice V, and ice VI layers. Callisto should be differentiated, albeit incompletely. It is proposed that this satellite was never molten at a large scale but differentiated through the convective gradual unmixing of the ice and the metal/rock component. Bulk iron-to-silicon ratios Fe/Si calculated for the inner pair of satellites, Io and Europa, are less than the CI carbonaceous chondrite value of 1.7±0.1, whereas ratios for the outer pair, Ganymede and Callisto, cover a broad range above the chondritic value. Although the ratios are uncertain, in particular for Ganymede and Callisto, the values are sufficiently distinct to suggest a difference in composition between these two pairs of satellites. This may indicate a difference in iron-silicon fractionation during the formation of both classes of satellites in the protojovian nebula.     

Tidal dissipation within large icy satellites: Applications to Europa and Titan

This paper describes a new approach based on variational principles to calculate the radial distribution of tidal energy dissipation in any satellite. The advantage of the model with respect to classical solutions, is that it relates in a straightforward way the radial distribution of the time-averaged dissipation rate to its sensitivity to the corresponding distribution of viscoelastic parameters. This method is applied to Io-, Europa-, and Titan-like interiors, and it is tested against the results obtained by two classical methods by determining global dissipation as well as radial and lateral distributions within satellite interiors. By exploring systematically the different parameters defining the interior models, we demonstrate that the presence of a deep ocean below an outer ice layer strongly influences the tidal dissipation distribution in both the outer ice layer and in the innermost part of the satellite. On the one hand, the ocean by imposing a large radial displacement at the base of the outer ice I layer, controls the distribution of tidal strain rate within the outer layer, making the tidal strain rate field very weakly sensitive to the viscosity variations. Conversely, in the high-pressure ice layer below the ocean, both tidal strain rate and dissipation are very sensitive to any variation of the ice viscosity. On the other hand, for identical structures of the mantle and of the core, the presence of a subsurface ocean reduces the strength of dissipation in the silicate mantle. The existence of a liquid layer within Europa makes models of the silicate mantle less dissipative than the predictions for Io.     

Secular changes of LOD associated with a growth of the inner core

From recent estimates of the age of the inner core based on the theory of thermal evolution of the core, we estimate that nowadays the growth of the inner core may perhaps contribute to the observed overall secular increase of LOD caused mainly by tidal friction (i.e., 1.72 ms per century) by a relative decrease of 2 to 7 µs per century. Another, albeit much less plausible, hypothesis is that crystallization of the inner core does not produce any change of LOD, but makes the inner core rotate differentially with respect to the outer core and mantle. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Origin and evolution of the earth-moon system

The origin and evolution of the Earth-Moon system is studied by comparing it to the satellite systems of other planets. The normal structure of a system of secondary bodies orbiting around a central body depends essentially on the mass of the central body. The Earth with a mass intermediate between Uranus and Mars should have a normal satellite system that consists of about half a dozen satellites each with a mass of a fraction of a percent of the lunar mass. Hence, the Moon is not likely to have been generated in the environment of the Earth by a normal accretion process as is claimed by some authors.Capture of satellites is quite a common process as shown by the fact that there are six satellites in the solar system which, because they are retrograde, must have been captured. There is little doubt that the Moon is also a captured satellite, but its capture orbit and tidal evolution are still incompletely understood.The Earth and the Moon are likely to have been formed from planetesimals accreting in particle swarms in Kepler orbits (jet streams). This process leads to the formation of a cool lunar interior with an outer layer accreted at increasingly higher temperatures. The primeval Earth should similarly have formed with a cool inner core surrounded in this case by a very strongly heated outer core and with a mantle accreted slowly and with a low average temperature but with intense transient heating at each individual impact site.     

Does the Moon Have a Metallic Core?: Constraints from Giant Impact Modeling and Siderophile Elements

The issue of whether the Moon has a small metallic core is reexamined in light of new information: improved dynamical modeling, new constraints on core size, and high temperature and pressure metal-silicate partition coefficients. Addressed specifically is the question of whether the Moon's siderophile element budget can be explained by derivation of the Moon from a differentiated impactor or proto-Earth (stage 1), followed by formation of a small metallic core within the Moon (stage 2). If the Moon is made of mantle material from either a “hot” impactor or a “warm” impactor or proto-Earth, a small metallic core (0.7 to 2 mass%) is predicted. If the Moon is made from mantle material from a “hot” proto-Earth, the lunar mantle would be more depleted in W or Re than is observed. Scenarios in which the Moon is made from impactor or proto-Earth mantle material that has equilibrated with metal at low pressures and temperatures (“cold” scenarios) would yield a much larger metallic core than observed. Finally, the greater depletions of Ni, Mo, and Re in the Moon (relative to the Earth) can be explained by low PT and reduced metal-silicate equilibrium in an impactor without later core formation in the Moon (i.e., no stage 2), but depletions of Co, Ga, and W cannot. Altogether, geochemically unlikely or geophysically inadequate non-metallic core alternatives, substantial geophysical evidence for a metallic core, and the successful models presented here for siderophile element depletions all favor the presence of a small lunar metallic core. Previous geochemical objections to an impactor origin of the Moon are eliminated because siderophile element concentrations in the lunar mantle are consistent with separation of a small core from a bulk Moon derived from impactor mantle material.     

Non-adiabatic effects on the pulsation periods

Weight functions for the non-adiabatic radial pulsations are introduced. It is shown from behavior of these functions that the pulsation periods in classical Cepheids are determined essentially in the adiabatic region of stellar envelopes and, on the other hand, those of low surface-gravity models are strongly affected in the region where the acoustic waves are strongly coupled with the radiation fields. The fact is important for understanding basic difference of the pulsation properties between classical Cepheids and low surfacegravity models.The non-adiabatic weight functions deviate from adiabatic ones in two ways in the stellar envelope layers. In the region where the acoustic waves are tightly coupled with radiation fields, the non-adiabatic weight functions have larger values than the corresponding adiabatic ones. On the contrary, the functions are smaller in the outer isothermal region.These results are discussed from the viewpoint on the propagation of the acoustic waves in radiation nelds.     

Westwanderung and the lunar tidal couple: Modulation of convection by Bulge Stress

Wegener concluded that the Earth's surface has suffered regionally variable westward displacement. Modern data support Wegener's conclusion, but a causative mechanism has not been evident. The retarding torque is too small to distort the viscous Earth. At the same time difficulty has been experienced in explaining the large value of the astronomically detected tidal dissipation. We have examined the effect of the secular rotational strain imposed by tidal bulge formation on convection in the mantle of arbitrary origin. The dissipation as measured by the lag in the bodily tides appears adequate to explain the missing part of the dissipation, some 8.5 × 10²⁶ erg yr^–1, without recourse to an unidentified mechanism in the seas. The convection must itself be influenced by the external force system. The effect to be expected is that circulation resulting in westward displacement at surface must be fostered at the expense of circulation in other directions. The history of the tidal couple, if this is based on dissipation in the mantle, is likely to differ greatly from that of a couple based on dissipation in the seas.