Magnetization of celestial bodies with special application to the primeval Earth and Moon

The magnetic fields of celestial bodies are usually supposed to be due to a ‘hydromagnetic dynamo’. This term refers to a number of rather speculative processes which are supposed to take place in the liquid core of a celestial body. In this paper we shall follow another approach which is more closely connected with hydromagnetic processes well-known from the laboratory, and hence basically less speculative. The paper should be regarded as part of a general program to connect cosmical phenomena with phenomena studied in the laboratory. As has been demonstrated by laboratory experiments, a poloidal magnetic field may be increased by the transfer of energy from a toroidal magnetic field through kink instability of the current system. This mechanism can be applied to the fluid core of a celestial body. Any differential rotation will produce a toroidal field from an existing poloidal field, and the kink instability will feed toroidal energy back to the poloidal field, and hence amplify it. In the Earth-Moon system the tidal braking of the Earth's mantle acts to produce a differential angular velocity between core and mantle. The braking will be transferred to the core by hydromagnetic forces which at the same time give rise to a strong magnetic field. The strength of the field will be determined by the rate of tidal braking. It is suggested that the magnetization of lunar rocks from the period ?4 to ?3 Gyears derives from the Earth's magnetic field. As the interior of the Moon immediately after accretion probably was too cool to be melted, the Moon could not produce a magnetic field by hydromagnetic effects in its core. The observed lunar magnetization could be produced by such an amplified Earth field even if the Moon never came closer than 10 or 20 Earth's radii. This hypothesis might be checked by magnetic measurements on the Earth during the same period.     

Contribution of tidal dissipation to lunar thermal history

The possible contributions of tidal heating to lunar thermal history are investigated. Analytic determinations of tidal dissipation in a homogeneous, incompressible Moon and in a two-layer Moon with a soft core and rigid mantle are given as a function of position in the Moon and as a function of Earth-Moon separation. The most recent information on the historical values of the lunar obliquity is employed, and we present results for the constant values of orbital eccentricity of e = 0.0 and e = 0.055. For a simplified orbital evolution and a dissipation factor Q = 100, the total increase in the mean lunar temperature for the homogeneous case does not exceed several tens of degrees. For the two-layer models the local dissipation may be enhanced over that of the homogeneous Moon by a factor of 5 for a core radius of 0.5 lunar radii and by a factor of 100 for a core radius of 0.95 lunar radii. The corresponding factors for the total dissipation are 3 and 15 for the two values of core radii, respectively. We conclude that tidal contributions to lunar thermal history are probably not important. But under special circumstances the enhanced dissipation in a two-layer Moon could have led to a spectacular thermal event.     

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.     

The proximity of Mercury's spin to Cassini state 1 from adiabatic invariance

In determining Mercury's core structure from its rotational properties, the value of the normalized moment of inertia, C/MR², from the location of Cassini 1 is crucial. If Mercury's spin axis occupies Cassini state 1, its position defines the location of the state, where the axis is fixed in the frame precessing with the orbit. Although tidal and core-mantle dissipation drive the spin to the Cassini state with a time scale O(¹⁰⁵) years, the spin might still be displaced from the Cassini state if the variations in the orbital elements induced by planetary perturbations, which change the position of the Cassini state, cause the spin to lag behind as it attempts to follow the state. After being brought to the state by dissipative processes, the spin axis is expected to follow the Cassini state for orbit variations with time scales long compared to the 1000 year precession period of the spin about the Cassini state because the solid angle swept out by the spin axis as it precesses is an adiabatic invariant. Short period variations in the orbital elements of small amplitude should cause displacements that are commensurate with the amplitudes of the short period terms. The exception would be if there are forcing terms in the perturbations that are nearly resonant with the 1000 year precession period. The precision of the radar and eventual spacecraft measurements of the position of Mercury's spin axis warrants a check on the likely proximity of the spin axis to the Cassini state. How confident should we be that the spin axis position defines the Cassini state sufficiently well for a precise determination of C/MR²? By following simultaneously the spin position and the Cassini state position during long time scale orbital variations over past 3 million years [Quinn, T.R., Tremaine, S., Duncan, M., 1991. Astron. J. 101, 2287-2305] and short time scale variations for 20,000 years [JPL Ephemeris DE 408; Standish, E.M., private communication, 2005], we show that the spin axis will remain within one arcsec of the Cassini state after it is brought there by dissipative torques. In this process the spin is located in the orbit frame of reference, which in turn is referenced to the inertial ecliptic plane of J2000. There are no perturbations with periods resonant with the precession period that could cause large separations. We thus expect Mercury's spin to occupy Cassini state 1 well within the uncertainties for both radar and spacecraft measurements, with correspondingly tight constraints on C/MR² and the extent of Mercury's molten core. Two unlikely caveats for this conclusion are: (1) an excitation of a free spin precession by an unknown mechanism or (2) a displacement by a dissipative core mantle interaction that exceeds the measurement uncertainties.     

The evolution of the moon

The thermal evolution of the Moon as it can be defined by the available data and theoretical calculations is discussed. A wide assortment of geological, geochemical and geophysical data constrain both the present-day temperatures and the thermal history of the lunar interior. On the basis of these data, the Moon is characterized as a differentiated body with a crust, a 1000-km-thick solid mantle (lithosphere) and an interior region (core) which may be partially molten. The presence of a crust indicates extensive melting and differentiation early in the lunar history. The ages of lunar samples define the chronology of igneous activity on the lunar surface. This covers a time span of about 1.5 billion yr, from the origin to about 3.16 billion yr ago. Most theoretical models require extensive melting early in the lunar history, and the outward differentiation of radioactive heat sources.Thermal history calculations, whether based on conductive or convective computation codes define relatively narrow bounds for the present day temperatures in the lunar mantle. In the inner region of the 700 km radius, the temperature limits are wider and are between about 100 and 1600°C at the center of the Moon. This central region could have a partially or totally molten core.The lunar heat flow values (about 30 ergs/cm²s) restrict the present day average uranium abundance to 60 ± 15 ppb (averaged for the whole Moon) with typical ratios of K/U = 2000 and Th/U = 3.5. This is consistent with an achondritic bulk composition for the Moon.The Moon, because of its smaller size, evolved rapidly as compared to the Earth and Mars. The lunar interior is cooling everywhere at the present and the Moon is tectonically inactive while Mars could be and the Earth is definitely active.     

The formation of the moon

Supporting evidence for the fission hypothesis for the origin of the Moon is offered. The maximum allowable amount of free iron now present in the Moon would not suffice to extract the siderophiles from the lunar silicates with the observed efficiency. Hence extraction must have been done with a larger amount of iron, as in the mantle of the Earth, of which the Moon was once a part, according to the fission hypothesis. The fission hypothesis gives a good resolution of the tektite paradox. Tektites are chemically much like products of the mantle of the Earth; but no physically possible way has been found to explain their production from the Earth itself. Perhaps they are a product of late, deep-seated lunar volcanism. If so, the Moon must have inside it some material with a strong resemblance to the Earth's mantle. Two dynamical objections to fission are shown to be surmountable under certain apparently plausible conditions.     

Accretional heating as the major cause of compositional differences among meteorite parent bodies,the Moon,and Earth

Accretional energy can be retained with sufficient efficiency in the outer layers of the Moon due to the considerable amount of debris falling back into large craters.Heating of meteorite parent bodies occurs mainly after their accretion, by destructive collisions. The heating was generally not sufficient to differentiate the parent bodies completely so that iron meteorites would originate from the mantle, rather than from the core of a meteorite parent body. Assuming that the Earth and Moon accreted from material of similar chemical composition, we suggest that only from the outer lunar shell is there a loss of gases and volatiles due to accretional melting. The Earth melted completely and degassing was efficient for the whole mass of the Earth leading to its ≈20% higher uncompressed mean density in comparison to the Moon. Because of its lower gravitational field, gases and volatiles escaped much more easily from the lunar atmosphere than from the terrestrial one, leading to the observed depletion in volatiles of the outer parts of the Moon.     

The fate of primordial lunar Trojans

Multiple large impact basins on the lunar nearside formed in a relatively-short interval around 3.8-3.9 Gyr ago, in what is known as the Lunar Cataclysm (LC; also known as Late Heavy Bombardment). It is widely thought that this impact bombardment has affected the whole Solar System or at least all the inner planets. But with non-lunar evidence for the cataclysm being relatively weak, a geocentric cause of the Lunar Cataclysm cannot yet be completely ruled out [Ryder, G., 1990. Eos 71, 313, 322-323]. In principle, late destabilization of an additional Earth satellite could result in its tidal disruption during a close lunar encounter (cf. [Asphaug, E., Agnor, C.B., Williams, Q., 2006. Nature 439, 155-160]). If the lost satellite had D>500 km, the resulting debris can form multiple impact basins in a relatively short time, possibly explaining the LC. Canup et al. [Canup, R.M., Levison, H.F., Stewart, G.R., 1999. Astron. J. 117, 603-620] have shown that any additional satellites of Earth formed together with (and external to) the Moon would be unable to survive the rapid initial tidally-driven expansion of lunar orbit. Here we explore the fate of objects trapped in the lunar Trojan points, and find that small lunar Trojans can survive the Moon's orbital evolution until they and the Moon reach 38 Earth radii, at which point they are destabilized by a strong solar resonance. However, the dynamics of Trojans containing enough mass to cause the LC (diameters >150 km) is more complex; we find that such objects do not survive the passage through a weaker solar resonance at 27 Earth radii. This distance was very likely reached by the Moon long before the LC, which seems to rule out the disruption of lunar Trojans as a cause of the LC.     

Consequences of a geosynchronous phase for the moon

Fission from the Earth's mantle explains why the density of the Moon is similar to that of the Earth's mantle.If following the fission origin of the Moon, the Earth-Moon distance increases progressively, the Moon can recollect chemicals evaporated by the Earth but not volatile enough to be lost as gases.In this way, the surface of the Moon can be enriched in refractory elements as most of the authors have proposed.At 3 Earth radii the long geosynchronous phase allows the formation of a solid crust which will record the Earth's magnetic field and the equilibrium hydrostatic from at that distance.When geosynchronism is broken the Moon will recede; its shape will no longer fit the hydrostatic form. The crust will either break or will exercise pressure on the lower layers. Meteor craters will allow lava to come to the surface. Such flows will be very large where the shape of the crust does not fit at all the geosynchronous form. Large lava flows will appear this way on the near side where the shape has changed the most. The new lava flows no longer record the magnetic field of the Earth because with the end of the synchronous position the field is alternative for the Moon; only the remanent field can influence the new lava.Three out of five samples dated at 3.6 b.y. suggest nevertheless that the field decreased slowly without becoming alternative. This means that the geosynchronous phase may have lasted longer and put the Moon on a more distant orbit, as Alfvén and Arrhenius suggested.The interpretation of lunar magnetism as influenced by the Earth cannot discard any interpretation or suggestion of its own lunar magnetic process. It is quite possible that both mechanisms have worked as some samples show.Paper presented at the European Workshop on Planetary Sciences, organised by the Laboratorio di Astrofisica Spaziale di Frascati, and held between April 23–27, 1979, at the Accademic Nazionale del Lincei in Rome, Italy.     

Differential Rotation Driven by Precession

The tidal force in the Earth–Moon system exerted on the Earth's equatorial bulge results in the Earth's precession. It was proposed a long time ago that the strong shear flow driven by the precession of the Earth may power the Earth's dynamo in its liquid core. We present a nonlinear analytical study investigating how the Poincaré force in a rotating, precessing spherical system drives a large-amplitude differential rotation which plays a major role in the modern theory of the geodynamo. The analysis is based on a perturbation approach in terms of the small Poincaré force parameter. It is found that the amplitude of the precession-driven differential rotation is consistent with that estimated from the geomagnetic secular variation.     

On the implications of an olivine dominated upper mantle on the development of a moon of fission origin

In a series of previous papers, a petrological model for the Moon has been developed based on the assumption that the Moon is a globe of differentiated terrestrial mantle material which fissioned from the Earth. One of the major constraints which this model matches is the hypothesis that the lunar upper mantle is dominated by pyroxene. However, it has been recently shown that olivine is most probably the major constituent of the lunar upper mantle and that, at least that part of the Moon has a composition which is very similar to that of pyrolite - the proposed composition of the Earth's mantle. As a result of this new model constraint, the previously proposed differentiation scheme for a Moon of fission origin is reviewed and found to be inadequate, despite modification, for explaining the near pyrolite composition of the lunar upper mantle. As a result, a solidification sequence, which has been proposed to explain the rhythmic banding in terrestrial ultra mafic complexes, is investigated and found to be able to account for the high olivine content of the upper mantle, assuming a pyrolite composition for the Moon.     

The evolution of the lunar orbit revisited. I

After recalling the contribution of Halley, J. Kepler, and G. Darwin to our understanding of the secular acceleration of the Moon, we establish a set of differential equations for the variation of the semi-major axis, and the inclination of the Moon on the maximum area plane. These equations are obtained without expanding the disturbing function, due to the tidal bulge, in term of the elliptic elements. The equations thus obtained are simple enough to allow us a qualitative discussion of the solution, followed by a numerical integration.The results obtained show the Moon was in the distant past in a retrograde orbit, approaching the Earth, its inclination increasing towards 90°; once after a closer approach to the Earth, the Moon receeded and it will finally reach an equilibrium point, the orbital and the equatorial planes being blended.The solution of the equations appears as a fascicle of curves, becoming extremely dense as we come nearer to the present. Owing to the high sensitivity of the solution to the initial conditions, a weak disturbance added to our modeled forces may lead to a past situation very different from the conclusion drawn by Goldreich (1966) and MacDonald (1964); the minimal approach distance could be greater than 10 Earth's radii.     

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.     

Sun-synchronous orbits near critical inclination

The long period dynamics of Sun-synchronous orbits near the critical inclination 116.6° are investigated. It is known that, at the critical inclination, the average perigee location is unchanged by Earth oblateness. For certain values of semimajor axis and eccentricity, orbit plane precession caused by Earth oblateness is synchronous with the mean orbital motion of the apparent Sun (a Sun-synchronism). Sun-synchronous orbits have been used extensively in meteorological and remote sensing satellite missions. Gravitational perturbations arising from an aspherical Earth, the Moon, and the Sun cause long period fluctuations in the mean argument of perigee, eccentricity, inclination, and ascending node. Double resonance occurs because slow oscillations in the perigee and Sun-referenced ascending node are coupled through the solar gravity gradient. It is shown that the total number and infinitesimal stability of equilibrium solutions can change abruptly over the Sun-synchronous range of semimajor axis values (1.54 to 1.70 Earth radii). The effect of direct solar radiation pressure upon certain stable equilibria is investigated.     

A magnetic dynamo in the moon?

The existence of fossil lunar magnetism has caused speculation that the Moon had, at one time, an internally produced dynamo magnetic field. Quantitative analysis of this idea, constrained by the largest iron lunar core compatible with observations, implies that the Moon would have had to rotate faster than its breakup angular velocity in order to support a dynamo magnetic field.A paper presented at the Lunar Science Institute Conference on Geophysical and Geochemical Exploration of the Moon and Planets, January 10–12, 1973.     

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.     

Siderophile elements in Earth's upper mantle and lunar breccias: Data synthesis suggests manifestations of the same late influx

Abstract— The platinum group elements (PGE; Ru, Rh, Pd, Os, Ir, Pt), Re and Au comprise the highly siderophile elements (HSE). We reexamine selected isotopic and abundance data sets for HSE in upper mantle peridotites to resolve a longstanding dichotomy. Re‐Os and Pt‐Os isotope systematics, and approximately chondritic proportions of PGE in these rocks, suggest the presence in undepleted mantle of a chondrite‐like component, which is parsimoniously explained by late influx of large planetisimals after formation of the Earth's core and the Moon. But some suites of xenolithic and orogenic spinel lherzolites, and abyssal peridotites, have a CI‐normalized PGE pattern with enhanced Pd that is sometimes termed “non‐chondritic”. We find that this observation is consistent with other evidence of a late influx of material more closely resembling enstatite, rather than ordinary or carbonaceous, chondrites. Regional variations in HSE patterns may be a consequence of a late influx of very large objects of variable composition. Studies of many ancient (>3.8 Ga) lunar breccias show regional variations in Au/Ir and suggest that “graininess” existed during the early bombardment of the Earth and Moon. Reliable Pd values are available only for Apollo 17 breccias 73215 and 73255, however. Differences in HSE patterns between the aphanitic and anorthositic lithologies in these breccias show fractionation between a refractory group (Re, Os and Ir) and a normal (Pd, Ni, and Au) group and may reflect the compositions of the impacting bodies. Similar fractionation is apparent between the EH and EL chondrites, whose PGE patterns resemble those of the aphanitic and anorthositic lithologies, respectively. The striking resemblance of HSE and chalcogen (S, Se) patterns in the Apollo aphanites and high‐Pd terrestrial peridotites suggest that the “non‐chondritic” abundance ratios in the latter may be reflected in the composition of planetisimals striking the Moon in the first 700 Ma of Earth–Moon history. Most notably, high Pd may be part of a general enhancement of HSE more volatile than Fe suggesting that the Au abundance in at least parts of the upper mantle may be 1.5 to 2x higher than previously estimated. The early lunar influx may be estimated from observed basin‐sized craters. Comparison of relative influx to Earth and Moon suggests that the enrichment of HSE is limited to the upper mantle above 670 km. To infer enrichment of the whole mantle would require several large lunar impacts not yet identified.     

The great-circle pattern of large circular maria: product of an earth-moon encounter

The circular maria - Orientale, Imbrium, Serenitatis, Crisium, Smythii, and Tsiolkovsky -lie nearly on a lunar great circle. This pattern can be considered the result of a very close, non-capture encounter between Moon and Earth early in solar-system history. Of critical importance in analyzing the effects of such an encounter is the position of the weightlessness limit of the Earth-Moon System which is located at about 1.63R _e, measured from the center of Earth to center of Moon. Within this weightlessness limit, material can be pulled from the lunar surface and interior by Earth's gravity and either escape from the Moon or be redistributed onto the lunar surface. In the case of an encounter with a non-spinning Moon, backfalling materials would be distributed along a lunar great circle. However, if the Moon is rotating during the encounter, the backfall pattern will deviate from the great circle, the amount depending on the rate and direction of spin. Such a close encounter model may be related to the pattern of circular maria if materials departing from the source region are visualized as spheroids of molten lunar upper mantle basalt. These spheroids, then, would impact onto the lunar surface to form a pattern of lava lakes. Radiometric dates from mare rocks are consistent with this model of mare formation if the older mare rock dates are considered to date the encounter and younger dates are considered to date subsequent volcanic eruptions on a structurally weakened Moon.     

Mars

Mars is the fourth planet out from the sun. It is a terrestrial planet with a density suggesting a composition roughly similar to that of the Earth. Its orbital period is 687 days, its orbital eccentricity is 0.093 and its rotational period is about 24 hours. Mars has two small moons of asteroidal shapes and sizes (about 11 and 6 km mean radius), the bigger of which, Phobos, orbits with decreasing semimajor orbit axis. The decrease of the orbit is caused by the dissipation of tidal energy in the Martian mantle. The other satellite, Deimos, orbits close to the synchronous position where the rotation period of a planet equals the orbital period of its satellite and has hardly evolved with time. Mars has a tenous atmosphere composed mostly of CO with strong winds and with large scale aeolian transport of surface material during dust storms and in sublimation-condensation cycles between the polar caps. The planet has a small magnetic field, probably not generated by dynamo action in the core but possibly due to remnant magnetization of crustal rock acquired earlier from a stronger magnetic field generated by a now dead core dynamo. A dynamo powered by thermal power alone would have ceased a few billions of years ago as the core cooled to an extent that it became stably stratified. Mars' topography and its gravity field are dominated by the Tharsis bulge, a huge dome of volcanic origin. Tharsis was the major center of volcanic activity, a second center is Elysium about 100° in longitude away. The Tharsis bulge is a major contributor to the non-hydrostaticity of the planet's figure. The moment of inertia factor together with the mass and the radius presently is the most useful constraint for geophysical models of the Martian interior. It has recently been determined by Doppler range measurements to the Mars Pathfinder Lander to be (Folkner et al. 1997). In addition, models of the interior structure use the chemistry of the SNC meteorites which are widely believed to have originated on Mars. According to the models, Mars is a differentiated planet with a 100 to 200 km thick basaltic crust, a metallic core with a radius of approximately half the planetary radius, and a silicate mantle. Mantle dynamics is essential in forming the elements of the surface tectonics. Models of mantle convection find that the pressure-induced phase transformations of -olivine to -spinel, -spinel to -spinel, and -spinel to perovskite play major roles in the evolution of mantle flow fields and mantle temperature. It is not very likely that the -spinel to perovskite transition is present in Mars today, but a few 100 km thick layer of perovskite may have been present in the lower mantle immediately above the core-mantle boundary early in the Martian history when mantle temperatures were hotter than today. The phase transitions act to reduce the number of upwellings to a few major plumes which is consistent with the bipolar distribution of volcanic centers of Mars. The phase transitions also cause a partial layering of the lower mantle which keeps the lower mantle and the core from extensive cooling over the past aeons. A relatively hot, fluid core is the most widely accepted explanation for the present lack of a self-generated magnetic field. Growth of an inner core which requires sub-liquidus temperatures in the core would have provided an efficient mechanism to power a dynamo up to the present day. Received 10 May 1997     

Determining parameters of Moon’s orbital and rotational motion from LLR observations using GRAIL and IERS-recommended models

The aim of this work is to combine the model of orbital and rotational motion of the Moon developed for DE430 with up-to-date astronomical, geodynamical, and geo- and selenophysical models. The parameters of the orbit and physical libration are determined in this work from lunar laser ranging (LLR) observations made at different observatories in 1970–2013. Parameters of other models are taken from solutions that were obtained independently from LLR. A new implementation of the DE430 lunar model, including the liquid core equations, was done within the EPM ephemeris. The postfit residuals of LLR observations make evident that the terrestrial models and solutions recommended by the IERS Conventions are compatible with the lunar theory. That includes: EGM2008 gravitational potential with conventional corrections and variations from solid and ocean tides; displacement of stations due to solid and ocean loading tides; and precession-nutation model. Usage of these models in the solution for LLR observations has allowed us to reduce the number of parameters to be fit. The fixed model of tidal variations of the geopotential has resulted in a lesser value of Moon’s extra eccentricity rate, as compared to the original DE430 model with two fit parameters. A mixed model of lunar gravitational potential was used, with some coefficients determined from LLR observations, and other taken from the GL660b solution obtained from the GRAIL spacecraft mission. Solutions obtain accurate positions for the ranging stations and the five retroreflectors. Station motion is derived for sites with long data spans. Dissipation is detected at the lunar fluid core-solid mantle boundary demonstrating that a fluid core is present. Tidal dissipation is strong at both Earth and Moon. Consequently, the lunar semimajor axis is expanding by 38.20 mm/yr, the tidal acceleration in mean longitude is \(-25.90 {{}^{\prime \prime }}/\mathrm{cy}^2\), and the eccentricity is increasing by \(1.48\times 10^{-11}\) each year.