Love numbers of the moon and of the terrestrial planets

In the IERS Standards (1989), for the Moon the adopted value of the tide Love number, k ₂, is equal to 0.0222. In this paper using the latest geodetic parameters of the Moon a group of internal structure models are constructed for this celestial body (see Table V), then the dependence of the Moon's core size on calculated value of k ₂ is explored. The obtained results indicate that the second degree Love number, k ₂ = 0.02664, of the lunar model 91–04 is near its observed value (0.027 ± 0.006). This implies that the Moon may possess an outer core of 660 km radius and of 300 kbar mean rigidity. With the same method the static Love numbers from degree 2 to 30 are computed for the terrestrial planets — Mercury, Venus, and Mars (see Table VII), and the influence of some parameters (such as the rigidity) of the outer core on low degree Love numbers is discussed. Finally, the likely range of the second degree Love numbers is determined for the terrestrial planets (see Table XI). It seems that if low degree Love numbers of a terrestrial planet can be detected in the future space explorations, there is some possibility to improve the planetary internal structure model. For example, as soon as space techniques yield an observed value of k ₂ > 0.10 for Mercury, there will be reason to anticipate that a partly melted iron core exists in this planet.     

Nuclear Planetology:Especially Concerning the Moon and Mars

To approach basic scientific questions on the origin and evolution of planetary bodies such as planets, their satellites and asteroids, one needs data on their chemical composition. The measurements of gamma-rays, X-rays and neutrons emitted from their surface materials provide information on abundances of major elements and naturally radioactive gamma-ray emitters. Neutron spectroscopy can provide sensitive maps of hydrogen-and carbon-containing compounds, even if buried, and can uniquely identify layers of carbon-dioxide frost. Nuclear spectroscopy, as a means of compositional analysis, has been applied via orbital and lander spacecraft to extrater-restrial planetary bodies:the Moon, Venus, Mars, Mercury and asteroids. The knowledge of their chemical abundances, especially concerning the Moon and Mars, has greatly increased in recent years. This paper describes the principle of nuclear spectroscopy, nuclear planetary instruments carried on planetary missions so far, and the nature of observational results and findings of the Moon and Mars, recently obtained by nuclear spectroscopy.     

Formation of the terrestrial planets

The early phases of formation in the inner solar system were dominated by collisions and short-range dynamical interactions among planetesimals. But the later phases, which account for most of the differences among planets, are unsure because the dynamics are more subtle. Jupiter's influence became more important, leading to drastic clearing out of the asteroid belt and the stunting of Mars's growth. Further in, the effect of Jupiter-- both directly and indirectly, through ejection of mass in the outer solar system-- was probably to speed up the process without greatly affecting the outcome. The great variety in bulk properties of the terrestrial bodies indicate a terminal phase of great collisions, so that the outcome is the result of small-N statistics. Mercury, 65 percent iron, appears to be a residual core from a high-velocity collision. All planets appear to require a late phase of high energy impacts to erode their atmospheres: including the Earth, to remove CO₂ so that its ocean could form by condensation of water.Consistent with this model is that the largest collision, about 0.2 Earth masses, was into the proto-Earth, although the only property that appears to require it is the great lack of iron in the Moon. The other large differences between the Earth and Venus, angular momentum (spin plus satellite) and inert gas abundances, must arise from origin circumstances, but neither require nor forbid the giant impact. Venus's higher ratio of light to heavy inert gases argues for it receiving a large icy impactor, about 10^–6 Earth masses from far out, requiring some improbable dynamics to get a low enough approach velocity. Core formation in both planets probably started rather early during accretion.Some geochemical evidences argue for the Moon coming from the Earth's mantle, but are inconclusive. Large scale melting of the mantle by the giant impact would plausibly have led to stratification. But the "lock-up" at the end of turbulent mantle convection is a trade-off between rates: crystallization of constituents of small density difference versus overall freezing. Also, factors such as differences in melting temperatures and densities, melt compressibilities, and phase transitions may have had homogenizing effects in the subsequent mantle convection.     

Cumulative subject index volumes 27–29

It is premature to establish a chronology for Mars and Mercury, relative to the known lunar chronology, to better than an order of magnitude. Lunar evidence neither requires nor excludes a “cataclysmic” episode of bombardment about 4.0 b.y. ago. Such a cataclysm might have resulted naturally from tidal disruption by a planet or collisional fragmentation in the asteroid belt of either a Uranus/Neptune-scattered planetesimal or a large asteroid, in which case any lunar cataclysm would have occurred as well on other planets. There is no independent evidence in Mariner 10 imagery for (or against) an early episodic bombardment on Mercury. Crater densities on plains units of the Moon, Mars, and Mercury have not been shown to be “strikingly similar” and do not imply, in the absence of definitive dynamical calculations of planetary impact rates of plausible populations of planetesimals, any similarity in the geological chronologies for those planets. Photogeological studies alone cannot determine absolute chronologies for planets. In combination with dynamical analyses, they can help us date to no better than a factor of 3 to 10 the formation of the Caloris Basin or the epoch when the Martian rivers ran.     

Thermal evolutions of the terrestrial planets

The thermal evolution of the Moon, Mercury, Mars, Venus and hypothetical minor planets is calculated theoretically, taking into account conduction, solid-state convection, and differentiation. An assortment of geological, geochemical, and geophysical data is used to constrain both the present day temperatures and thermal histories of the planets' interiors. Such data imply that the planets were heated during or shortly after formation and that all the terrestrial planets started their differentiations early in their history. Initial temperatures and core formation play the most important roles in the early differentiation. The size of the planet is the primary factor in determining its present day thermal state. A planetary body with radius less than 1000 km is unlikely to reach melting given heat source concentrations similar to terrestrial values and in the absence of intensive early heating such as short half-life radioactive heating and inductive heating.Studies of individual planets are constrained by varying amounts of data. Most data exist for the Earth and Moon. The Moon is a differentiated body with a crust, a thick solid mantle and an interior region which may be partially molten. It is presently cooling rapidly and is relatively inactive tectonically.Mercury most likely has a large core. Thermal calculations indicate it may have a 500 km thick solid lithosphere, and the core may be partially molten if it contains some heat sources. If this is not the case, the planet's interior temperatures are everywhere below the melting curve for iron. The thermal evolution is dominated by core separation and the high conductivity of iron which makes up the bulk of Mercury.Mars, intermediate in size among the terrestrial planets, is assumed to have differentiated an Fe–FeS core. Differentiation and formation of an early crust is evident from Mariner and Viking observations. Theoretical models suggest that melting and differentiation of the mantle silicates has occurred at least up until 1 billion years ago. Present day temperature profiles indicate a relatively thick (250 km) lithosphere with a possible asthenosphere below. The core is molten.Venus is characterized as a planet similar to the Earth in many respects. Core formation probably occurred during the first billion years after the formation. Present day temperatures indicate a partially molten upper mantle overlain by a 100 km thick lithosphere and a molten Fe–Ni core. If temperature models are good indicators, we can expect that today, Venus has tectonic processes similar to the Earth's.Paper dedicated to Professor Hannes Alfvén on the occasion of his 70th birthday, 30 May 1978.     

Magnetic fields of mars and venus: Solar wind interactions

Recent U.S.S.R. studies of the magnetic field and solar wind flow in the vicinity of Mars and Venus confirm earlier U.S.A. reports of a bow shock wave developed as the solar wind interacts with these planets. Mars 2 and 3 magnetometer experiments report the existence of an intrinsic planetary magnetic field, sufficiently strong to form a magnetopause, deflecting the solar wind around the planet and its ionosphere. This is in contrast to the case for Venus, where it is assumed to be the ionosphere and processes therein which are responsible for the solar wind deflection. An empirical relationship appears to exist between planetary dipole magnetic moments and their angular momentum for Moon, Mars, Venus, Earth and Jupiter. Implications for the magnetic fields of Mercury and Saturn are discussed.Paper presented at the Lunar Science Institute Conference on Geophysical and Geochemical Exploration of the Moon and Planets, January 10–12, 1973     

On the internal structures of mercury and venus

Recent radar measures of the radius and mass of Mercury imply a composition for the planet containing about 60% iron. One or other of two conclusions seems inescapable: either that Mercury is a highly exceptional object among terrestrial planets, or that all measures to date of the planet involve substantial systematic error. In either case the situation is such that independent checking of the radius and mass of Mercury by some entirely different means has become of the greatest importance to planetary physics and cosmogony.The recent radar and other determinations of the solid radius of Venus imply an internal structure similar to that of the Earth, namely a liquid core surrounded by a solid mantle and outer-shell zone. The theory also implies that the temperatures within Venus should be slightly higher than at the corresponding parts of the Earth. The proportion of mass in the core of Venus (about 25% of the whole) is entirely consistent with the phase-change hypothesis as to its nature, as of course is also the absence of any liquid or iron core in both Mars and the Moon. On the older iron-core hypothesis, Venus with considerably less iron content by mass than the Earth, and Mars and the Moon with none, would all present problems in different degrees to account for the differences of composition.If Venus began as an all-solid planet, the initial radius would have been about 6300 km, and the total amount of surface reduction to date owing to contraction of the planet would have been almost 40 million km², and as a proportion of the total area only slightly less than the contraction of the Earth. The theory thus predicts the existence of folded and thrusted mountain-systems of terrestrial type at the surface of Venus.     

On planetary cores

The early part of the article traces the implications on planetary cores of various revisions of the writer's original Earth modelsA andB. Recent evidence indicates that it is appropriate to consider at most two-layer cores in the terrestrial planets. Current evidence on equations of state for cores is presented. The later part of the article puts forward a proposal which, though quite distinct from the mantle-core phase transition proposal of some twenty years ago, retains the assumption that the pressurepc at the Earth's mantle-core boundaryN is a critical pressure crucially involved in the changes atN. The proposal envisages an outer core of Fe₂O which is unstable at pressures less thanpc. In the form set down, the proposal restores the agreement of the Earth, Mars and Venus with a common overall composition and meets various revisions of earlier planetary and other observational data. Although the calculations so far made are only preliminary, the agreement appears to be very striking. While still requiring the present Mercury to be significantly different from the primitive Mercury, the Fe₂O has an advantage over the phase transition proposal in providing for a larger iron core. Brief comments are made on the Moon.Paper dedicated to Professor Harold C. Urey on the occasion of his 80th birthday on 29 April 1973.     

Did 26Al and impact‐induced heating differentiate Mercury?

Numerical models dealing with the planetary scale differentiation of Mercury are presented with the short‐lived nuclide, ²⁶Al, as the major heat source along with the impact‐induced heating during the accretion of planets. These two heat sources are considered to have caused differentiation of Mars, a planet with size comparable to Mercury. The chronological records and the thermal modeling of Mars indicate an early differentiation during the initial ~1 million years (Ma) of the formation of the solar system. We theorize that in case Mercury also accreted over an identical time scale, the two heat sources could have differentiated the planets. Although unlike Mars there is no chronological record of Mercury's differentiation, the proposed mechanism is worth investigation. We demonstrate distinct viable scenarios for a wide range of planetary compositions that could have produced the internal structure of Mercury as deduced by the MESSENGER mission, with a metallic iron (Fe‐Ni‐FeS) core of radius ~2000 km and a silicate mantle thickness of ~400 km. The initial compositions were derived from the enstatite and CB (Bencubbin) chondrites that were formed in the reducing environments of the early solar system. We have also considered distinct planetary accretion scenarios to understand their influence on thermal processing. The majority of our models would require impact‐induced mantle stripping of Mercury by hit and run mechanism with a protoplanet subsequent to its differentiation in order to produce the right size of mantle. However, this can be avoided if we increase the Fe‐Ni‐FeS contents to ~71% by weight. Finally, the models presented here can be used to understand the differentiation of Mercury‐like exoplanets and the planetary embryos of Venus and Earth.     

Planetary brightness temperature measurements at 8.6 mm and 3.1 mm wavelengths

New measurements of the Sun, Moon, Mercury, Venus, Mars, Jupiter, and Saturn at 3.1 and 8.6 mm wavelengths are given. The temperatures reported for the planets at 3.1 mm wavelength are higher than previous measurements in this wavelength range and change the interpretation of some planetary spectra. For Mercury, it is found that the mean brightness temperature is independent of wavelength and that a temperature dependent thermal conductivity is not required to match the observations. In the case of Mars, the spectrum is shown to rise in the millimeter region as simple models predict. For Jupiter, the need to recalculate the spectrum with recent models is demonstrated. The flux density scale proposed by Dent (1972) has been revised according to a more accurate determination of the millimeter brightness temperature of Jupiter.     

Large scale chaos and marginal stability in the solar system

Large scale chaos is present everywhere in the solar system. It plays a major role in the sculpting of the asteroid belt and in the diffusion of comets from the outer region of the solar system. All the inner planets probably experienced large scale chaotic behavior for their obliquities during their history. The Earth obliquity is presently stable only because of the presence of the Moon, and the tilt of Mars undergoes large chaotic variations from 0° to about 60°. On billion years time scale, the orbits of the planets themselves present strong chaotic variations which can lead to the escape of Mercury or collision with Venus in less than 3.5 Gyr. The organization of the planets in the solar system thus seems to be strongly related to this chaotic evolution, reaching at all time a state of marginal stability, that is practical stability on a time-scale comparable to its age.This lecture was given at the XIth International Congress of Mathematical Physics, Paris, july 1994     

Could giant impacts cripple core dynamos of small terrestrial planets?

Large impacts not only create giant basins on terrestrial planets but also heat their interior by shock waves. We investigate the impacts that have created the largest basins existing on the planets: Utopia on Mars, Caloris on Mercury, Aitken on Moon, all formed at ∼4 Ga. We determine the impact-induced temperature increases in the interior of a planet using the “foundering” shock heating model of Watters et al. (Watters, W.A., Zuber, M.T., Hager, B.H. [2009]. J. Geophys. Res. 114, E02001. doi:10.1029/2007JE002964). The post-impact thermal evolution of the planet is investigated using 2D axi-symmetric convection in a spherical shell of temperature-dependent viscosity and thermal conductivity, and pressure-dependent thermal expansion. The impact heating creates a superheated giant plume in the upper mantle which ascends rapidly and develops a strong convection in the mantle of the sub-impact hemisphere. The upwelling of the plume rapidly sweeps up the impact-heated base of the mantle away from the core-mantle boundary and replaces it with the colder surrounding material, thus reducing the effects of the impact-heated base of the mantle on the heat flux out of core. However, direct shock heating of the core stratifies the core, suppresses the pre-existing thermal convection, and cripples a pre-existing thermally-driven core dynamo. It takes about 17, 4, and 5 Myr for the stratified cores of Mars, Mercury, and Moon to exhaust impact heat and resume global convection, possibly regenerating core dynamos.     

The Leonard Award Address Presented 1998 July 27, Dublin,Ireland: On the difficulties of making Earth-like planets

Abstract— Here I discuss the series of events that led to the formation and evolution of our planet to examine why the Earth is unique in the solar system. A multitude of factors are involved: These begin with the initial size and angular momentum of the fragment that separated from a molecular cloud; such random factors are crucial in determining whether a planetary system or a double star develops from the resulting nebula. Another requirement is that there must be an adequate concentration of heavy elements to provide the 2% “rock” and “ice” components of the original nebula. An essential step in forming rocky planets in the inner nebula is the loss of gas and depletion of volatile elements, due to early solar activity that is linked to the mass of the central star. The lifetime of the gaseous nebula controls the formation of gas giants. In our system, fine timing was needed to form the gas giant, Jupiter, before the gas in the nebula was depleted. Although Uranus and Neptune eventually formed cores large enough to capture gas, they missed out and ended as ice giants. The early formation of Jupiter is responsible for the existence of the asteroid belt (and our supply of meteorites) and the small size of Mars, whereas the gas giant now acts as a gravitational shield for the terrestrial planets. The Earth and the other inner planets accreted long after the giant planets, from volatile-depleted planetesimals that were probably already differentiated into metallic cores and silicate mantles in a gas-free, inner nebula. The accumulation of the Earth from such planetesimals was essentially a stochastic process, accounting for the differences among the four rocky inner planets—including the startling contrast between those two apparent twins, Earth and Venus. Impact history and accretion of a few more or less planetesimals were apparently crucial. The origin of the Moon by a single massive impact with a body larger than Mars accounts for the obliquity (and its stability) and spin of the Earth, in addition to explaining the angular momentum, orbital characteristics, and unique composition of the Moon. Plate tectonics (unique among the terrestrial planets) led to the development of the continental crust on the Earth, an essential platform for the evolution of Homo sapiens. Random major impacts have punctuated the geological record, accentuating the directionless course of evolution. Thus a massive asteroidal impact terminated the Cretaceous Period, resulted in the extinction of at least 70% of species living at that time, and led to the rise of mammals. This sequence of events that resulted in the formation and evolution of our planet were thus unique within our system. The individual nature of the eight planets is repeated among the 60-odd satellites—no two appear identical. This survey of our solar system raises the question whether the random sequence of events that led to the formation of the Earth are likely to be repeated in detail elsewhere. Preliminary evidence from the “new planets” is not reassuring. The discovery of other planetary systems has removed the previous belief that they would consist of a central star surrounded by an inner zone of rocky planets and an outer zone of giant planets beyond a few astronomical units (AU). Jupiter-sized bodies in close orbits around other stars probably formed in a similar manner to our giant planets at several astronomical units from their parent star and, subsequently, migrated inwards becoming stranded in close but stable orbits as “hot Jupiters”, when the nebula gas was depleted. Such events would prevent the formation of terrestrial-type planets in such systems.     

How common are Earth-Moon planetary systems?

The Earth’s comparatively massive moon, formed via a giant impact on the proto-Earth, has played an important role in the development of life on our planet, both in the history and strength of the ocean tides and in stabilizing the chaotic spin of our planet. Here we show that massive moons orbiting terrestrial planets are not rare. A large set of simulations by Morishima et al. (Morishima, R., Stadel, J., Moore, B. [2010]. Icarus. 207, 517-535), where Earth-like planets in the habitable zone form, provides the raw simulation data for our study. We use limits on the collision parameters that may guarantee the formation of a circumplanetary disk after a protoplanet collision that could form a satellite and study the collision history and the long term evolution of the satellites qualitatively. In addition, we estimate and quantify the uncertainties in each step of our study. We find that giant impacts with the required energy and orbital parameters for producing a binary planetary system do occur with more than 1 in 12 terrestrial planets hosting a massive moon, with a low-end estimate of 1 in 45 and a high-end estimate of 1 in 4.     

On the thermal evolution of the terrestrial planets

Physical and chemical constraints for such different planetary objects as the Earth, the Moon and meteorite parent bodies can best be satisfied by thermal history models having high initial temperatures. On the basis of thermal calculations it is suggested that the evolution of the other terrestrial planets (Mars, Venus and Mercury) was also characterized by high initial temperatures. Under these conditions, melting and, consequently, fractionation would set in at an early stage. Because of the resulting redistribution of the long-lived radioactive heat sources and the concentration of these elements in the surface layers, large-scale differentiation could be achieved by partial melting.Paper presented at the Lunar Science Institute Conference on Geophysical and Geochemical Exploration of the Moon and Planets, January 10–12, 1973.     

2000—2049年行星天象（一）

本文给出 2 0 0 0 - 2 0 4 9年行星天象的一部分 ,包括水星、金星的东、西大距 ,留及上、下合日 ;金星最亮和最接近地球 ;外行星冲日、最接近地球、合日、留 ;地球和外行星过远近日点计1 5个表     

Comparison of the crater morphology-size relationship for Mars,Moon, and Mercury

New central peak-crater size data for Mars shows that a higher percentage of relatively unmodified Martian craters have central peaks than do fresh lunar craters below a diameter of 30 km. For example, in the diameter range 10 to 20 km, 60% of studied Martian craters have central peaks compared to 26% for the Moon. Gault et al. (1975, J. Geophys. Res.80, 2444–2460) have demonstrated that central peaks occur in smaller craters on Mercury than on the Moon, and that this effect is due to the different gravity fields in which the craters formed. Similar differences when comparing Mars and the Moon show that gravity has affected the diameter at which central peaks form on Mars. Erosion on Mars, therefore, does not completely mask differences in crater interior structure that are caused by differences in gravity. Effects of Mars' higher surface gravity when compared to the Moon are not detected when comparing terrace and crater shape data. The morphology-crater size statistics also show that a full range of crater shapes occur on Mars, and craters tend to become more morphologically complex with increasing diameter. Comparisons of Martian and Mercurian crater data show differences which may be related to the greater efficacy of erosion on Mars.     

Accretion of the terrestrial planets. II

Some aspects and consequences of the theory of gravitational accretion of the terrestrial planets are examined. The concept of a “closed feeding zone” is somewhat unrealistic, but provides a lower bound on the accretion time. Safronov's relative velocity relation for planetesimals is not entirely consistent with the feeding zone model. A velocity relation which includes an initial velocity component is suggested. The orbital parameters of the planetesimals and the dimensions of the feeding zone are related to their relative velocities. The assumption of an initial velocity does not seriously change the accretion time.Mercury, Venus, and the Earth have accretion times on the order of 10⁸yr. Mars requires well over 10⁹yr to accrete by the same assumptions. Currently available data do not rule out a late formation of Mars, but the lunar cratering history makes it unlikely. If Mars is as old as the Earth, nongravitational forces or a violation of the feeding zone concept is required. One such possibility is the removal of matter from the zone of Mars by Jupiter's influence. The final sweeping up by Mars after this event would result in the scattering of a considerable mass among the other terrestrial planets. The late postaccretional bombardments infrerred for the Moon and Mercury may have had this source.     

Nonuniform cratering of the terrestrial planets

We estimate the impact flux and cratering rate as a function of latitude on the terrestrial planets using a model distribution of planet crossing asteroids and comets [Bottke, W.F., Morbidelli, A., Jedicke, R., Petit, J.-M., Levison, H.F., Michel, P., Metcalfe, T.S., 2002. Icarus 156, 399-433]. After determining the planetary impact probabilities as a function of the relative encounter velocity and encounter inclination, the impact positions are calculated analytically, assuming the projectiles follow hyperbolic paths during the encounter phase. As the source of projectiles is not isotropic, latitudinal variations of the impact flux are predicted: the calculated ratio between the pole and equator is 1.05 for Mercury, 1.00 for Venus, 0.96 for the Earth, 0.90 for the Moon, and 1.14 for Mars over its long-term obliquity variation history. By taking into account the latitudinal dependence of the impact velocity and impact angle, and by using a crater scaling law that depends on the vertical component of the impact velocity, the latitudinal variations of the cratering rate (the number of craters with a given size formed per unit time and unit area) is in general enhanced. With respect to the equator, the polar cratering rate is about 30% larger on Mars and 10% on Mercury, whereas it is 10% less on the Earth and 20% less on the Moon. The cratering rate is found to be uniform on Venus. The relative global impact fluxes on Mercury, Venus, the Earth and Mars are calculated with respect to the Moon, and we find values of 1.9, 1.8, 1.6, and 2.8, respectively. Our results show that the relative shape of the crater size-frequency distribution does not noticeably depend upon latitude for any of the terrestrial bodies in this study. Nevertheless, by neglecting the expected latitudinal variations of the cratering rate, systematic errors of 20-30% in the age of planetary surfaces could exist between equatorial and polar regions when using the crater chronology method.     

Magnetism and thermal evolution of the terrestrial planets

Of the terrestrial planets, Earth and probably Mercury possess substantial intrinsic magnetic fields generated by core dynamos, while Venus and Mars apparently lack such fields. Thermal histories are calculated for these planets and are found to admit several possible present states, including those which suggest simple explanations for the observations; whule the cores of Earth and Mercury are continuing to freeze, the cores of Venus and Mars may still be completely liquid. The models assume whole mantle convection, which is parameterized by a simple Nusselt-Rayleigh number relation and dictates the rate at which heat escapes from the core. It is found that completely fluid cores, devoid of intrinsic heat sources, are not likely to sustain thermal convection for the age of the solar system but cool to a subadiabatic, conductive state that can not maintain a dynamo. Planets which nucleate an inner core continue to sustain a dynamo because of the gravitational energy release and chemically driven convection that accompany inner core growth. The absence of a significant inner core can arise in Venus because of its slightly higher temperature and lower central pressure relative to Earth, while a Martian core avoids the onset of freezing if the abundance of sulfur in the core is ?15% by mass. All of the models presented assume that (I) core dynamos are driven by thermal and/or chemical convection; (ii) radiogenic heat production is confined to the mantle; (iii) mantle and core cool from initially hot states which are at the solidus and superliquidus, respectively; and (iv) any inner core excludes the light alloying material (sulfur or oxygen) which then mixes uniformly upward through the outer core. The models include realistic pressure and composition-dependent freezing curves for the core, and material parameters are chosen so that the correct present-day values of heat outflow, upper mantle temperature and viscosity, and inner core radius are obtained for the earth. It is found that Venus and Mars may have once had dynamos maintained by thermal convection alone. Earth may have had a completely fluid core and a dynamo maintained by thermal convection for the first 2 to 3 by, but an inner core nucleates and the dynamo energetics are subsequently dominated by gravitational energy release. Complete freezing of the Mercurian core is prohibited if it contains even a small amount of sulfur, and a dynamo can be maintained by chemical convection in a thin, fluid shell.