Planetary core size: A seismological approach

A key parameter for understanding the geodynamics of a terrestrial planet is the size of its core. Numerical evaluation of 28 different interior structure models of Mercury, Venus, Earth, the Moon, and Mars suggests that there is an almost linear relationship between the core radius and the extent of the seismic P-wave core shadow. A scaling law is derived from a simple mantle density and velocity model that permits the interpretation of respective seismic measurements on terrestrial planetary bodies.     

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.     

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.     

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.     

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     

Giant impacts and the initiation of plate tectonics on terrestrial planets

Earth is the only terrestrial planet with present-day lithosphere recycling through plate tectonics. However, theoretical models of mantle convection based on general considerations find that all the terrestrial planets should be operating in the stagnant lid regime, in which the planets are one-plated and there is no lithosphere recycling. The stagnant lid regime is a consequence of the strong viscosity contrast across the convective layer, and therefore the upper lid (roughly equivalent to the lithosphere) must be sufficiently weakened in order to be mobilized. Here I propose that giant impacts could have provided the upper layer weakening required for surface recycling, and hence for plate tectonics, to initiate on the early Earth. Additionally, giant impacts originated lithosphere thickness and density differences, which might contribute to the initiation of subduction. Impacts are more energetic for Earth than for Mars, which could explain the likely early existence of plate tectonics on the Earth whereas Mars never had lithosphere recycling. On the other hand, convection on Mercury and the Moon might be sluggish or even inexistent, implying a reduced influence of giant impacts on their internal dynamics, whereas there is no record of the earliest geological history of Venus, which obscures any discussion on the influence of giant impacts on their internal dynamics.     

Disharmony of the spheres: Recent trends in planetary surface nomenclature

Inadvisable departures from tradition in naming newly mapped features on Mars, Mercury, and the Moon have been implemented and proposed since 1970. Functional need for place names also has become confused with cartographic convenience. Much of the resulting new nomenclature is neither unique, efficient, nor imaginative. The longstanding classical orientation in Solar System geography needs to be firmly reasserted. The Mädler scheme for designating smaller craters on the Moon should be retained and extended to the farside. Names of surface features on other bodies might best reflect the traditional connotations of planet and satellite names: for example, most crates on Mars would be named for mythical heroes and military personalities in ancient history, craters on Mercury might commemorate explorers or commercial luminaries, and features on Venus would bear the names of famous women.     

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.     

Characterization of terrestrial exoplanets based on the phase curves and albedos of Mercury, Venus and Mars

The empirically derived phase curves of terrestrial planets strongly distinguish between airless Mercury, cloud-covered Venus, and the intermediate case of Mars. The function for Mercury is steeply peaked near phase angle zero due to powerful backscattering from its surface, while that for Venus has 100 times less contrast and exhibits a brightness excess near 170° due to Mie scattering from droplets in the atmosphere. The phase curve of Mars falls between those of Mercury and Venus, and there are variations in luminosity due to the planet’s rotation, seasons, and atmospheric states. The phase function and geometric albedo of the Earth are estimated from published albedos values. The curves for Mercury, Venus and Mars are compared to that of the Earth as well as theoretical phase functions for giant planets. The parameters of these different phase functions can be used to characterize exoplanets.     

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.     

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.     

Atmospheric angular momentum variations of Earth, Mars and Venus at seasonal time scales

Atmospheric angular momentum variations of a planet are associated with the global atmospheric mass redistribution and the wind variability. The exchange of angular momentum between the fluid layers and the solid planet is the main cause for the variations of the planetary rotation at seasonal time scales. In the present study, we investigate the angular momentum variations of the Earth, Mars and Venus, using geodetic observations, output of state-of-the-art global circulation models as well as assimilated data. We discuss the similarities and differences in angular momentum variations, planetary rotation and angular momentum exchange for the three terrestrial planets. We show that the atmospheric angular momentum variations for Mars and Earth are mainly annual and semi-annual whereas they are expected to be “diurnal” on Venus. The wind terms have the largest contributions to the LOD changes of the Earth and Venus whereas the matter term is dominant on Mars due to the CO₂ sublimation/condensation. The corresponding LOD variations (ΔLOD) have similar amplitudes on Mars and Earth but are much larger on Venus, though more difficult to observe.     

Delivery of Water and Volatiles to the Terrestrial Planets and the Moon

From modeling the evolution of disks of planetesimals under the influence of planets, it has been shown that the mass of water delivered to the Earth from beyond Jupiter’s orbit could be comparable to the mass of terrestrial oceans. A considerable portion of the water could have been delivered to the Earth’s embryo, when its mass was smaller than the current mass of the Earth. While the Earth’s embryo mass was growing to half the current mass of the Earth, the mass of water delivered to the embryo could be near 30% of the total amount of water delivered to the Earth from the feeding zone of Jupiter and Saturn. Water of the terrestrial oceans could be a result of mixing the water from several sources with higher and lower D/H ratios. The mass of water delivered to Venus from beyond Jupiter’s orbit was almost the same as that for the Earth, if normalized to unit mass of the planet. The analogous per-unit mass of water delivered to Mars was two?three times as much as that for the Earth. The mass of water delivered to the Moon from beyond Jupiter’s orbit could be less than that for the Earth by a factor not more than 20.     

Rummaging through Earth's Attic for Remains of Ancient Life

We explore the likelihood that early remains of Earth, Mars, and Venus have been preserved on the Moon in high enough concentrations to motivate a search mission. During the Late Heavy Bombardment, the inner planets experienced frequent large impacts. Material ejected by these impacts near the escape velocity would have had the potential to land and be preserved on the surface of the Moon. Such ejecta could yield information on the geochemical and biological state of early Earth, Mars, and Venus. To determine whether the Moon has preserved enough ejecta to justify a search mission, we calculate the amount of terran material incident on the Moon over its history by considering the distribution of ejecta launched from the Earth by large impacts. In addition, we make analogous estimates for Mars and Venus. We find, for a well-mixed regolith, that the median surface abundance of terran material is roughly 7 ppm, corresponding to a mass of approximately 20,000 kg of terran material over a 10×10-square-km area. Over the same area, the amount of material transferred from Venus is 1-30 kg and material from Mars as much as 180 kg. Given that the amount of terran material is substantial, we estimate the fraction of this material surviving impact with intact geochemical and biological tracers.     

Evidence for convection in planetary interiors from first-order topography

Center of mass-center of figure offsets are known for the Earth, Moon, Mars and Venus. Such an offset requires a density distribution asymmetric about the center of mass. Observational evidence indicates that the terrestrial, lunar and Martian offsets result from crusts of variable thickness rather than lateral density inhomogeneities and that the thickness variations are more likely caused by internal convection than impact.Paper dedicated to Professor Harold C. Urey on the occasion of his 80th birthday on 29 April, 1973.     

Venus’ internal structure,temperature and core composition

The mass and radius of our closest neighbour Venus are only slightly smaller than those of the Earth indicating a similarity in composition. However, the lack of self-sustained internal magnetic field in Venus points to a difference in the core structure. The theory of tricritical phenomena has recently been used to study solidification at the high pressures and temperatures of the Earth, revealing how the Earth’s core works. This theoretical approach is here applied to Venus. While keeping Venus’ mantle density similar to the Earth’s, one obtains the gravitational acceleration g inside Venus, its moment of inertia factor, the size, pressure and density of its core, together with the planet’s temperature profile. Mainly due to the temperature difference between the core–mantle boundary and surface being 21% smaller than on the Earth, and the 11.5% smaller gravitational acceleration, Venus’ Rayleigh number Ra parameterizing mantle convection is only 54% of the Earth’s, offering a possible explanation for the present lack of plate tectonics on Venus. The theory as discussed predicts that Venus is molten at the centre, with temperature about 5200 K, and has 8 mol.% impurities there, slightly more impurities than in the Earth’s inner core boundary fluid. These impurities are likely to be a combination of MgO and MgSiO₃.     

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.     

The end of the iron-core age

The terrestrial planets aggregated essentially from small particles, to begin as solid cool bodies with the same general compositions, and there is no possibility of an iron-core developing within any of them at any stage. Their differing internal and surface properties receive ready explanation from their different masses which determine whether the pressures within are sufficient to bring about phase-changes. The claim that the terrestrial core can be identified by means of shockwave data as nickel-iron is based on theoretical misconception, whereas the actual seismic data establish an uncompressed-density value much lower than any such mixture could have. The onset of the Ramsey phase-change in the Earth takes the form of a rapid initial collapse to produce a large core in metallic state which thereafter continues to grow secularly as a result of radioactive heating and leads to reduction of surface-area at long last adequate to account for folded and thrusted mountain-building. The hypothesis implies a similar but retarded evolution for Venus. The Moon and Mars are too small in mass to have undergone the phase-change to a metallic core, and can have no resulting dipole field, nor can they develop terrestrial-type mountains. Effects resulting from a transition corresponding to the 20°-discontinuity will occur for Mars, including large-scale rifting at the surface, but will not occur on the Moon. Finally brief reference is made to subjective non-scientific factors associated with continued efforts to rely on the iron-core hypothesis despite its lack of any success in rendering the properties of the Earth explicable.Paper dedicated to Professor Harold C. Urey on the occasion of his 80th birthday on 29 April, 1973.     

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.