Alkali elements in the Earth's core: Evidence from enstatite meteorites

Abstract— The abundances of alkali elements in the Earth's core are predicted by assuming that accretion of the Earth started from material similar in composition to enstatite chondrites and that enstatite achondrites (aubrites) provide a natural laboratory to study core-mantle differentiation under extremely reducing conditions. If core formation on the aubrite parent body is comparable with core formation on the early Earth, it is found that 2600 (±1000) ppm Na, 550 (±260) ppm K, 3.4 (±2.1) ppm Rb, and 0.31 (±0.24) ppm Cs can reside in the Earth's core. The alkali-element abundances are consistent with those predicted by independent estimates based on nebula condensation calculations and heat flow data.     

The Earth's core formation due to the Rayleigh-Taylor instability

The recent theories of planetary formation lead to a gravitationally unstable structure of the proto-Earth in the accretion stage, which is composed of three layers: an innermost undifferentiated solid core, an intermediate metal-melt layer, and an outermost silicate-melt layer. Taking this configuration as an initial state, we investigate the Earth's core formation due to the Rayleigh-Taylor instability by using the quantitative results on the instability in a self-gravitating fluid sphere obtained from another paper (S. Ida, Y. Nakagawa, and K. Nakagawa, submitted). We find that the instability occurs through the translational mode on a time scale of about 10 hr if the thickness of the metal-melt layer ⪆1 km. This leads to the conclusion that the Earth's core began to form through the translation of the innermost undifferentiated solid core as soon as the outer layer was melted and differentiated in the late accretion stage. In addition, we examine the rotational effects of the instability; the translation occurs most often along the rotational axis. But this preference is weak, since the rotational energy is small compared to the gravitational one.     

A new investigation of the secular drift of the Earth's pole

A new investigation of the secular drift of the Earth's pole was made based on nine long series of latitude observations. This led to the following conclusions: 1) During this century, the Earth's pole has been moving approximately along meridian 70 °W at a mean rate of 0.0016″/yr, much less than the 0.0035″/yr derived from the ILS sequence. 2) Relative to the North American Continent, the Ukiah Station located on the western shore of the U.S. shows a local drift of about 6 cm/yr toward north, in good agreement with the result from the new techniques. 3) Relative to the Europe-Asia plate, the whole North American Continent shows a northward drift of about 8 cm/yr. The Mediterranean shows a similar drift of about 6 cm/yr. 4) Three of five ILS stations, Ukiah, Gaithersberg and Carloforte, show significant drifts. Therefore, the Conventional International Origin (CIO), which is defined by the mean latitudes at 1903.0 of the five stations, is far from being fixed on the Earth's surface, and is not suitable as the origin of the Earth Reference System.     

Source regions and timescales for the delivery of water to the Earth

Abstract— In the primordial solar system, the most plausible sources of the water accreted by the Earth were in the outer asteroid belt, in the giant planet regions, and in the Kuiper Belt. We investigate the implications on the origin of Earth's water of dynamical models of primordial evolution of solar system bodies and check them with respect to chemical constraints. We find that it is plausible that the Earth accreted water all along its formation, from the early phases when the solar nebula was still present to the late stages of gas‐free sweepup of scattered planetesimals. Asteroids and the comets from the Jupiter‐Saturn region were the first water deliverers, when the Earth was less than half its present mass. The bulk of the water presently on Earth was carried by a few planetary embryos, originally formed in the outer asteroid belt and accreted by the Earth at the final stage of its formation. Finally, a late veneer, accounting for at most 10% of the present water mass, occurred due to comets from the Uranus‐Neptune region and from the Kuiper Belt. The net result of accretion from these several reservoirs is that the water on Earth had essentially the D/H ratio typical of the water condensed in the outer asteroid belt. This is in agreement with the observation that the D/H ratio in the oceans is very close to the mean value of the D/H ratio of the water inclusions in carbonaceous chondrites.     

Theoretische Betrachtungen zum Verhalten des Magnetfeldes in einem sphärischen Erdmodell

The theoreticl treatment of several geophysical problems presupposes the solution of field equations of the magnetic field in the Earth's mantle. The field equations are given in a scalar form for a spherical model of the Earth. It will be shown that analytical solutions are possible in all cases. The boundary conditions are discussed with regard to the dynamo process in the Earth's core and the existence of a field representation, which is investigated on the Earth's surface. The question is discussed, to what extend the mantle's field is given by this field representation, when some special assumptions about the Earth's model are made.     

Speculations on the origin of the magnetic field of Mercury

The intrinsic magnetic field of Mercury may be generated by a dynamo process in a liquid core, despite the planet's slow rotation rate. It is argued that, provided the core of Mercury is partially liquid, it will be dynamically very similar to that of the Earth.     

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

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

Tidal-friction theory of the Earth-Moon system

The standard discussion of tidal friction in the Earth-Moon system has been that given by Jeffreys in successive editions ofThe Earth over the past several decades. It is herein shown to contain several erros vitiating its results. The dynamical equation utilised for finding the rate of change of angular velocity of the Earth fails to take account of the fact that the moment of inertia of the Earth may be changing with time, and all subsequent equations which depend on this are incorrect as a result. Simple equations have been left unsolved that ought to have been solved, and the alleged numerical conclusions in no way follow from the values set down initially for the observed apparent secular accelerations of the Moon and Sun.The revised dynamical equations are shown to enable the lunar and solar tidal couples to conform to theory, and may imply that the moment of inertia of the Earth is decreasing at a non-negligible rate. Recognition of this is the key to the whole problem. The only available hypothesis providing adequate contraction is that following from the phase-change theory of the nature of the terrestrial core, and the value of the rate of decrease of moment of inertia calculated from this is in close agreement with that implied by modern improved values of the secular accelerations.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 Accademia Nazionale del Lincei in Rome, Italy.     

Evidence in a glassy cosmic spherule from Antarctica for grazing incidence encounters with the Earth's atmosphere

Abstract— Cosmic dust accreted by the Earth can be extensively reprocessed during atmospheric encounters. The textures and compositions of reprocessed material provide important constraints by which the processes affecting extraterrestrial matter in the Earth's atmosphere can be better understood. Here we report results on an unusual Antarctic glassy cosmic spherule that demonstrates strong textural evidence for at least two grazing incidence encounters with the Earth's atmosphere prior to final reentry. The particle consists of a central glassy core with four peripheral glass lobes that transect a silicate particle rim. The texture of the particle confirms previous theoretical speculations that some high velocity, low incidence angle interplanetary particles experience numerous encounters with the Earth's atmosphere and also indicates that micrometeorites demonstrating multiple melting episodes should be interpreted with caution.     

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.     

The periodic variations of the core drift rate: global and zonal motions (Mitteilung des Zentralinstituts für Physik der Erde,Nr. 1746)

Toroidal zonal motions at the top of the Earth's core were computed from the observed secular variation and investigated with regard to their time dependence. Previously derived results for a pure westward drifting core could be re-examined. Additionally, the well-known 66.7 years period was found to be an oscillation of the zonal velocity field of third degree. With respect to periodic constituents, the total magnetic core-mantle coupling torque according to the zonal motions is comparable with that derived for a pure westward drifting core. Some differences in period lengthes and amplitudes do not remove previously stated differences between the spectra of the magnetic and mechanical torques on principle.     

On some aspects of the albedo effect application to the ERS-1 satellite

Some aspects of the perturbative influence of radiation reflected by the Earth's surface on the motion of an artificial satellite are discussed. We concentrate on consequences of the extreme models with anisotropic reflection on the Earth's surface (specular reflection, clouds with anisotropic phase function). The possible effects of Lála's modification of the Earth's albedo nominal value are investigated. The role of the satellite surface optical properties is pointed out in the context of the albedo effect. All mentioned models are purely numerical. The whole message of the paper can be summarized in the following items

-It is very doubtful that the 10^?8 ÷ 10^?9 m s^?2 level is reached when determining the perturbing accelerations caused by the albedo effect in the case of the ERS-1 satellite due to poorly defined optical characteristics of the Earth's atmosphere, the Earth and the satellite's surface.

-In the general case this albedo effect uncertainty level is about 50% with respect to the averaged values, and probably as high as 100% with respect to the instantaneous values of the perturbing accelerations.

     

Third-order secular Solution of the variational equations of motion of a satellite in orbit around a non-spherical planet

We constructed an analytical theory of satellite motion up to the third order relative to the oblateness parameter of the Earth (J ₂). Equations of secular variations was developed for the first three orbital elements (a, e, i) of an artificial satellite. The secular variations are solved in a closed form.     

Fission origin of the Moon: Cause and timing

A new scenario is offered for the origin of the Moon. It is assumed that the Earth formed initially with about the maximum amount of angular momentum consistent with dynamical stability. This state is approximated by the secularly unstable Maclaurin spheroids (highly flattened, hamburger-shaped bodies). It is shown that the Earth cannot depart from this state at a resonable rate as long as its viscosity is in the range of liquid rock. Since core formation supplies about 1600 kJ kg^?1 the Earth will not leave this state until core formation is complete. When cooling produces a rise in viscosity, the Earth will necessarily evolve along a path which is approximated by the Riemann ellipsoids (which have rapid internal motion). The evolution is toward a Jacobi ellipsoid, but it is intercepted by the development of a third-harmonic (pearshaped) instability, which is catastrophic and leads to fission. The process of fission itself may be fundamentally analogous to the breaking of a wave in water. We cannot exclude the possibility that some other planets evolved similarly.     

Meteor storm evidence against the recent formation of lunar crater Giordano Bruno

Abstract— It has been suggested that the formation of the 22 km diameter lunar crater Giordano Bruno was witnessed in June 1178 A.D. To date, this hypothesis has not been well tested. Such an impact on the Earth would be “civilization threatening”. Previous studies have shown that the formation of Giordano Bruno would lead to the arrival of 10 million tonnes of ejecta in the Earth's atmosphere in the following week. I calculate that this would cause a week‐long meteor storm potentially comparable to the peak of the 1966 Leonids storm. The lack of any known historical records of such a storm is evidence against the recent formation of Giordano Bruno. Other tests of the hypothesis are also discussed, with emphasis on the lack of corroborating evidence for a very recent formation of the crater.     

Secular variation of the obliquity of the ecliptic from a core-mantle coupling

The Earth is assumed to consist of a rigid core and a rigid mantle coupled by a non-isotropic friction. It is shown that if the core rotates slightly faster than the mantle, then the observed secular change of the obliquity of the ecliptic can be accounted for without giving rise to an unacceptably high rate of spin-down of the Earth.     

Satellite motion in a non-singular gravitational potential

We study the effects of a non-singular gravitational potential on satellite orbits by deriving the corresponding time rates of change of its orbital elements. This is achieved by expanding the non-singular potential into power series up to second order. This series contains three terms, the first been the Newtonian potential and the other two, here R ₁ (first order term) and R ₂ (second order term), express deviations of the singular potential from the Newtonian. These deviations from the Newtonian potential are taken as disturbing potential terms in the Lagrange planetary equations that provide the time rates of change of the orbital elements of a satellite in a non-singular gravitational field. We split these effects into secular, low and high frequency components and we evaluate them numerically using the low Earth orbiting mission Gravity Recovery and Climate Experiment (GRACE). We show that the secular effect of the second-order disturbing term R ₂ on the perigee and the mean anomaly are 4″.307×10⁻⁹/a, and −2″.533×10⁻¹⁵/a, respectively. These effects are far too small and most likely cannot easily be observed with today’s technology. Numerical evaluation of the low and high frequency effects of the disturbing term R ₂ on low Earth orbiters like GRACE are very small and undetectable by current observational means.     

Meteorites from the asteroid 6 Hebe

We have numerically integrated the orbits of 18 fictitious fragments ejected from the asteroid 6 Hebe, an S-type object about 200km across which is located very close to theg=g ₆ (orv ₆) secular resonance at a semimajor axis of 2.425AU and a (proper) inclination of 15° .0. A realistic ejection velocity distribution, with most fragments escaping at relative speeds of a few hundredsm/s, has been assumed. In four cases we have found that the resonance pumps up the orbital eccentricity of the fragments to values >0.6, which result into Earth-crossing, within a time span of 1Myr; subsequent close encounters with the Earth cause strongly chaotic orbital evolution. The closest Earth and Mars encounters recorded in our integration occur at miss distances of a few thousandths ofAU, implying collision lifetimes <10⁹ yr. Some other fragments affected by the secular resonance become Mars-crossers but not Earth-crossers over the integration time span. Two bodies are injected into the 3 : 1 mean motion resonance with Jupiter, and also display macroscopically chaotic behaviour leading to Earth-crossing. 6 Hebe is the first asteroid for which a realistic collisional/dynamical evolutionroute to generate meteorites has been fully demonstrated. It may be the parent body of one of the ordinary chondrite classes.     

50-day Oscillation of Length-of-day Change

Variations of Earth’s rotation rate (length-of-day, LOD) occur over a wide range of time scales from a few hours to the geological age. Studies showed that the 50-day fluctuation exists in LOD change. In the present paper, the authors use wavelet technique to study the 50-day oscillation in LOD series. Temporal variations of the oscillation are presented in this work. After analyzing the axial component of atmospheric angular momentum (AAM) and oceanic angular momentum (OAM), the 50-day periodic signal is also found in atmospheric and oceanic motion with remarkable time-variation. Meanwhile, the 50-day oscillation of the axial AAM is in good consistence with that of LOD change. This suggests that the 50-day oscillation of LOD change is mainly excited by the axial AAM. Possible origin of the oscillation for Earth system is discussed in the end of this paper.     

From planetesimals to terrestrial planets: N-body simulations including the effects of nebular gas and giant planets

We present results from a suite of N-body simulations that follow the formation and accretion history of the terrestrial planets using a new parallel treecode that we have developed. We initially place 2000 equal size planetesimals between 0.5 and 4.0 AU and the collisional growth is followed until the completion of planetary accretion (>100 Myr). A total of 64 simulations were carried out to explore sensitivity to the key parameters and initial conditions. All the important effect of gas in laminar disks are taken into account: the aerodynamic gas drag, the disk-planet interaction including Type I migration, and the global disk potential which causes inward migration of secular resonances as the gas dissipates. We vary the initial total mass and spatial distribution of the planetesimals, the time scale of dissipation of nebular gas (which dissipates uniformly in space and exponentially in time), and orbits of Jupiter and Saturn. We end up with 1-5 planets in the terrestrial region. In order to maintain sufficient mass in this region in the presence of Type I migration, the time scale of gas dissipation needs to be 1-2 Myr. The final configurations and collisional histories strongly depend on the orbital eccentricity of Jupiter. If today’s eccentricity of Jupiter is used, then most of bodies in the asteroidal region are swept up within the terrestrial region owing to the inward migration of the secular resonance, and giant impacts between protoplanets occur most commonly around 10 Myr. If the orbital eccentricity of Jupiter is close to zero, as suggested in the Nice model, the effect of the secular resonance is negligible and a large amount of mass stays for a long period of time in the asteroidal region. With a circular orbit for Jupiter, giant impacts usually occur around 100 Myr, consistent with the accretion time scale indicated from isotope records. However, we inevitably have an Earth size planet at around 2 AU in this case. It is very difficult to obtain spatially concentrated terrestrial planets together with very late giant impacts, as long as we include all the above effects of gas and assume initial disks similar to the minimum mass solar nebular.