Earth Core

Earth's Core

David Loper , in Encyclopedia of Physical Science and Technology (Third Edition), 2003

III Evolution of the Core

III.A Initial Formation

The existence of stony and iron meteorites provides strong evidence that planetary cores, in general, and earth's core, in particular, formed by separation of less dense silicate phases and more dense metallic phases as they accreted during the formation of the solar system some 4.5 billion years ago. This was a strongly exothermic process; the gravitational potential energy released by this process is sufficient to heat earth by some 2000   °. It follows that earth likely was very hot soon after its formation and has been cooling since then.

III.B Formation and Growth of Inner Core

It is very likely that the inner core has grown by solidification from the outer core as earth has cooled during the past 4.5 billion years and that solidification and growth is continuing. The inner core may well be a relatively recent feature; in some models of the evolution of the core it begins to grow roughly 2 billion years ago.

The core is cooled by transfer of heat to the mantle, and the rate of cooling is largely controlled by the thermal structure of the lowermost mantle (the D′′ layer). The outer core is coolest at the top, near the CMB, but freezing proceeds from the center outward because the increase of the freezing (liquidus) temperature with pressure is greater than the adiabatic gradient:

d T L / d p d T A / d p .

As the inner core grows, both latent heat and buoyant material are released at the base of the outer core. These work in parallel to drive convective motions in the outer core.

Solidification of outer-core material at the ICB is similar to the metallurgical process of unidirectional solidification of molten metallic alloys; the mathematical model is called a Stefan problem. The simplest solution to the Stefan problem involves the steady advance of a planar solidification front into a quiescent liquid. This simple solution has two known forms of instability. If the freezing process involves a change of composition (see Fig. 2) and the material rejected by the solid phase is buoyant compared with the parent liquid, the static state is prone to a compositional convective instability. It is very likely that this instability occurs in the outer core and that the resulting convective motions participate in the dynamo process which sustains earth's magnetic field.

Solidification of an alloy at a planar interface is prone to a second, morphological instability. The material rejected by the solid phase accumulates on the liquid side of the freezing interface, depressing the liquidus and making that liquid compositionally (or constitutionally) supercooled. This causes the flat freezing interface to be unstable and become convoluted. These convolutions can become extreme, forming a so-called mushy zone. Again, it is very likely that this instability occurs in the core and that the inner core is, in fact, an intimate mixture of solid and liquid. Dynamic processes cause the fraction of liquid phase to be small, so that the inner core acts structurally as a solid even though, thermodynamically, it behaves as a solid-liquid mixture.

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The Mantle and Core

W.F. McDonough , in Treatise on Geochemistry, 2003

2.15.1 Introduction

The remote setting of the Earth's core tests our ability to assess its physical and chemical characteristics. Extending out to half an Earth radii, the metallic core constitutes a sixth of the planet's volume and a third of its mass (see Table 1 for physical properties of the Earth's core). The boundary between the silicate mantle and the core (CMB) is remarkable in that it is a zone of greatest contrast in Earth properties. The density increase across this boundary represents a greater contrast than across the crust-ocean surface. The Earth's gravitational acceleration reaches a maximum (10.7 m s−2) at the CMB and this boundary is also the site of the greatest temperature gradient in the Earth. (The temperature at the base of the mantle (∼2,900 °C) is not well established, and that at the top of the inner core is even less securely known (∼3,500–4,500 °C).) The pressure range throughout the core (i.e., 136 GPa to >360 GPa) makes recreating environmental conditions in most experimental labs impossible, excepting a few diamond anvil facilities or those with high-powered, shock-melting guns (see Chapter 2.14). Thus, our understanding of the core is based on very few pieces of direct evidence and many fragments of indirect observations. Direct evidence comes from seismology, geodesy, geo- and paleomagnetism, and, relatively recently isotope geochemistry (see Section 2.15.6). Indirect evidence comes from geochemistry, cosmochemistry, and meteoritics; further constraints on the core system are gained from studies in experimental petrology, mineral physics, ab initio calculations, and evaluations of the Earth's energy budget (e.g., geodynamo calculations, core crystallization, heat flow across the core–mantle boundary). Figure 1 provides a synopsis of research on the Earth's core, and the relative relationship between disciplines. Feedback loops between all of these disciplines refine other's understanding of the Earth's core.

Table 1. Physical properties of the Earth's core

Units Refs.
Mass
  Earth 5.9736E+24 kg 1
  Inner core 9.675E+22 kg 1
  Outer core 1.835E+24 kg 1
  Core 1.932E+24 kg 1
  Mantle 4.043E+24 kg 1
  Inner core to core (%) 5.0%
  Core to Earth (%) 32.3%
Depth
  Core–mantle boundary 3,483±5 km 2
  Inner–outer core boundary 1,220±10 km 2
  Mean radius of the Earth 6,371.01±0.02 km 1
Volume relative to planet
  Inner core 7.606E+09(0.7%) km3
  Inner core relative to the bulk core 4.3%
  Outer core 1.694E+11(15.6%) km3
  Bulk core 1.770E+11(16.3%) km3
  Silicate earth 9.138E+11(84%) km3
  Earth 1.083E+12 km3
Moment of inertia constants
  Earth mean moment of inertia (I) 0.3299765 Ma 2 1
  Earth mean moment of inertia (I) 0.3307144 M R 0 2 1
  Mantle: I m/Ma 2 0.29215 Ma 2 1
  Fluid core: I f/Ma 2 0.03757 Ma 2 1
  Inner core: I ic/Ma 2 2.35E−4 Ma 2 1
  Core: I f + ic / M f + ic a f 2 0.392 Ma 2 1

1—Yoder (1995), 2—Masters and Shearer (1995). M is the Earth's mass, a is the Earth's equatorial radius, R 0 is the radius for an oblate spheroidal Earth, I m is the moment of inertia for the mantle, I f is the moment of inertia for the outer (fluid) core, I ic is the moment of inertia for the inner core, and I f + ic / M f + ic a f 2 is the mean moment of inertia for the core.

Figure 1. The relative relationship between disciplines involved in research on the Earth's core and the nature of data and information that come from these various investigations. Studies listed in the upper row yield direct evidence on properties of the core. Those in the middle row yield indirect evidence on the composition of the Earth's core, whereas findings from disciplines listed on the bottom row provide descriptions of the state conditions for the core and its formation.

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Renewable Energy, Taxonomic Overview

Daniel M. Kammen , in Encyclopedia of Energy, 2004

6.1 Introduction

Geothermal energy, the natural heat within the earth, arises from the ancient heat remaining in Earth's core, from friction where continental plates slide beneath each other and from the decay of radioactive elements that occur naturally in small amounts in all rocks. The amount of geothermal energy is enormous. Scientists estimate that just 1% of the heat contained in the uppermost 10 km of Earth's crust is equivalent to 500 times the energy contained in all of Earth's oil and gas resources. Yet, despite the fact that this heat is present in practically inexhaustible quantities, it is unevenly distributed, seldom concentrated, and often at depths too great to be exploited industrially and economically.

Geothermal energy has been produced commercially for 70 years for both electricity generation and direct use; its use has increased rapidly during the past three decades. From 1975 to 1995, the growth rates worldwide for electricity generation and direct use of geothermal energy were about 9%/year and about 6%/year, respectively. In 1997, geothermal resources had been identified in over 80 countries and there were quantified records of geothermal utilization in at least 46 countries.

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Geomagnetism

C. Constable , in Treatise on Geophysics, 2007

5.09.6.1 Jerks, Drifts, and Waves

The westward drift of geomagnetic features noted by Halley during the seventeenth century is widely interpreted to reflect aspects of the fluid motion at the surface of Earth's core (Bullard et al., 1950; Yukutake and Tachinaka, 1969). Two possible dynamical sources for these effects have received attention – the first discussed by Braginskiy (1972, 1974) is the superposition of propagating MAC (magnetic, Archimedean, Coriolis) waves at the core surface resulting in phase propagation of the field, and reflecting a balance among Lorentz, Coriolis, and buoyancy forces; the second interpretation is that the drifts of the field reflect mean azimuthal flow at the core surface. Core surface flows have been mapped under various constraints about the field evolution in addition to the frozen flux approximation, which specifically requires that the magnetic field is advected with the material flow. Conservation of angular momentum also provides a firm theoretical foundation linking decadal geomagnetic secular variation to changes in the length of day (LOD). These changes are linked to torsional oscillations in the core fluid as it adjusts to small departures from the Taylor state, and have been tied to the sharp accelerations in geomagnetic field records known as geomagnetic jerks (Bloxham et al., 2002). No such firm theoretical footing exists to link longer-term changes in LOD to millennial-scale core flows, as there is little justification for supposing that the core motions are without axial shear over these longer timescales. Nevertheless, Dumberry and Bloxham (2006) have made some substantial preliminary efforts to assess the contributions of millennial-scale geomagnetic field changes to the longer-term changes in LOD now documented back to 2700   BP (Stephenson and Morrison, 1984, 1995; Morrison and Stephenson, 2001).

Studies of regional westward drift in distinct paleomagnetic records are generally limited by inaccuracies in the assigned timescales for records that are separated by a few thousand kilometers or less (e.g., Lund, 1996). In more distant records the identification of the same magnetic features at different times has proved challenging, probably reflecting the temporal and spatial scales associated with westward drift. An assessment of drift in individual paleomagnetic records has often been made on the basis of the interpretation of Bauer (1895) plots, generally of declination versus inclination centered on the axial dipole or mean field direction at a site. Occasionally the path traced by the VGP is used. Under Runcorn's (1959) rule clockwise motion is taken to represent westward drift of an underlying magnetic source, although it is well known that this interpretation is nonunique (e.g., Skiles, 1970; Dodson, 1979). Nevertheless the general idea can be supported by an analysis of the GUFM historical field model shown in Figure 17 . Regional VGP trajectories mainly show clockwise motion, and the motion is largest in amplitude in the regions where westward drift of the magnetic field is most pronounced. Local application of Runcorn's Rule has led to numerous reports of eastward drift in millennial-scale magnetic records (e.g., Constable and McElhinny, 1985; Snowball and Sandgren, 2002).

Figure 17. VGP trajectories calculated on a 15° geographic grid using field predictions from GUFM. Pluses indicate the geographic location for which the VGP is calculated, and form the center for each local VGP projection with scale as at upper left, where 70°   N is the inner circle, and 50°   N the outer one. Paths are for the time interval AD 1590–1990 with arrowheads indicating the position in 1990. Note the broad clockwise looping in the Atlantic/African region.

Gallet et al. (2003) have recently drawn attention to coincident features in the western European archeomagnetic directional secular variation curve and archeomagnetic intensity changes in France and the Middle East. Changes in curvature in the directional variations on Bauer plots are inferred to occur at the same time as local maxima in intensity variations. They call these coincident features archeomagnetic jerks, and raise questions about their regional versus global significance and whether such relationships are a general characteristic of short-term geomagnetic field variations. It should be noted that despite the similarity in terminology they should not be thought of as similar to the geomagnetic jerks observed by direct observations for the most recent century. Instead, as outlined below these archeomagnetic jerks seem to be associated with broad regional changes in directions of drift and wave motions as recently shown in a global assessment by Dumberry and Finlay (2007).

The advent of time-varying millennial-scale geomagnetic models enables analyses of drift to move from a regional to a global context, and there have been two recent attempts using CALS7K.2 to map the predominant direction of drift (Dumberry and Finlay, 2007), and to determine whether oscillating mean azimuthal flows are the predominant cause of the observed drift (Dumberry and Bloxham, 2006). Dumberry and Finlay (2007) have used the global time-varying CALS7K.2 model to conduct a global study of episodes of eastward and westward drift during the past 3   ky. They find both eastward and westward motion at mid-to-high latitudes in the Northern Hemisphere, corresponding to displacements and changes in the two major quasi-stationary high-latitude magnetic flux patches. Poor resolution in the model may prevent similar motions from being discovered in the Southern Hemisphere. They note that the direction changes are associated with the times of the archeomagnetic jerks identified by Gallet et al. (2003) – these direction changes are moderately rapid (centennial timescales) but there is no evidence for a sharp change in the geomagnetic field. Dumberry and Bloxham (2006) showed that the observed drift is consistent with the motions being caused by advection of magnetic field features by azimuthal flows, although it is worth noting that their arguments clearly spell out that this is a plausible rather than a unique interpretation of the observations. The quality of the CALS7K.2 model makes it difficult to determine whether westward drift is a persistent feature of the field for 0–3   ka, but it does seem that the longitudinal region in which it is seen has remained fixed, lending support to the idea that thermal core–mantle interactions may produce both the high-latitude flux lobes, and a regime that produces westward drift in the Atlantic hemisphere. However, the westward drift seen in the millennial-scale models should be distinguished from that seen in the modern field which tends to be dominated by rapid motions in equatorial regions – these cannot be resolved with the limited temporal and geographical resolution achieved in the current time-varying global paleomagnetic models.

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DETERMINATION OF PRESSURE-DEPENDENT PHASE DIAGRAMS

Surendra K. Saxena , Yanbin Wang , in Methods for Phase Diagram Determination, 2007

6 PHASE DIAGRAMS USING DAC

Geoscientists have used high-pressure techniques to understand the nature of earth materials at high pressures and temperatures. Iron is considered to be the main component of Earth's core and therefore its high-pressure/temperature phase diagram has been a topic of active research. The LVP results were further advanced to ultra high pressure and temperature by laser-heated DAC. Recent reviews of these results have been done by Shen and Heinz [70] and Boehler [71].

The following information from Shen (pers. comm.) gives a modern view of the iron phase diagram. At ambient pressure, the stable phase is α-Fe with a bodycentered cubic (bcc) structure. At high pressure it transforms to ɛ-Fe with hexagonalclose-packed (hcp) structure. At high temperature there is a large stability field for γ-Fe with face-centered cubic (fcc) structure. In several X-ray data particularly those obtained by using external heating a double hcp structure of iron was noted (Fig. 13.22). In laser-heated samples, this has never been found [74,75].

Figure 13.22. X-ray data on phase relations in iron. Only data collected with in situ heating are shown. Open diamonds – fcc; squares – hcp; open circles – fcc (Funamori et al. [78]); circles with plus – fcc/hcp transition from Dubrovinsky et al. [44]; open triangles – β and corresponding hcp phase, respectively. The latter is obtained after cooling to the temperature shown.

For the melting curve, there is a converging consensus at pressures below 60 GPa, reflected by a narrow uncertainty range in Fig. 13.23. As pressure increases, uncertainties in phase boundaries, including the melting curve, become large as shown by wide bands in Fig. 13.23. The width of the bands represents the scatter in literature data from recent years. Factors causing these uncertainties include those in pressure determinations (neglecting thermal pressure, different EOS, and/or different standard materials), in temperature determinations (large temperature gradient and temporal variation, chromatic aberration in optics), and in sample characterizations (different melting criteria, transition kinetics).

Figure 13.23. Iron phase diagram. Shaded areas represent the range of literature values in recent years with static DAC experiments. Symbols are shock-wave data: square – Ahrens et al. [79], diamonds – Brown and McQueen [76], circle – Nguyen and Holmes [77]. Brown and McQueen's point at 200 GPa was interpreted as a solid–solid transition. All other points are referred as melting.

Uncertainties in the melting curve and the γ–ɛ transition lead to significant variations in the location of γ–ɛ–liquid triple point. Knowledge of its location is important because it is the starting point used for extrapolation of the melting curve of ɛ-Fe to core pressures. As shown in Fig. 13.23, the slope of γ–ɛ transition ranges from 25 to 40K/GPa, placing the triple point between 60 and 100 GPa. Such large uncertainties in the slope of the γ–ɛ transition mainly arise from the coexisting nature of these two phases in the pressure-temperature range, causing difficulties in identifying the boundary. The uncertainties are also contributed by the pressure–temperature determination associated with the use of different standard materials and/or different EOS.

The melting data for iron above the triple point are scarce and scattered, reflecting the difficulty level of such experiment. It appears that the early DAC data [72,73] represent a lower bound of the melting curve in this region. The later experimental data falls at higher melting temperatures [74,75]. The shock-wave data [76,77] lie close to the upper bound. Extrapolating the data to the inner core boundary, the melting temperature of iron is between 4800K and 6000K at 330 GPa.

While the use of the LVP in constructing the phase diagrams is well established, the DAC technique has resulted in only partial data. Excellent examples of such work are the studies conducted on the phase MgSiO3-perovskite [80] and magnesiowustite [81]. The geo-scientific interest on these phases is enormous because of their occurrence in Earth's mantle. The difficulty in obtaining such data, which could be useful in creating thermodynamic database, is due to the difficulty of conducting the in situ high-pressure, high-temperature experiments. As discussed elsewhere, long time sustained heating in a DAC reaching temperatures in excess of 1500K can only be achieved with double-side laser heating. Such facilities are rare.

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Radiation Sources and Detectors

H. Yamada , ... M. Haque , in Comprehensive Biomedical Physics, 2014

8.04.7.2 Study of Materials at High Pressures

The study of materials at high pressures is currently experiencing an unprecedented surge of breakthroughs that were deemed inconceivable only a few years ago. With the development of the ultrahigh-pressure diamond cell technique, it is now possible to reach pressures equivalent to the Earth's core (i.e., 300   GPa or 3   Mbar). Study of the effect of pressure on materials is fundamental to a range of problems spanning condensed-matter physics and chemistry, Earth and planetary science, and materials science and technology. Infrared optical spectroscopy provides information on pressure-induced changes in electronic excitations, including crystal field, charge transfer, and excitonic spectra of insulators and semiconductors, interband and intraband transitions in metals, novel transitions such as pressure-induced metallization, and pressure dependence of low-energy collective excitations, such as phonon modes.

The technique has been shown to be relevant especially in the far-infrared region, where the low brilliance of conventional techniques strongly limits the measurements with diamond anvil cells. There, the intense flux of synchrotron beam increases the brightness of the collimated beam by two to three orders of magnitude over conventional globar source. Examples of important breakthrough made possible by the use of IRSR concern the study of dense hydrogen (>   200   GPa) where many unexpected results have been revealed. The theoretically predicted molecular atomic transition of H2O ice to the symmetrical hydrogen-bonded structure identified by means of infrared transmission is another demonstration of the strong potential of this class of experiments (Mao et al., 1984; Miura et al., 2007, 2010; Nanba, 1989).

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SOLAR SYSTEM | Mars

M.R. Walter , ... S.A. Chamberlain , in Encyclopedia of Geology, 2005

Interior of Mars

Some of the physical characteristics of Mars are listed in Table 1. An interpretation of the interior of Mars is presented at Figure 1. The interior structure of Earth is well constrained due to our ability to measure seismic reflections throughout the mantle and into Earth's core. At present, without similar seismic information on Mars, it is possible only to postulate what the Martian interior may be like – for example, does it have a solid core, or a partly liquid core like Earth has? The current view is that Mars has a liquid outer and a solid inner core with a radius of approximately 1700   km. The resultant reduced mantle depth compared to Earth implies that the Martian interior is likely to have cooled substantially faster than Earth did, and convection of the mantle, if it ever occured, may now have slowed or ceased. This implies that volcanism on the Martian surface is less likely today, and may provide an explanation for the current lack of a strong magnetic field on Mars.

Table 1. Physical characteristics of Earth and Mars

Characteristic Mars Earth
Orbit (million km) 207–249 147–152
Year (in Earth days) 687 356.25
Day (hours) 24.6 23.9
Mean radius (km) 3390 6371
Core radius (km) ∼1700 3485
Average mantle depth (km) 1690 2886
Present obliquity to orbit (degrees) 25.19 23.45
Surface temperature variations (degrees C) −100 to +17 −82 to +54

Figure 1. An interpretation of the interior of Mars, showing the core, mantle, and crust. Image courtesy of Calvin J. Hamilton.

The Mars Global Surveyor orbiter did find enigmatic strong local magnetism in rocks of the southern highlands, but an extremely weak overall global magnetic field on Mars. The absence of crustal magnetism near large impact basins such as Hellas and Argyre implies cessation of internal dynamo action during the Early Noachian epoch (similar to 4   billion years ago). Although massive tectonic events most probably caused the formation of Valles Marineris, plate tectonics as is understood on Earth is unlikely to have played a major role in Martian geology. This implies that granites, which are dependent on recycling of the crust in the presence of water, are unlikely to form on Mars. To date, this has been borne out by spectroscopic investigations of the planet.

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Planets and Moons

F. Sohl , G. Schubert , in Treatise on Geophysics, 2007

10.02.8.1 General

Unlike Earth, Venus has no magnetic field (Russell, 1980; Phillips and Russell, 1987; Donahue and Russell, 1997). This is likely a consequence of the smaller pressure at the center of Venus compared with the pressure at the center of Earth's core. Because of the lower pressure, it is possible that Venus' core has not yet cooled sufficiently to initiate inner-core growth, but has cooled enough to prevent the operation of a purely thermally driven dynamo (Stevenson et al., 1983). Venus' lack of a magnetic field could also be due to its lack of plate tectonics, perhaps indicative of a sluggish form of mantle convection that is unable to cool the core efficiently enough to initiate thermal dynamo action (Nimmo and Stevenson, 2000). Still another possibility, though probably unlikely, is that the core of Venus has solidified enough that a dynamo cannot operate in the remaining liquid outer shell (Arkani-Hamed, 1994). Another consequence of Venus' slightly smaller size compared with Earth is that the perovskite–post-perovskite phase transition that occurs near the base of the Earth's mantle may not occur in Venus' mantle. If the core were to contain less light elements than the Earth's core, however, the Venusian mantle could be even deeper than that of the Earth.

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Dams, Dikes, and Levees

Robert B. Jansen , in Encyclopedia of Physical Science and Technology (Third Edition), 2003

V.C Rockfill Dams

Close coordination of design and construction engineers is also required throughout the development of a rockfill project. The ultimate foundation treatment and the optimum use of the available materials may have to be decided as the site conditions are exposed. The foundations for rockfills are usually sound rock, but at some projects dense glacial or alluvial deposits have served as a base for pervious embankment zones. The properties of the rock sources influence construction procedures. Since about 1960, the increasingly common use of vibratory rollers for compaction of rockfill in relatively thin layers has greatly improved the quality of this type of dam. Before that, the established practice was to dump and sluice the rockfill in high lifts without mechanical compaction, which resulted in embankments that were susceptible to excessive deformation and consequent cracking of the impervious elements (concrete face slab or earth core). In current projects, the common transport of rockfill to the damsite from the quarry or other source is by heavy dump trucks or bottom-dump wagons. Final placement and leveling of the rockfill layers are generally by bulldozer for the large sizes and often by grader for the finer material. The amount of water applied to the fill to enhance the compactive effort varies with the quality of the rockfill, the hardest and least friable rock requiring a minimum of sprinkling.

Illustrative of current U.S. practice in construction of large embankment dams is the Eastside Reservoir Project of the Metropolitan Water District of Southern California, completed in 1999. It comprises three earth-core rockfill dams with total volume of 84   million   m3 (110   million   yd3), 70% of which is rockfill. The project involved the largest available heavy equipment and machinery and set new records for handling earth and rock materials. Loading of the rock required five hydraulic shovels, each with 17   m3 (22   yd3) capacity, plus large front-end loaders. Dump trucks weighing up to 350   tons when full hauled the rock to the embankment, where it was spread by 100-ton bulldozers. The rockfill was compacted by smooth-drum vibratory rollers. The materials for the earth cores of the dams were excavated and moved by belt loaders at the source and hauled to the fill by 120-yd3 belly-dump trailers. The three dams required a total of about 10   million   yd3 of processed rock for filters and drains. The larger of two rock-crushing plants for this purpose had a maximum design capacity of 3200   tons per hour.

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String Theory and the Real World: From Particle Physics to Astrophysics

Thibault Damour , Marc Lilley , in Les Houches, 2008

3.2.3 Universality of free fall

The most recent limits on the deviation from the universality of free fall have been obtained by Eric's Adelberger's group [27]. In particular, they compared the acceleration of a Beryllium mass and a Copper one in the Earth's gravitational field and found

(3.13) ( Δ a a ) Be - Cu = ( - 1 ⋅ 9 ± 2 ⋅ 5 ) × 10 - 12 ,

where Δa = a Be-a Cu. Other limits exist, such as, for instance, the fractional difference in acceleration of earth-core-like (∼ iron) and moon-mantle-like (silica) bodies,

(3.14) ( Δ a a ) Earth - core - Moon - mantel = ( - 3 ⋅ 6 ± 5 ⋅ 0 ) × 10 - 13 ⋅

There are also excellent limits concerning celestial bodies. In particular the possible difference in the accelerations of the Earth and the Moon towards the Sun have been measured using laser ranging (with 5   mm accuracy) with retro-reflectors (corner cubes) placed on the Moon, giving the result [28]

(3.15) ( Δ a a ) Earth - Moon = ( - 1 ⋅ 0 ± 1 ⋅ 4 ) × 10 - 13 ⋅

One should, however, remember that only a fraction (∼ 1/3) of the Earth mass is made of iron, while the rest is mostly silica (which is the main material the Moon is made of). As, independently of the equivalence principle, silica must fall like silica, one looses a factor 3, so that the resulting bound on a possible violation of the equivalence principle is only around the 5 × 10-1 level, which is comparable to laboratory bounds.

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