The giant impact hypothesis for Moon formation successfully explains the dynamic properties of the Earth-Moon system but remains challenged by the similarity of isotopic fingerprints of the terrestrial and lunar mantles. Moreover, recent geochemical evidence suggests that the Earth's mantle preserves ancient (or "primordial") heterogeneity that predates the Moon-forming giant impact. Using a new hydrodynamical method, we here show that Moon-forming giant impacts lead to a stratified starting condition for the evolution of the terrestrial mantle. The upper layer of the Earth is compositionally similar to the disk, out of which the Moon evolves, whereas the lower layer preserves proto-Earth characteristics. As long as this predicted compositional stratification can at least partially be preserved over the subsequent billions of years of Earth mantle convection, the compositional similarity between the Moon and the accessible Earth's mantle is a natural outcome of realistic and high-probability Moon-forming impact scenarios. The preservation of primordial heterogeneity in the modern Earth not only reconciles geochemical constraints but is also consistent with recent geophysical observations. Furthermore, for significant preservation of a proto-Earth reservoir, the bulk composition of the Earth-Moon system may be systematically shifted towards chondritic values.
To understand the evolution of the Moon, we numerically modeled mantle convection and magmatism in a two-dimensional polar rectangular mantle. Magmatism occurs as an upward permeable flow of magma generated by decompression melting through the convecting matrix. The mantle is assumed to be initially enriched in heat-producing elements (HPEs) and compositionally dense ilmenite-bearing cumulates (IBC) at its base. Here, we newly show that magma generation and migration play a crucial role in the calculated volcanic and radial expansion/contraction history. Magma is generated in the deep mantle b…
The evolution of the interior of stagnant-lid bodies is comparatively easier to model and predict with respect to the Earth's due to the absence of the large uncertainties associated with the physics of plate tectonics, its onset time and efficiency over the planet's history. Yet, the observational record for these bodies is both scarcer and sparser with respect to the Earth's. It is restricted to a limited number of samples and a variety of remote-sensing measurements of billions-of-years-old surfaces whose actual age is difficult to determine precisely. Combining these observations into a co…
The Earth's Moon is thought to have formed by an impact between the Earth and an impactor around 4.5 billion years ago. This impact could have been so energetic that it could have mixed and homogenized the Earth's mantle. However, this view appears to be inconsistent with geochemical studies that suggest that the Earth's mantle was not mixed by the impact. Another plausible outcome is that this energetic impact melted the whole mantle, but the extent of mantle melting is not well understood even though it must have had a significant effect on the subsequent evolution of the Earth's interior an…
Analyses of Lunar Laser Ranging data show that the spin-symmetry axis of the Moon is ahead of its expected Cassini state by an angle of $ϕ_p$ = 0.27 arcsec. This indicates the presence of one or more dissipation mechanisms acting on the lunar rotation. A combination of solid-body tides and viscous core-mantle coupling have been proposed in previous studies. Here, we investigate whether viscoelastic deformation within a solid inner core at the centre of the Moon can also account for a part of the observed phase lead angle $ϕ_p$. We build a rotational dynamic model of the Cassini state of the Mo…
According to the generally accepted scenario, the last giant impact on the Earth formed the Moon and initiated the final phase of core formation by melting the Earth's mantle. A key goal of geochemistry is to date this event, but different ages have been proposed. Some argue for an early Moon-forming event, approximately 30 million years (Myr) after the condensation of the first solids in the Solar System, whereas others claim a date later than 50 Myr (and possibly as late as around 100 My) after condensation. Here we show that a Moon-forming event at 40 Myr after condensation, or earlier, is …
The early thermal evolution of Moon has been numerically simulated to understand the magnitude of the impact induced heating and the initially stored thermal energy of the accreting Moonlets. The main objective of the present study is to understand the nature of processes leading to core-mantle differentiation and the production and cooling of the initial convective magma ocean. The accretion of Moon was commenced over a timescale of 100 years after the giant impact event around 30-100 million years in the early solar system. We studied the dependence of the planetary processes on the impact s…
The spin axes of the mantle, fluid core and solid inner core of the Moon precess at frequency $Ω_p=2π/18.6$ yr$^{-1}$ though with different orientations, leading to viscous friction at the core-mantle boundary (CMB) and inner core boundary (ICB). Here, we use a rotational model of the Moon with a range of inner core and outer core radii to investigate the relative importance of viscous dissipation at the CMB and ICB, and to show how this dissipation is connected to the phase lead angle ($ϕ_p$) of the mantle ahead of its Cassini state. We show that when the inner core radius is $>80$ km and the…
The importance of highly siderophile elements (HSEs) to track planetary late accretion has long been recognized. However, the precise nature of the Moon's accretional history remains enigmatic. There exists a significant mismatch of HSE budgets between the Earth and Moon, with the Earth disproportionally accreted far more HSEs than the Moon did. Several scenarios have been proposed to explain this conundrum, including the delivery of HSEs to Earth by a few big impactors, the accretion of pebble-sized objects on dynamically cold orbits that enhanced the Earth's gravitational focusing factor, an…
The chemical compositions of Earth's core and mantle provide insight into the processes that led to their formation. N-body simulations, on the other hand, generally do not contain chemical information, and seek to only reproduce the masses and orbits of the terrestrial planets. These simulations can be grouped into four potentially viable scenarios of Solar System formation (Classical, Annulus, Grand Tack, and Early Instability) for which we compile a total of 433 N-body simulations. We relate the outputs of these simulations to the chemistry of Earth's core and mantle using a melt-scaling la…
Terrestrial and lunar rocks share chemical and isotopic similarities in refractory elements, suggestive of a common precursor. By contrast, the marked depletion of volatile elements in lunar rocks together with their enrichment in heavy isotopes compared to Earth s mantle suggests that the Moon underwent evaporative loss of volatiles. However, whether equilibrium prevailed during evaporation, and, if so, at what conditions (temperature, pressure and oxygen fugacity) remain unconstrained. Chromium may shed light on this question, as it has several thermodynamically-stable, oxidised gas species …
Once the terrestrial planets had mostly completed their assembly, bombardment continued by planetesimals left-over from accretion. Highly siderophile element (HSE) abundances in Mars' mantle imply its late accretion supplement was 0.8 wt.%; Earth and the Moon obtained an additional 0.7 wt.% and 0.02 wt.%, respectively. The disproportionately high Earth/Moon accretion ratio is explicable by stochastic addition of a few remaining Ceres-sized bodies that preferentially targeted Earth. Here we show that Mars' late accretion budget also requires a colossal impact, a plausible visible remnant of whi…
Recent high-precision measurements of the isotopic composition of lunar rocks demonstrate that the bulk silicate Earth and the Moon show an unexpectedly high degree of similarity. This is inconsistent with one of the primary results of classic dynamical simulations of the widely accepted giant impact model for the formation of the Moon, namely that most of the mass of the Moon originates from the impactor, not Earth. Resolution of this discrepancy without changing the main premises of the giant impact model requires total isotopic homogenisation of Earth and impactor material after the impact …
The Moon is known to have a small liquid core, and it is thought that in the distant past the core may have produced strong magnetic fields recorded in lunar samples. Here we implement a numerical model of lunar orbital and rotational dynamics that includes the effects of a liquid core. In agreement with previous work, we find that the lunar core is dynamically decoupled from the lunar mantle, and that this decoupling happened very early in lunar history. Our model predicts that the lunar core rotates sub-synchronously, and the difference between the core and the mantle rotational rates was si…
We present fully three-dimensional equations to describe the rotations of a body made of a deformable mantle and a fluid core. The model in its essence is similar to that used by INPOP (Integration Planétaire de l'Observatoire de Paris), e.g. Viswanathan et al. (2019), and by JPL (Jet Propulsion Laboratory), e.g. Folkner et al. (2014), to represent the Moon. The intended advantages of our model are: straightforward use of any linear-viscoelastic model for the rheology of the mantle; easy numerical implementation in time-domain (no time lags are necessary); all parameters, including those relat…
Knowing the isotopic composition of Theia, the proto-planet which collided with the Earth in the Giant Impact that formed the Moon, could provide interesting insights on the state of homogenization of the inner solar system at the late stages of terrestrial planet formation. We use the known isotopic and modeled chemical compositions of the bulk silicate mantles of Earth and Moon and combine them with different Giant Impact models, to calculate the possible ranges of isotopic composition of Theia in O, Si, Ti, Cr, Zr and W in each model. We compare these ranges to the isotopic composition of c…
From iodine-plutonium-xenon isotope systematics, we re-evaluate time constraints on the early evolution of the Earth-atmosphere system and, by inference, on the Moon-forming event. Two extinct radioactivites (129I, T1/2 = 15.6 Ma, and 244Pu, T1/2 = 80 Ma) have produced radiogenic 129Xe and fissiogenic 131-136Xe, respectively, within the Earth, which related isotope fingerprints are seen in the compositions of mantle and atmospheric Xe. Recent studies of Archean rocks suggest that xenon atoms have been lost from the Earth's atmosphere and isotopically fractionated during long periods of geologi…
Subsequent to the Moon's formation, late accretion to the terrestrial planets strongly modified the physical and chemical nature of silicate crusts and mantles. This alteration came in the form of melting through impacts, as well as the belated addition of volatiles and the highly siderophile elements (HSEs). Current debate centres on whether the lunar HSE record is representative of its whole late accretion history or alternatively that these were only retained in the mantle and crust after a particular time, and if so, when. Here we employ improved Monte Carlo impact simulations of late accr…
Mapping deep-mantle compositional heterogeneity using a directional geoneutrino detector
Tohoku University(东北大学);Research Center for Neutrino Science, Tohoku University(东北大学中微子科学研究中心);Center for Geoneutrino Research, Institute of Oceanology, Chinese Academy of Sciences(中国科学院海洋研究所地球中微子研究中心);Department of Earth Science, Tohoku University(东北大学地球科学系);Department of Geological, Environmental, and Planetary Sciences, University of Maryland(马里兰大学地质、环境与行星科学系);University of Maryland(马里兰大学);High Energy Accelerator Research Organization (KEK)(高能加速器研究机构(KEK))
Impactors of different types and sizes can produce a final crater of the same diameter on a planet under certain conditions. We derive the condition for such "isocrater impacts" from scaling laws, as well as relations that describe how the different impactors affect the interior of the target planet; these relations are also valid for impacts that are too small to affect the mantle. The analysis reveals that in a given isocrater impact, asteroidal impactors produce anomalies in the interior of smaller spatial extent than cometary or similar impactors. The differences in the interior could be u…
Forming the Moon by a high-angular momentum impact may explain the Earth-Moon isotopic similarities, however, the post-impact angular momentum needs to be reduced by a factor of 2 or more to the current value (1 L_EM) after the Moon forms. Capture into the evection resonance, occurring when the lunar perigee precession period equals one year, could remove the angular momentum excess. However the appropriate angular momentum removal appears sensitive to the tidal model and chosen tidal parameters. In this work, we use a constant-time delay tidal model to explore the Moon's orbital evolution thr…
The giant impact hypothesis is the dominant theory of how the Earth-Moon system was formed. Models have been created that can produce a disk of debris with the proper mass and composition to create our Moon. Models have also been created which start with a disk of debris that eventually coalesces into a Moon. To date, no model has been created that produces a stable Earth-Moon system in a single simulation. Here we combine two recently published ideas in this field, along with a new gravity-centered model, and generate such a simulation. In addition, we show how the method can produce a hetero…
In the canonical model of Moon formation, a Mars-sized protoplanet "Theia" collides with proto-Earth at close to their mutual escape velocity $v_{\rm esc}$ and a common impact angle 45°. The "graze-and-merge" collision strands a fraction of Theia's mantle into orbit, while Earth accretes most of Theia and its momentum. Simulations show that this produces a hot, high angular momentum, silicate-dominated protolunar system, in substantial agreement with lunar geology, geochemistry, and dynamics. However, a Moon that derives mostly from Theia's mantle, as angular momentum dictates, is challenged b…
Composition of terrestrial planets records planetary accretion, core-mantle and crust-mantle differentiation, and surface processes. Here we compare the compositional models of Earth and Mars to reveal their characteristics and formation processes. Earth and Mars are equally enriched in refractory elements (1.9 $\times$ CI), although Earth is more volatile-depleted and less oxidized than Mars. Their chemical compositions were established by nebular fractionation, with negligible contributions from post-accretionary losses of moderately volatile elements. The degree of planetary volatile elemen…
The energy associated with giant impacts is large enough to generate global magma oceans during Earth's accretion. However, geochemical evidence requiring a terrestrial magma ocean is scarce. Here we present evidence for at least two separate magma ocean outgassing episodes on Earth based on the ratio of primordial 3He to 22Ne in the present-day mantle. We demonstrate that the depleted mantle 3He/22Ne ratio is at least 10 while a more primitive mantle reservoir has a 3He/22Ne ratio of 2.3 to 3. The 3He/22Ne ratios of the mantle reservoirs are higher than possible sources of terrestrial volatil…
Prevailing models for the formation of the Moon invoke a giant impact between a planetary embryo and the proto-Earth \citep{Canup_2004, Cuk_Stewart_2012}. Despite similarities in the isotopic and chemical abundances of refractory elements compared to Earth's mantle, the Moon is depleted in volatiles \citep{Wolf_Anders_1980}. Current models favour devolatilisation via incomplete condensation of the proto-Moon in an Earth-Moon debris-disk \citep{Charnoz_Michaut_2015,Canup_2015,Lock_2018}. However the physics of this protolunar disk is poorly understood and thermal escape of gas is inhibited by t…
In the past, clues on the potential radiogenic activity of the lunar interior have been obtained from the isotopic composition of noble gases like Argon. Excess Argon (40) relative to Argon (36), as compared to the solar wind composition, is generally ascribed to the radiogenic activity of the lunar interior. Almost all the previous estimates were based on, 'on-the-spot' measurements from the landing sites. Relative concentration of the isotopes of 40Ar and 36Ar along a meridian by the Chandra's Altitudinal Composition Explorer (CHACE) experiment, on the Moon Impact Probe (MIP) of India's firs…
Despite its importance to questions of lunar origin, the chemical composition of the Moon is not precisely known. In recent years, however, the isotopic composition of lunar samples has been determined to high precision and found to be indistinguishable from the terrestrial mantle despite widespread isotopic heterogeneity in the Solar System. In the context of the giant-impact hypothesis, this level of isotopic homogeneity can evolve if the proto-lunar disk and post-impact Earth undergo turbulent mixing into a single uniform reservoir while the system is extensively molten and partially vapori…
We address the thermal history of the Earth after the Moon-forming impact, taking tidal heating and thermal blanketing by the atmosphere into account. The atmosphere sets an upper bound of ~100 W/m^2 on how quickly the Earth can cool. The liquid magma ocean cools over 2-10 Myrs, with longer times corresponding to high angular-momentum events. Tidal heating is focused mostly in mantle materials that are just beginning to freeze. The atmosphere's control over cooling sets up a negative feedback between viscosity-dependent tidal heating and temperature-dependent viscosity of the magma ocean. Whil…
Impacts that leave the Earth-Moon system with a large excess in angular momentum have recently been advocated as a means of generating a protolunar disc with a composition that is nearly identical to that of the Earth's mantle. We here investigate the accretion of the Moon from discs generated by such "non-canonical" impacts, which are typically more compact than discs produced by canonical impacts and have a higher fraction of their mass initially located inside the Roche limit. Our model predicts a similar overall accretional history for both canonical and non-canonical discs, with the Moon …
The composition of the lower mantle $-$ comprising 56% of Earth's volume $-$ remains poorly constrained. Among the major elements, Mg/Si ratios ranging from $\sim$0.9$-$1.1, such as in rocky solar-system building blocks (or chondrites), to $\sim$1.2$-$1.3, such as in upper-mantle rocks (or pyrolite), have been proposed. Geophysical evidence for subducted lithosphere deep in the mantle has been interpreted in terms of efficient mixing and thus homogeneous Mg/Si across most of the mantle. However, previous models did not consider the effects of variable Mg/Si on the viscosity and mixing efficien…
Variance spectral analysis of superconducting gravimeter (SG) decadal data (noise inclusive) is presented suggesting that the Earth tectonogenesis is based on magnification of the mass (mainly the mantle) mechanical resonance, in addition to or instead of previously hypothesized causes. Here the use of raw (gapped and unaltered) data is regarded as the criterion for a physical result validity, so data were not altered in any way. Then analogously to the atmospheric tidal forcing of global high frequency free oscillation, I propose that the Moon synodically recurring pull could likewise drive t…
The object that resulted in the creation of the Moon started in the same orbital path as Earth around the Sun, but at Earth's L4. This proto-Moon (PM) was 4 times less massive than the usual Giant Impact (GI) object "Theia" and was captured into Earth orbit. It had a 32% Iron-Nickel-Sulfur core supporting a dynamo, which explains magnetized lunar rocks. Following capture, it was torn apart by tidal forces and its core of iron plastered itself, with some of its rock mantle, on the surface of Earth at a very flat angle (producing the "Late Veneer"). After tidal stripping, the remaining PM rock w…
The Earths core formation process has decisive effect in the chemical differentiation between the Earths core and its mantle. Here, we propose a new core formation model which is caused by a special giant impact. This model suggests that the impactors core can be kept intact by its own sticky mantle under appropriate impacting conditions and let it merge into the targets core without contact with the targets mantle. We call this special giant impact that caused the new core formation mode as glue ball impact model (GBI). By simulating hundreds of giant impacts with the sizes from planetesimals…
The giant impact hypothesis remains the leading theory for lunar origin. However, current models struggle to explain the Moon's composition and isotopic similarity with Earth. Here we present a new lunar origin model. High-energy, high-angular momentum giant impacts can create a post-impact structure that exceeds the corotation limit (CoRoL), which defines the hottest thermal state and angular momentum possible for a corotating body. In a typical super-CoRoL body, traditional definitions of mantle, atmosphere and disk are not appropriate, and the body forms a new type of planetary structure, n…
A high-angular momentum giant impact with the Earth can produce a Moon with a silicate isotopic composition nearly identical to that of Earth's mantle, consistent with observations of terrestrial and lunar rocks. However, such an event requires subsequent angular momentum removal for consistency with the current Earth-Moon system. The early Moon may have been captured into the evection resonance, occurring when the lunar perigee precession period equals one year. It has been proposed that after a high-angular momentum giant impact, evection removed the angular momentum excess from the Earth-Mo…
The Moon exhibits striking geological asymmetries in elevation, crustal thickness, and composition between its nearside and farside. Although several scenarios have been proposed to explain these asymmetries, their origin remains debated. Recent remote sensing observations suggest that (1) the crust on the farside highlands consists of two layers: a primary anorthositic layer with thickness of ~30-50 km and on top a more mafic-rich layer ~10 km thick; and (2) the nearside exhibits a large area of low-Ca pyroxene that has been interpreted to have an impact origin. These observations support the…
We comprehensively compile and review N content in geologic materials to calculate a new N budget for Earth. Using analyses of rocks and minerals in conjunction with N-Ar geochemistry demonstrates that the Bulk Silicate Earth (BSE) contains \sim7\pm4 times present atmospheric N (4\times10^18 kg N, PAN), with 27\pm16\times10^18 kg N. Comparison to chondritic composition, after subtracting N sequestered into the core, yields a consistent result, with BSE N between 17\pm13\times10^18 kg to 31\pm24\times10^18 kg N. In the chondritic comparison we calculate a N mass in Earth's core (180\pm110 to 30…
At present, the giant impact (GI) is the most widely accepted model for the origin of the Moon. Most of the numerical simulations of GI have been carried out with the smoothed particle hydrodynamics (SPH) method. Recently, however, it has been pointed out that standard formulation of SPH (SSPH) has difficulties in the treatment of a contact discontinuity such as a core-mantle boundary and a free surface such as a planetary surface. This difficulty comes from the assumption of differentiability of density in SSPH. We have developed an alternative formulation of SPH, density independent SPH (DIS…
The distribution and isotopic composition of volatile elements in planetary materials holds a key to the characterization of the early solar system and the Moon's formation. The Moon and Earth are chemically and isotopically very similar. However, the Moon is highly depleted in volatile elements and the origin of this depletion is still debated. We present gallium isotopic and elemental measurements in a large set of lunar samples to constrain the origin of this volatile depletion. We show that while Ga has a geochemical behavior different from zinc, both elements show a systematic enrichment …
The moon-forming impact and the subsequent evolution of the proto-Earth is strongly dependent on the properties of materials at the extreme conditions generated by this violent collision. We examine the high pressure behavior of MgO, one of the dominant constituents in the earth's mantle, using high-precision, plate impact shock compression experiments performed on Sandia National Laboratories Z-Machine and extensive quantum simulations using Density Functional Theory (DFT) and quantum Monte Carlo (QMC). The combined data span from ambient conditions to 1.2 TPa and 42,000 K, showing solid-soli…
While the seismic quality factor and phase lag are defined solely by the bulk properties of the mantle, their tidal counterparts are determined both by the bulk properties and self-gravitation of a body as a whole. For a qualitative estimate, we model the body with a homogeneous sphere and express the tidal phase lag through the lag in a sample of material. Although simplistic, our model is sufficient to understand that the lags are not identical. The difference emerges because self-gravitation pulls the tidal bulge down. At low frequencies, this reduces strain and makes tidal damping less eff…
The concept of Late Veneer has been introduced by the geochemical community to explain the abundance of highly siderophile elements in the Earth's mantle and their chondritic proportions relative to each other. However, in the complex scenario of Earth accretion, involving both planetesimal bombardment and giant impacts from chondritic and differentiated projectiles, it is not obvious what the "Late Veneer" actually corresponds to. In fact, the process of differentiation of the Earth was probably intermittent and there was presumably no well-defined transition between an earlier phase where al…
Low-spin ferrous iron suppresses mantle oxidation beyond Earth-like pressures
ETH Zürich(苏黎世联邦理工学院);European Synchrotron Radiation Facility(欧洲同步辐射装置);Université Paris Cité, Institut de Physique du Globe de Paris, CNRS(巴黎西岱大学,巴黎地球物理研究所,法国国家科学研究中心);Nantes Université, Univ Angers, Le Mans Université, CNRS, Laboratoire de Planétologie et Géosciences, LPG UMR 6112(南特大学,昂热大学,勒芒大学,法国国家科学研究中心,行星学与地质学实验室);School of Earth, Atmosphere and Environment, Monash University(蒙纳士大学地球、大气与环境学院);Guangzhou Institute of Geochemistry, Chinese Academy of Sciences(中国科学院广州地球化学研究所)
The classical scenario of terrestrial planet formation is characterized by a phase of giant impacts among Moon-to-Mars mass planetary embryos. While the classic model and its adaptations have produced adequate analogs of the outer three terrestrial planets, Mercury's origin remains elusive. Mercury's high-core mass fraction compared to the Earth's is particularly outstanding. Among collisional hypotheses, this feature has been long interpreted as the outcome of an energetic giant impact among two massive protoplanets. Here, we revisit the classical scenario of terrestrial planet formation with…
Phobos and Deimos are the two small moons of Mars. Recent works have shown that they can accrete within an impact-generated disk. However, the detailed structure and initial thermodynamic properties of the disk are poorly understood. In this paper, we perform high-resolution SPH simulations of the Martian moon-forming giant impact that can also form the Borealis basin. This giant impact heats up the disk material (around $\sim 2000$ K in temperature) with an entropy increase of $\sim 1500$ J K$^{-1}$ kg$^{-1}$. Thus, the disk material should be mostly molten, though a tiny fraction of disk mat…
Overabundances in highly siderophile elements (HSEs) of Earth's mantle can be explained by conveyance from a singular, immense (3000 km in a diameter) "Late Veneer" impactor of chondritic composition, subsequent to lunar formation and terrestrial core-closure. Such rocky objects of approximately lunar mass (about 0.01 M_E) ought to be differentiated, such that nearly all of their HSE payload is sequestered into iron cores. Here, we analyze the mechanical and chemical fate of the core of such a Late Veneer impactor, and trace how its HSEs are suspended - and thus pollute - the mantle. For the s…
In this review, three major changes in our understanding of the early history of the Solar System are presented. 1) Early differentiation: A few recent results support the idea that protoplanet formation and differentiation occurred partly simultaneously than CAI formation. First, some iron meteorites, eucrites, and angrites older than the chondrules or even than the CAI have been found. Second, iron meteorites could be debris of early disrupted differentiated planetesimals, scattered from the terrestrial planet region to the Main Belt. Finally, chondrules contain fragments of planetesimal mat…
Giant impacts dominate the final stages of terrestrial planet formation and set the configuration and compositions of the final system of planets. A giant impact is believed to be responsible for the formation of Earth's Moon, but the specific impact parameters are under debate. Because the canonical Moon-forming impact is the most intensely studied scenario, it is often considered the archetypal giant impact. However, a wide range of impacts with different outcomes are possible. Here we examine the total energy budgets of giant impacts that form Earth-mass bodies and find that they differ sub…