Ceres’s internal evolution: The view after Dawn

As the Dawn mission approaches a successful conclusion at Ceres, it seems time to assess how its findings have sharpened the picture of Ceres’s evolution. Before Dawn, we inferred from Ceres's bulk density of about 2100 kg m^?3 that Ceres contained about 25% water by mass. Thermodynamic modeling of the interior evolution suggested that the original accreted ice had to melt even if only long‐lived radionuclides were present, leading to the aqueous alteration of the original chondritic silicates and differentiation of the altered silicates from any remaining water, consistent with telescopic detection of aqueously altered silicates (serpentine and clay minerals) on Ceres’s surface. Earth‐based observations of Ceres’s shape were not accurate enough to constrain the extent of differentiation of its interior. Dawn's results confirm these early findings and extend them dramatically to reveal an evolved and active small planet, probably even today, due to water/ice‐driven processes. A nearly uniform global distribution of surface mineralogy, which includes Mg‐serpentines, ammoniated clays, and salts including carbonates, suggests extensive, endogenous, planet‐wide aqueous alteration. Local exceptions show salt‐rich deposits of varied composition, which suggests subsurface heterogeneities. Concentration of Fe below carbonaceous chondrite levels suggests chemical fractionation, leading to Ceres being chemically differentiated. The high spatial uniformity of element abundance measurements of equatorial regolith also indicates that some ice‐rock fractionation occurred on a global scale. Even some local exposures of ice are seen, especially in higher latitudes and in low‐illumination regions that must be very young, as surface water ice is unstable on time scales of 1–1000 years under Ceres’s surface temperatures. Subsurface ice is also likely in abundance at higher latitudes in at least the upper few meters of the surface, as suggested by near‐surface H‐rich polar deposits. Observations of bright ice deposits in permanently shadowed regions suggest cold‐trapping of migrating H₂O across the surface. Gravity field measurements indicate a concentration of mass toward the center and near isostatic equilibrium, consistent with at least some mass differentiation driven by water‐related processes. Abundant small and midsize craters but relaxed or missing large craters suggest a stiff upper crust with water abundance lower than 30 vol%. A sharp decrease in viscosity at ~40 km depth suggests the occurrence of a small fraction of liquid, consistent with earlier thermophysical models. Surface cryogenic features, such as flows, extrusions, and domes, some geologically very recent, are evidence of active water/ice‐driven subsurface processes. Ceres experienced extensive water‐related processes and at least some mass and chemical fractionation and is probably active today, consistent with previous moderate heating thermodynamic models. Clearly, Ceres is a “wet,” evolved planet at the edge of the inner solar system, as described in this special issue. We conclude with a list of questions suggested by the Dawn findings; they especially regard the state and fate of water and its role in driving past and possibly current chemical and physical activity in this dwarf planet.     

Water,heat, bombardment: The evolution and current state of (2) Pallas

Using recent constraints on the shape and density of (2) Pallas, we model the thermal evolution of the body as a function of possible formation scenarios that differ in the time of formation and composition assumed for the protoplanet. We develop possible evolution scenarios for Pallas and compare these to available observations. Our models imply two distinct types of end states: those with a hydrosphere and silicate core, and those where the body is dominated by hydrated silicates. We show that for an initial ice-rock mixture with density 2400 kg/m³, Pallas is likely to differentiate and form a rocky core and icy shell. If Pallas accreted from material with lower initial ice content, our models indicate that Pallas’s interior is dominated by hydrated silicates, possibly with a core of anhydrous silicates.We also investigate the possibility that Pallas’s initial density was similar to Ceres’, i.e., that it formed from an ice–rock mixture of density 2100 kg/m³. This implies that the object lost a significant fraction of its hydrosphere as a consequence of thermal oscillations and impacts, a distinct possibility given its density, evidence for impact excavation and current orbital parameters. Its blue spectral slope and observed surface variation may also be evidence for such a process (e.g. Jewitt, D.C. [2002]. Astron. J. 123, 1039–1049; Schmidt, B.E. et al. [2009]. Science 326, 275–279; Yang, B., Jewitt, D. [2010]. Astron. J. 140, 692–698). If Pallas still contains a thin layer of water ice, then that layer corresponds to the bottom of a former icy shell, and as such, could be enriched in non-ice materials such as organics. We evaluate the likeliness of each scenario and show the general magnitude of water loss processes for Pallas. Given a balance of observational and theoretical constraints, we favor a water-rich accretion for Pallas that implies that Pallas has lost a significant fraction of its initial water content through exogenic processes since its internal evolution ceased. We also discuss implications of this work to other hydrated asteroids.     

Compositional variability on the surface of 1 Ceres revealed through GRaND measurements of high‐energy gamma rays

High‐energy gamma rays (HEGRs) from Ceres’s surface were measured using Dawn's Gamma Ray and Neutron Detector (GRaND). Models of cosmic‐ray‐initiated gamma ray production predict that the HEGR flux will inversely vary with single‐layer hydrogen concentrations for Ceres‐like compositions. The measured data confirm this prediction. The hydrogen‐induced variations in HEGR rates were decoupled from the measurements by detrending the HEGR data with Ceres single‐layer hydrogen concentrations determined by GRaND neutron measurements. Models indicate that hydrogen‐detrended HEGR counting rates correlate with water‐free average atomic mass, which is denoted as <A>*. HEGR variations across Ceres’s surface are consistent with <A>* variations of ±0.5 atomic mass units. Chemical variations in the CM and CI chondrites, our closest analogs to Ceres’s surface, suggest that <A>* variations on Ceres are primarily driven by variations in the concentration of Fe, although other elements such as Mg and S could contribute. Dawn observations have shown that Ceres’s interior structure and surface composition have been modified by some combination of physical (i.e., ice‐rock fractionation) and/or chemical (i.e., alteration) processes that has led to variations in bulk surface chemistry. Locations of the highest inferred <A>* values, and thus possibly the highest Fe and least altered materials, tend to be younger, less cratered surfaces that are broadly associated with the impact ejecta of Ceres’s largest craters.     

Ceres’ evolution and present state constrained by shape data

We model Ceres’ thermo-physical-chemical evolution by considering a large range of initial conditions as well as various evolutionary scenarios. Models are constrained by available shape measurements, which point to a differentiated interior for Ceres. We address the role played by hydrothermal activity in the long-term evolution of Ceres and especially the evolution of its hydrosphere. We suggest that models with times of formation shorter than about 5 My after the production of calcium-aluminum inclusions are more likely to undergo hydrothermal activity in their early history, which affects Ceres’ long-term thermal evolution. We evaluate the conditions for preserving liquid water inside Ceres, a possibility enhanced by its warm surface temperature and the enrichment of its hydrosphere in a variety of chemical species. However, thermal modeling of the hydrosphere needs to be further investigated. We show that shape data can help constrain the amount of hydrated silicate in the core, and thus the extent of hydrothermal activity in Ceres. We discuss the importance of these results for the Dawn mission’s arrival at Ceres in 2015.     

Carbonaceous chondrites as analogs for the composition and alteration of Ceres

The mineralogy and geochemistry of Ceres, as constrained by Dawn's instruments, are broadly consistent with a carbonaceous chondrite (CM/CI) bulk composition. Differences explainable by Ceres’s more advanced alteration include the formation of Mg‐rich serpentine and ammoniated clay; a greater proportion of carbonate and lesser organic matter; amounts of magnetite, sulfide, and carbon that could act as spectral darkening agents; and partial fractionation of water ice and silicates in the interior and regolith. Ceres is not spectrally unique, but is similar to a few other C‐class asteroids, which may also have suffered extensive alteration. All these bodies are among the largest carbonaceous chondrite asteroids, and they orbit in the same part of the Main Belt. Thus, the degree of alteration is apparently related to the size of the body. Although the ammonia now incorporated into clay likely condensed in the outer nebula, we cannot presently determine whether Ceres itself formed in the outer solar system and migrated inward or was assembled within the Main Belt, along with other carbonaceous chondrite bodies.     

Condensation processes in astrophysical environments: The composition and structure of cometary grains

Abstract— We review the results of our recent experimental studies of astrophysical dust analogs. We discuss the condensation of amorphous silicates from mixed metal vapors, including evidence that such condensates form with metastable eutectic compositions. We consider the spectral evolution of amorphous magnesium silicate condensates as a function of time and temperature. Magnesium silicate smokes anneal readily at temperatures of about 1000–1100 K. In contrast we find that iron silicates require much higher temperatures (?1300 K) to bring about similar changes on the same timescale (days to months). We first apply these results to infrared space observatory observations of crystalline magnesium silicate grains around high‐mass‐outflow asymptotic giant branch stars in order to demonstrate their general utility in a rather simple environment. Finally, we apply these experimental results to infrared observations of comets and protostars in order to derive some interesting conclusions regarding large‐scale nebular dynamics, the natural production of organic molecules in protostellar nebulae, and the use of crystalline magnesium silicates as a relative indicator of a comet's formation age.     

Overtones of silicate and aluminate minerals and the 5–8 μm ice bands of deeply embedded objects

The distinct patterns, relatively low intensities and peak positions of overtone-combination bands of silicates and oxides suggest that the 5–8 μm spectral region can provide clues for the dust composition when near optically thick conditions exist for the 10-μm silicate feature. We present 1000–2500 cm⁻¹ room-temperature laboratory spectra obtained from powders of silicate, aluminate and nitride minerals and silicate glasses. The spectra exhibit overtone absorption bands with mass absorption coefficients ∼100 times weaker than the fundamentals. These data are compared with the 5–8 μm spectra of deeply embedded young stellar objects observed with the Short Wavelength Spectrometer on the Infrared Space Observatory . Fits of the laboratory data to the observations, after subtraction of the 6.0-μm H₂O ice feature and the 6.0-μm feature identified with organic refractory material, indicate that crystalline melilite (a silicate) or metamict hibonite (a radiation-damaged crystalline aluminate) may be responsible for much of the 6.9-μm absorption feature in the observations, with melilite providing the best match. A weaker 6.2-μm absorption in the young stellar object spectra is well matched by the spectra of hydrous crystalline amphibole silicates (actinolite and tremolite). Relative abundances of Si–O in room-temperature amphiboles to low-temperature H₂O ice are in the range 0.46–3.9 and in melilite are in the range 2.5–8.6. No astronomical feature was matched by the overtones of amorphous silicates because these bands are too broad and peak at the wrong wavelength. Hence, this analysis is consistent with the 10-μm features of these objects being due to a mixture of crystalline and amorphous silicates, rather than only amorphous silicates.     

Hydrothermal dynamics in a CM‐based model of Ceres

A 2‐D numerical study of the evolution of Ceres from a “frozen mudball” to the present era emphasizes the importance of hydrothermal processes. Particulates released as the “frozen mudball” thaws settle to form a roughly 290 km radius core. Hydrothermal flow is driven by radiogenic heating and serpentinization. Both salt‐free and brine fluids are considered. Our modeling suggests that Ceres’s core has been warm over most of its history and is still above freezing, and convective processes are active in core and mantle to the present. The addition of low eutectic solutes greatly expands the region of active convection. A global muddy ocean persists for the first 3 Gyr, and at present, there may be several regional mud seas buried under a frozen crust. Transport of interior material to the near surface occurs throughout our model's history. Eutectic brines drive convective flow to near the surface, even breaching the surface in isolated regions, on the order of 30 km in width, similar in size to some mounds detected using the Dawn visible imaging camera (Sizemore et al. 2015). Surface features such as the bright spot in Occator crater and Ahuna Mons could be the result of eutectic plumes. The CM‐based model density profile is within 10% of Ermakov et al.'s ( 2017 ) results. The model mud mantle has a roughly 42:58 volumetric partitioning of H₂O to rock. Our mud model is consistent with the absence of large craters (Marchi et al. 2016 ) and an internal viscosity decreasing with depth (Fu et al. 2017 ).     

The composition of asteroid 2 Pallas and its relation to primitive meteorites

High resolution spectroscopic observations of asteroid 2 Pallas from 1.7-3.5 μm are reported. These data are combined with previous measurements from 0.4-1.7 μm to interpret Pallas' surface mineralogy. Evidence is found for low-Fe²⁺ hydrated silicates, opaque components, and low-Fe²⁺ anhydrous silicates. This assemblage is very similar to carbonaceous chondrite matrix material such as is found in type CI and CM meteorites, but it has been subjected to substantial aqueous alteration and there is a major extraneous anhydrous silicate component. This composition is compared to that of asteroid 1 Ceres. Although there are substantial differences in their broad band spectral reflectances, it appears that both asteroids are genetically related to known carbonaceous chondrites.     

The presolar grain inventory of fine‐grained chondrule rims in the Mighei‐type (CM) chondrites

We investigated the inventory of presolar silicate, oxide, and silicon carbide (SiC) grains of fine‐grained chondrule rims in six Mighei‐type (CM) carbonaceous chondrites (Banten, Jbilet Winselwan, Maribo, Murchison, Murray and Yamato 791198), and the CM‐related carbonaceous chondrite Sutter's Mill. Sixteen O‐anomalous grains (nine silicates, six oxides) were detected, corresponding to a combined matrix‐normalized abundance of ~18 ppm, together with 21 presolar SiC grains (~42 ppm). Twelve of the O‐rich grains are enriched in ¹⁷O, and could originate from low‐mass asymptotic giant branch stars. One grain is enriched in ¹⁷O and significantly depleted in ¹⁸O, indicative of additional cool bottom processing or hot bottom burning in its stellar parent, and three grains are of likely core‐collapse supernova origin showing enhanced ¹⁸O/¹⁶O ratios relative to the solar system ratio. We find a presolar silicate/oxide ratio of 1.5, significantly lower than the ratios typically observed for chondritic meteorites. This may indicate a higher degree of aqueous alteration in the studied meteorites, or hint at a heterogeneous distribution of presolar silicates and oxides in the solar nebula. Nevertheless, the low O‐anomalous grain abundance is consistent with aqueous alteration occurring in the protosolar nebula and/or on the respective parent bodies. Six O‐rich presolar grains were studied by Auger Electron Spectroscopy, revealing two Fe‐rich silicates, one forsterite‐like Mg‐rich silicate, two Al‐oxides with spinel‐like compositions, and one Fe‐(Mg‐)oxide. Scanning electron and transmission electron microscopic investigation of a relatively large silicate grain (490 nm × 735 nm) revealed that it was crystalline åkermanite (Ca₂Mg[Si₂O₇]) or a an åkermanite‐diopside (MgCaSi₂O₆) intergrowth.     

Ceres - Neither a porous nor salty ball

This study explores the geophysical implications of two compositional models recently proposed for Ceres, which assume that the dwarf planet is a homogeneous mixture of chondritic material devoid with free water. In order to reproduce Ceres’ density, the rock density has to be offset by the presence of porosity and/or an abundance of hydrated salts resulting from the extensive hydration and oxidation of the chondritic material. Thermal modeling shows that a mixture of hydrated minerals is bound to compact and partly dehydrate as a consequence of long-lived radioisotope decay heat. The resulting interior structure is differentiated in a silicate-rich core and water-rich shell, with little porosity. Hence, this study confirms previous suggestion that Ceres contains a large fraction of free water.     

Experimental aqueous alteration of cometary dust

Abstract– Recent spacecraft missions to comets have reopened a long‐standing debate about the histories and origins of cometary materials. Comets contain mixtures of anhydrous minerals and ices seemingly unaffected by planetary processes, yet there are indications of a hydrated silicate component. We have performed aqueous alteration experiments on anhydrous interplanetary dust particles (IDPs) that likely derived from comets. Hydrated silicates rapidly formed from submicrometer amorphous silicates within the IDPs at room temperature in mildly alkaline solution. Hydrated silicates may thus form in the near‐surface regions of comets if liquid water is ever present. Our findings provide insight into origins of cometary IDPs containing both anhydrous and hydrated minerals and help reconcile the seemingly inconsistent observations of hydrated silicates from the Stardust and Deep Impact missions.     

The structure of circumstellar envelopes

Copious mass loss on the Asymptotic Giant Branch dominates the late stages of stellar evolution. Maps of extended circumstellar envelopes provide a history of mass loss and trace out anisotropic mass loss. This review concentrates on observations of millimeter wavelength molecular line emission, on high resolution maps of maser emission and on observations of submillimeter, millimeter and radio wavelength continuum emission. Radio continuum observations show that AGB stars are larger at radio than at optical wavelengths. The extended chromospheres indicated by these observations extend to distances from the star large enough for dust to form, thereby initiating mass loss. Molecular line maps have found time-variable mass loss for some stars, including detached shells indicating interrupted mass loss and evidence for a rapid increase in the mass loss rate at the end of the AGB phase. Maps of circumstellar envelopes show evidence of flattening, bipolar outflow and angular variations in both the mass loss rate and the outflow velocity. As stars evolve away from the AGB and planetary nebula formation begins, these structures become more pronounced, and fast bipolar molecular winds are observed. The time scales derived from the dynamical times of these winds and from the expansion rates of the central planetary nebulae are very rapid in some cases, about 100 years, in agreement with the predictions of stellar evolution theory.     

On the origin of rim textures surrounding anhydrous silicate grains in CM carbonaceous chondrites

Abstract— Fine‐grained, optically opaque rims coat individual olivine and pyroxene grains in CM matrices and chondrules. Bulk chemical analyses and observations of these rims indicate the presence of phyllosilicates and disseminated opaques. Because phyllosilicates could not have survived the chondrule formation process, chondrule silicate rims must have formed entirely by late‐state aqueous reactions. As such, these textures provide a useful benchmark for isolating alteration features from more complex CM matrix materials. Both chondrule silicate and matrix silicate rims exhibit morphological features commonly associated with advancing stages of replacement reactions in terrestrial serpentinites. Contacts between many matrix silicate rims and the adjacent matrix materials suggest that these rims formed entirely by aqueous reactions in a parent‐body setting. This contrasts with previous assertions that rim textures can only form by the accretion of nebular dust but does not imply an origin for the rims surrounding other types of CM core components, such as chondrules.     

Moderately and slightly siderophile element constraints on the depth and extent of melting in early Mars

The thermal history of Mars during accretion and differentiation is important for understanding some fundamental aspects of its evolution such as crust formation, mantle geochemistry, chronology, volatile loss and interior degassing, and atmospheric development. In light of data from new Martian meteorites and exploration rovers, we have made a new estimate of Martian mantle siderophile element depletions. New high pressure and temperature metal–silicate experimental partitioning data and expressions are also available. Using these new constraints, we consider the conditions under which the Martian mantle may have equilibrated with metallic liquid. The resulting conditions that best satisfy six siderophile elements—Ni, Co, W, Mo, P, and Ga—and are consistent with the solidus and liquidus of the Martian mantle phase diagram are a pressure of 14 ± 3 GPa and temperature of 2100 ± 200 K. The Martian mantle depletions of Cr and V are also consistent with metal–silicate equilibration in this pressure and temperature range if deep mantle silicate phases are also taken into account. The results are not consistent with either metal–silicate equilibrium at the surface or at the current‐day Martian core–mantle boundary. Recent measurements and modeling have concluded that deep (～17 GPa or 1350 km) mantle melting is required to explain isotopic data for Martian meteorites and the nature of differentiation into core, mantle, and crust. This is in general agreement with our estimates of the conditions of Martian core formation based on siderophile elements that result in an intermediate depth magma ocean scenario for metal–silicate equilibrium.     

Gravity field and interior of Rhea from Cassini data analysis

The Cassini spacecraft encountered Rhea on November 26, 2005. Analysis of the Doppler data acquired at and around closest approach yields the mass of Rhea and the quadrupole moments of its gravity field with unprecedented accuracy. We obtained which corresponds to a density of . Our results for J₂ and C₂₂ are (7.947±0.892)×¹⁰⁻⁴ and (2.3526±0.0476)×¹⁰⁻⁴, respectively. These values are consistent with hydrostatic equilibrium. From the value of C₂₂, we infer the non-dimensional moment of inertia C/MR²=0.3721±0.0036. Our models of Rhea's interior based on the gravity data favor an almost undifferentiated satellite. A discontinuity between a core and a mantle is possible but not required by the data. Models with a constant silicate mass fraction throughout the body cannot account for the determined quadrupole coefficients. The data exclude fully differentiated models in which the core would be composed of unhydrated silicates and the mantle would be composed of pure ice. If the mantle contains 10% in mass of silicates, the core extends to 630 km in radius and has a silicate mass fraction of 40%. A continuous model in which the silicates are more concentrated toward the center of the body than in the outer layers is allowed by the gravity data but excluded by thermal evolution considerations. The one model that fits the gravity data and is self-consistent when energy transport and ice melting are qualitatively considered is an “almost undifferentiated” Rhea, in which a very large uniform core is surrounded by a relatively thin ice shell containing no rock at all.     

On the composition of ices incorporated in Ceres

We use the clathrate hydrate trapping theory and gas drag formalism to calculate the composition of ices incorporated in the interior of Ceres. Utilizing a time-dependent solar nebula model, we show that icy solids can drift from beyond 5 au to the present location of the asteroid and be preserved from vaporization. We argue that volatiles were trapped in the outer solar nebula in the form of clathrate hydrates, hydrates and pure condensates prior to having been incorporated in icy solids and subsequently in Ceres. Under the assumption that most of volatiles were not vaporized during the accretion phase and the thermal evolution of Ceres, we determine the per mass abundances with respect to H₂O of CO₂, CO, CH₄, N₂, NH₃, Ar, Xe and Kr in the interior of the asteroid. The Dawn space mission, scheduled to explore Ceres in August 2014, may have the capacity to test some predictions. We also show that an in situ measurement of the D/H ratio in H₂O in Ceres could constrain the distance range in the solar nebula where its icy planetesimals were produced.     

Stardust in Antarctic micrometeorites

Abstract— We report the discovery of presolar silicate, oxide (hibonite), and (possibly) SiC grains in four Antarctic micrometeorites (AMMs). The oxygen isotopic compositions of the eighteen presolar silicate (and one oxide) grains found are similar those observed previously in primitive meteorites and interplanetary dust particles, and indicate origins in oxygen‐rich red giant or asymptotic giant branch stars, or in supernovae. Four grains with anomalous C isotopic compositions were also detected. ¹²C/¹³C as well as Si ratios are similar to those of mainstream SiC grains; the N isotopic composition of one grain is also consistent with a mainstream SiC classification. Presolar silicate grains were found in three of the seven AMMs studied, and are heterogeneously distributed within these micrometeorites. Fourteen of the 18 presolar silicate grains and 3 of the 4 C‐anomalous grains were found within one AMM, T98G8. Presolar silicate‐bearing micrometeorites contain crystalline silicates that give sharp X‐ray diffractions and do not contain magnesiowüstite, which forms mainly through the decomposition of phyllosilicates and carbonates. The occurrence of this mineral in AMMs without presolar silicates suggests that secondary parent body processes probably determine the presence or absence of presolar silicates in Antarctic micrometeorites.     

On the composition and differentiation of Ceres

The dwarf planet Ceres has a density of 2040-2250 kg m⁻³, and a dark non-icy surface with signs of hydrated minerals. As opposed to a differentiated internal structure with a nonporous rocky core and a water mantle, there are arguments for undifferentiated porous interior structure. Ceres’ mass and dimensions are uncertain and do not exclude undifferentiated interior even if hydrostatic equilibrium is attained. The rocky surface may be inconsistent with a large-scale water-rock differentiation. A differentiated structure with a thick water mantle below a rocky crust is gravitationally unstable and an overturn would have led to abundant surface salt deposits, which are not observed. A formation of hydrated surface minerals caused by internal heating implies a major density increase through devolatilization of the interior. A later accumulation of hydrated materials is inconsistent with anhydrous surfaces of many asteroids and with a low rate of the cosmic dust deposition in the inner Solar System. Ceres’ internal pressures (<140-200 MPa) are insufficient to significantly reduce porosity of chondritic materials and there is no need for abundant water phases to be present to account for the bulk density. Having the porosity of ordinary chondrites (∼10%), Ceres can consist of rocks with the grain density of pervasively hydrated CI carbonaceous chondrites. However, additional low-density phases (e.g., water ice) require to be present in the body with the grain density of CM chondrites. The likely low-density mineralogy of the interior implies Ceres’ accretion from pervasively aqueously altered carbonaceous planetesimals depleted in short-lived radionuclide ²⁶Al. Abundant water ice may not have accreted. Limited heat sources after accretion may not have caused major mineral dehydration leading to formation of water mantle. These inferences can be tested with the Dawn spacecraft in 2015.     

Remarks on dynamical ellipticity at the Earth's

In this paper, two factors — the redistribution of the density and the variation in the angular velocity of the Earth rotation, that affect the adopted value of the flattening for equidensity surface within the Earth, are discussed. The computational results show that the contribution of the redistribution of the density in the Earth interior (especially in the core) on the change of the flattening at the core-mantle boundary (CMB) is marginal, and that the calculated value of the flattening at the CMB can be in good agreement with the VLBI observed value so long as the fact that the angular velocity of the Earth rotation has undergone the tidal evolution is taken into account. As a result, this paper presents a set of recommended values of the dynamical parameters of the Earth (see Table III) for computing Earth's forced nutation series.