Internal Density Structure Research Articles

Three-dimensional laser interferometric CT (LICT) measurement of shock wave interaction around a circular cylinder

Three-dimensional (3-D) laser interferometric computed tomography (LICT) measurement has been applied to high-speed and unsteady flow including shock waves. The purpose of our investigation is to clarify 3-D flow phenomena quantitatively by using LICT. We used a diaphragm-less shock tube to clarify the unsteady shock wave behavior with the shot by shot method. The diaphragm-less shock tube enables us to obtain shock wave propagation reproduction in quick succession. By LICT the 3-D internal density structure of the shock–vortex flow field can be clarified. In this LICT method the observation system consists of a CCD camera, Mach–Zehnder interferometer, and nitrogen pulse laser as a light source with a suitable delay signal controller. The 3-D density CT data can be reconstructed typically from the 19 2-D density images which have a 5° interval among every shot of the diaphragm-less shock tube. As for the method to get many projection images, the optical system is fixed, while the model with a cylindrical duct and a cylinder is rotated by a fixed degree of intervals in the designated observation angle for every shot. In this paper the shock wave interaction with a finite length circular cylinder is observed by LICT measurement. For reconstruction of density distribution the Algebraic Reconstruction Technique (ART) is applied to reduce the artifact, together with precise observation.

Jupiter’s moment of inertia: A possible determination by Juno

The moment of inertia of a giant planet reveals important information about the planet’s internal density structure and this information is not identical to that contained in the gravitational moments. The forthcoming Juno mission to Jupiter might determine Jupiter’s normalized moment of inertia NMoI=C/MR2 by measuring Jupiter’s pole precession and the Lense–Thirring acceleration of the spacecraft (C is the axial moment of inertia, and M and R are Jupiter’s mass and mean radius, respectively). We investigate the possible range of NMoI values for Jupiter based on its measured gravitational field using a simple core/envelope model of the planet assuming that J2 and J4 are perfectly known and are equal to their measured values. The model suggests that for fixed values of J2 and J4 a range of NMoI values between 0.2629 and 0.2645 can be found. The Radau–Darwin relation gives a NMoI value that is larger than the model values by less than 1%. A low NMoI of ∼0.236, inferred from a dynamical model (Ward, W.R., Canup, R.M. [2006]. Astrophys. J. 640, L91–L94) is inconsistent with this range, but the range is model dependent. Although we conclude that the NMoI is tightly constrained by the gravity coefficients, a measurement of Jupiter’s NMoI to a few tenths of percent by Juno could provide an important constraint on Jupiter’s internal structure. We carry out a simplified assessment of the error involved in Juno’s possible determination of Jupiter’s NMoI.

SELF-SIMILAR SOLUTIONS OF TRIAXIAL DARK MATTER HALOS

We investigate the collapse and internal structure of dark matter halos. We consider halo formation from initially scale-free perturbations, for which gravitational collapse is self-similar. Fillmore and Goldreich (1984) and Bertschinger (1985) solved the one dimensional (i.e. spherically symmetric) case. We generalize their results by formulating the three dimensional self-similar equations. We solve the equations numerically and analyze the similarity solutions in detail, focusing on the internal density profiles of the collapsed halos. By decomposing the total density into subprofiles of particles that collapse coevally, we identify two effects as the main determinants of the internal density structure of halos: adiabatic contraction and the shape of a subprofile shortly after collapse; the latter largely reflects the triaxiality of the subprofile. We develop a simple model that describes the results of our 3D simulations. In a companion paper, we apply this model to more realistic cosmological fluctuations, and thereby explain the origin of the nearly universal (NFW-like) density profiles found in N-body simulations.

An ion acceleration mechanism in laser illuminated targets with internal electron density structure

1D and 2D PIC simulations of light ion acceleration by irradiation of structured thin foils by short pulse, high intensity lasers have been performed. When the back coating material is thicker than the typical scale length for TNSA fields the ion energy spectra contain peaks. These peaks are found to be due to the acceleration of ions by an electric field which builds up at internal interfaces between materials with different electron number densities. The electric field is generated by incomplete neutralization of the charge built up at the head of the hot electron beam as it crosses the interface between the two materials. In these simulations the back material layer is sufficiently thick that the sheath field drops to zero before reaching the vacuum boundary. The acceleration responsible for the peaks is therefore from within the material and is superimposed on the normal TNSA acceleration from the back material–vacuum surface, i.e. there are two distinct sites of particle acceleration. It is possible that this mechanism may explain features previously observed in simulations. A comparison is also made with experiments with thick rear coatings.

Upper mantle thermochemical structure from seismic–geodynamic flow models: constraints from the Lithoprobe initiativeThis article is one of a series of papers published in this Special Issue on the theme Lithoprobe — parameters, processes, and the evolution of a continent.

High-resolution seismic models of three-dimensional mantle heterogeneity are interpreted in terms of upper mantle thermal and compositional anomalies. These anomalies produce density perturbations that drive mantle flow and corresponding convection-related geophysical observables, such as the nonhydrostatic geoid, free-air gravity anomalies, and dynamic surface topography, and provide constraints on internal mantle density structure. The convection related observables are corrected for the isostatically compensated crustal heterogeneity and compared with those predicted by tomography-based mantle flow models. Occam inversions of the surface topography and gravity data provide inferences of the velocity–density scaling coefficients, which characterize mantle density anomalies below North America. The inferred density anomalies require simultaneous contributions from temperature and composition. The density and seismic shear velocity anomalies place constraints on the thermochemical structure of the mantle beneath the North American craton. Perturbations in the molar ratio of iron, R = XFe/(XFe + XMg), are used to quantify the compositional anomalies in terms of iron depletion in the sub-continental mantle. Estimates of the extent of basalt depletion in the tectosphere beneath North America are obtained. This depletion is interpreted to produce a local balance between positive chemical buoyancy and the negative thermal buoyancy that would otherwise be produced by the colder temperatures of the sub-cratonic mantle relative to its sub-oceanic counterpart.

Internal sediment density structures around bars and troughs due to beach deformations using X-ray CT

Internal sediment density structures around bars and troughs due to beach deformations using X-ray CT

Turbidity Currents and Their Deposits

The article surveys the current state of our understanding of turbidity currents, with an emphasis on their fluid mechanics. It highlights the significant role these currents play within the global sediment cycle, and their importance in environmental processes and in the formation of hydrocarbon reservoirs. Events and mechanisms governing the initiation of turbidity currents are reviewed, along with experimental observations and findings from field studies regarding their internal velocity and density structure. As turbidity currents propagate over the seafloor, they can trigger the evolution of a host of topographical features through the processes of deposition and erosion, such as channels, levees, and sediment waves. Potential linear instability mechanisms are discussed that may determine the spatial scales of these features. Finally, the hierarchy of available theoretical models for analyzing the dynamics of turbidity currents is outlined, ranging from dimensional analysis and integral models to both depth-averaged and depth-resolving simulation approaches.

Dynamics of Rotating Shallow Gravity Currents Passing through a Channel. Part II: Analysis

Abstract The physics of frictional control for channelized rotating gravity currents are analyzed using an extensive dataset including hydrographic, current, and microstructure measurements from the western Baltic Sea. Rotational effects in these gravity currents, characterized by Ekman numbers of the order of one and subcritical Froude numbers, induce a complex transverse circulation that strongly affects the internal dynamics. The key component of this circulation is a geostrophically balanced transverse jet in the interface that modifies the entrainment process by (i) laterally draining the interface and (ii) providing additional interfacial shear comparable to the down-channel shear. The recirculation of mixed interfacial fluid into the interior distorts the internal density structure of the gravity current, and creates a thermal wind shear in the interior that is comparable to the observed shear. Using a theoretical model, this effect is shown to be responsible for the three-layer structure of the transverse velocity with the near-bottom velocity and stress directed opposite to the Ekman transport. The analysis confirms the key assumption in available models for frictional control in rotating gravity currents: the transverse Ekman transport is balanced by the geostrophic transport due to the down-channel tilt of the interface.

Stellar disruption by a supermassive black hole: is the light curve really proportional tot−5/3?

In this paper we revisit the arguments for the basis of the time evolution of the flares expected to arise when a star is disrupted by a supermassive black hole. We present a simple analytic model relating the lightcurve to the internal density structure of the star. We thus show that the standard lightcurve proportional to $t^{-5/3}$ only holds at late times. Close to the peak luminosity the lightcurve is shallower, deviating more strongly from $t^{-5/3}$ for more centrally concentrated (e.g. solar--type) stars. We test our model numerically by simulating the tidal disruption of several stellar models, described by simple polytropic spheres with index $\gamma$. The simulations agree with the analytical model given two considerations. First, the stars are somewhat inflated on reaching pericentre because of the effective reduction of gravity in the tidal field of the black hole. This is well described by a homologous expansion by a factor which becomes smaller as the polytropic index becomes larger. Second, for large polytropic indices wings appear in the tails of the energy distribution, indicating that some material is pushed further away from parabolic orbits by shocks in the tidal tails. In all our simulations, the $t^{-5/3}$ lightcurve is achieved only at late stages. In particular we predict that for solar type stars, this happens only after the luminosity has dropped by at least two magnitudes from the peak. We discuss our results in the light of recent observations of flares in otherwise quiescent galaxies and note the dependence of these results on further parameters, such as the star/hole mass ratio and the stellar orbit.

Evaporation and condensation of spherical interstellar clouds. Self-consistent models with saturated heat conduction and cooling

Aims. The fate of interstellar clouds embedded in a hot tenuous medium depends on whether the clouds suffer from evaporation or whether material condensates onto the clouds. The knowledge of the evaporation or condensation rates of interstellar clouds at rest is therefore of prime importance for their further evolution. Analytic solutions for the rate of evaporative mass loss from an isolated spherical cloud embedded in a hot tenuous gas are deduced by Cowie & McKee (1977, ApJ, 211, 135). Their approach is limited to the integration of the time-independent energy conservation equation for the heat-conductive interface. Therefore it is crucial to test the validity of the analytical results for more realistic interstellar conditions. This requires that the full hydrodynamical equations must be treated taking the whole cloud into account with a sufficiently large hot-gas reservoir. Methods. By two-dimensional numerical simulations in an Eulerian, explicit hydrodynamical grid the evolution of interstellar clouds with different internal density structures and surrounded by a hot plasma is simulated. Self-gravity, interstellar heating and cooling effects and heat conduction by electrons are added. We use the classical thermal conductivity of a fully ionized hydrogen plasma proposed by Spitzer and a saturated heat flux according to Cowie and McKee in regions where the mean free path of the electrons is large compared to the temperature scaleheight. Results. Using pure hydrodynamics and taking only the classical heat flux into account, we can reproduce the Cowie and McKee analytical results. If we allow for heat flux saturation the evaporation rate is reduced, but in the simulations even to about one order of magnitude below the predicted saturated one. This happens because the saturated heat flux is density dependent and due to the mixing of the two phases, the warm cloud material on one side and the hot intercloud medium, also the density distribution changes drastically there during the simulation. And this cannot be considered in the analytical study. This main result still holds if we add self gravity or choose another cloud density structure while keeping the cloud radius and temperature of the cloud edge constant. As a further issue the evolution changes, however, totally for more realistic conditions when interstellar heating and cooling effects stabilize the self-gravity. The clouds' evaporation then turns into condensation, because the additional energy input due to heat conduction can be transported away from the interface and radiated off very efficiently from the cloud's inner parts. Conclusions. The assumption of pure classical heat conduction is invalid for the description of the evolution of interstellar clouds in a hot tenuous gas. The consideration of a limited saturated heat flux is inevitable for this kind of simulations and leads to a dramatic decrease of the evaporation rate. And even more realisticly with radiative cooling heat conduction leads to condensation in contradiction to analytical predictions which require evaporation. This has two consequences: Interstellar clouds are stabilized against evaporation. On the other hand this provides an efficient way to accrete and mix intercloud material into clouds.

What can we learn about convection from asteroseismology?

AbstractAsteroseismology—using stellar oscillations to study the interiors of stars—is a relatively new and growing research field in astrophysics. Oscillations are found in stars of most masses and essentially all stages of evolution. Their frequencies are determined by the internal sound speed and density structure of the star, as well as rotation, convection processes and possibly effects of magnetic fields. Recent developments have led to a breakthrough in our ability to study the details of cores of solar-like stars and it is foreseen that a number of key science questions will be addressed through the analysis of frequencies and other properties of stellar oscillations. In this paper we review some of the latest results from asteroseismology of solar-like stars, with the focus on properties of convection.

Similarity theory and parameterization of mixing in the upper ocean

Boundary layers with small thermal and mechanical inertia are close to steady-state condi- tions. This underlies the Monin-Obukhov similarity theory and explains why the surface values of the fluxes can be chosen as external parameters. For fluids with large thermal inertia, such as the ocean, the thermal time scale is relatively large, and the density flux is a complex function of depth; thus, the external thermal forcing is no longer a governing parameter. However, the mechanical inertia of the upper ocean is about three orders of magnitude smaller than the thermal inertia. Consequently, the upper ocean can be considered as steady-state in the dynamic sense, to any dynamic property depends primarily on the depth, the surface momentum flux, and the vertical density structure. This property allows us to suggest an alternative formulation of the similarity theory for the stratified boundary layers through specification of a new stratification parameter which characterizes the internal density structure instead of the external density flux. The turbulent mixing coefficient is derived as dependent on the stratification parameter. The latter includes the surface stress and the integral density deficit for the entire layer above. The general form and the asymptotic behavior of the nondimensional tur- bulent mixing coefficient as a function of the stratification parameter are obtained using dimensional considerations. Determination of numerical parameters is based on 8 years of temperature profiles acquired at the Ocean Weather Ship (OWS) PAPA. Finally, a method for calculating the profile of the turbulent mixing coefficient is obtained. This approach reproduces the 8-year evolution of the upper ocean with the maximum rms difference of approximately 1C and the bias of 1C over the depth range 0-150 m. Additional 1-year simulation of the upper ocean at OWS CHARLEY and 9-year simulation at OWS NOVEMBER confirms reasonable applicability of this approach. The proposed simple turbulent mixing scheme reproduces the evolution of the upper ocean with accuracies similar to those obtained using much more complicated models.

Turbulent diapycnal mixing in the Nordic seas

The distribution of turbulent diapycnal mixing in the Nordic seas is mapped from observations of internal wave density and velocity fine structure. The uppermost 500–1500 m host two distinct mixing regimes. In the eastern basins, the diapycnal diffusivity (Kρ) straddles 10−5 m2 s−1, whereas in the weakly stratified Greenland and Boreas basins it is raised by an order of magnitude. Below ∼2000 m, low stratification is associated with intense turbulent mixing across the Nordic seas, with diffusivities in the range 3 × 10−4–10−2 m2 s−1. These mixing rates agree within uncertainties with three tracer‐based diffusivity estimates in the region and are associated with turbulent dissipation rates (ɛ) that are at most moderately enhanced above typical open ocean values. A minimum in both ɛ and Kρ is commonly found at ∼1500 m, a depth level that is most efficiently sheltered from shallow and bottom energy sources for the mixing. Available evidence points to wind work on upper ocean inertial motions as a shallow source, with semidiurnal internal tides generated at different levels of the topography contributing to both shallow and deep turbulence. While the closure of the North Atlantic meridional overturning circulation in the Nordic seas appears to be primarily driven by air‐sea interaction, turbulent mixing has the potential to play a critical role in shaping the stratification and ventilation of the region via a range of complex interactions with convection.

The internal magnetic field structures and current density profiles in the Helicity Injected Spherical Torus plasma driven by coaxial helicity injection

In the Helicity Injected Spherical Torus device [Nagata et al., Proceedings of the 17th International Atomic Energy Agency Fusion Energy Conference, Yokohama, 1998 (International Atomic Energy Agency, Vienna, 1998) CD-ROM, EXP4/10], internal magnetic field and current density structures of spherical torus (ST) plasmas sustained by coaxial helicity injection (CHI) have been revealed via intensive internal magnetic measurements. The internal magnetic configuration of the ST plasma formed by CHI is in good agreement with the results of numerical equilibrium fitting calculations. The generation of closed poloidal flux of ST has been verified by varying the external toroidal field strength in the same device. Interestingly, the transition of the current profile from hollow to peaked has been observed during the sustainment phase, which could be explained by inductive effects of currents on open field lines winding the central conductor.

Carbon Monoxide Observations of Small Dark Globules. I. Internal Structure

To probe internal structures of small interstellar clouds, we have observed 12 dark globules in the emission of CO isotopes. Full mappings were made in the transition of 13CO(J = 1 → 0), while in the 12CO only cross-scan observations were done. We have identified 18 subcondensations from the column-density maps of the 12 globules and derived various physical properties for each of them. The line widths of most subcondensations show little variation with distance from center. Some of the condensations, however, seem to undergo systematic motions of expansion or contraction. The internal density structure of the subcondensations closely resembles that of the truncated isothermal gas sphere. The observed line width ΔV of the subcondensations varies with the size, R, in a power-law fashion, ΔV ∝ Rβ, with β = 0.61 ± 0.11, which is a somewhat steeper exponent than the one for the cores of giant molecular clouds. The result is compared with those from a wide variety of interstellar clouds.

Use of a shoal analysis and patch estimation system (SHAPES) to characterise sardine schools

The use of a shoal analysis and patch estimation system (SHAPES) to analyse hydro-acoustic data is discussed. SHAPES was used to detect and characterise sardine schools from four echo integration surveys off the coast of South Africa. Methods of school detection and characterisation, assumptions made and corrections applied to school variables are presented. Measurements of school morphology and internal school features are discussed and compared to other relevant works. Significant relationships were established, both between measures of school morphology and internal density structure. Several variables showed significant differences between surveys. Composite factors derived from principle component analyses showed that morphological variables are the most important school descriptors. No differences in the loading of composite factors between surveys are evident. This suggests an inherent spatial and temporal stability in sardine school characteristics. This fact may prove beneficial for comparisons of school structure between co-occurring fish species and possibly aid fish school identification in the future.

Mixing in lock-release gravity currents

The density front bounding a gravity current is usually highly unstable and this leads to mixing between the fluid of the gravity current and that of the surroundings. This mixing plays an important part in the dynamics of gravity currents and determines how fluid properties are transported and distributed by the flow. In this paper we describe a new experimental technique to determine the density structure of gravity currents, and present some results for the lock-release case. We find that substantial mixing occurs in the early stages of the evolution of lock-release gravity currents and that this mixing leads to the formation of a complex internal density structure. Mixed fluid is produced across the concentration range and we examine the mixing rates. By contrasting three experiments with different lock aspect ratios, we examine the effect of the aspect ratio of the release on the subsequent evolution of the flow. Gravity currents are produced when fluid of one density is released into fluid of a different density at a horizontal boundary. The variation in buoyancy force along the boundary, which is caused by the density difference, produces a horizontal pressure gradient which drives a flow along the boundary. Typically, this flow has the form of a penetrating current bounded downstream by a strong frontal region, called the 'head', and a shallower following flow, called the 'tail' (Simpson, 1987). The simplest situation, and the one we shall consider in this paper, is the lock-release case. This consists of two fluids of different densities contained in a rectangular channel, initially at rest and separated by a vertical barrier. When the

Structure of Dense Cores in M17 SW. I. A Multitransition CS and C 34S Study

view Abstract Citations (47) References (51) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Structure of Dense Cores in M17 SW. I. A Multitransition CS and C 34S Study Wang, Yangsheng ; Jaffe, Daniel T. ; Evans, Neal J., II ; Hayashi, Masahiko ; Tatematsu, Ken'ichi ; Zhou, Shudong Abstract We present results of a multitransition CS and C34S study of the M17 SW molecular cloud core. Fully sampled maps were obtained in the CS J = 1 → 0, 2 → 1, and 7 → 6 lines and the C34S J = 2 → 1 line with 1 8"-36" resolution. Velocity channel maps reveal the clumpy emission from the dense gas on scales of ∼0.2 pc (20"). The overall agreement in the cloud morphology among maps of different CS and C34S transitions suggests that all CS and C34S lines originate in the same dense gas. Excitation and opacity effects probably cause the modest differences between the maps. We carried out a detailed excitation analysis of the multitransition data. The J = 2 → 1 and J = 7 → 6 transitions of CS, analyzed with a large velocity gradient (LVG) radiative transfer model, produced 250 pixel maps of the volume density and the CS column density over an area of about 1.8 pc × 2.4 pc. Peaks in the CS and the C34S line temperature maps are maxima in column density, but not in density. The density maps shows a fairly uniform, high density (n ∼105.7 cm-3) throughout the cloud core. An independent estimate of the gas densities from analysis of the C34S observations confirms the CS results. Along with other evidence, these results imply a clumpy cloud model in which the CS emission arises from structures smaller than our beam. We compared the observed CS maps with a specific clumpy cloud model with 179 clumps decomposed from the C18O J = 2 → 1 maps (Stutzki & Güsten 1990). Model channel maps of CS were synthesized based on the clump parameters listed in Stutzki & Güsten (1990) and were compared with the observed maps. The gas densities used in the models were derived from the clump column densities (based on the C18O J = 2 → 1 emission) and sizes. Most of the dominant clumps had densities near 105 cm-3. The resulting synthesized map does not reproduce the observed CS J = 7 → 6 emission along the eastern ridge of the core. By assuming a constant gas density for all clumps, we were able to synthesize CS channel maps which reproduce the observed cloud morphology and the line intensities reasonably well. A mean clump density in the models of about 5 × 105 cm-3 (about 5 times higher than the density derived from C18O) matches the observed CS line ratios and a CS/H2 abundance ratio of about 4 × 10-9 fits the observed line intensities of the J = 1 → 0, 2 → 1, and 7 → 6 transitions of CS. The discrepancy between densities derived from C18O and CS can be resolved if the clumps have internal density structure. Either smooth density gradients in clumps with sizes just below our angular resolution or a continuation of high-contrast clumping to still smaller scales could account for the difference. While we cannot rule out either of these pictures, it is noteworthy that the scale of the C18O observations (∼0.15 pc) is the largest for which the density discrepancy can be resolved with smooth density gradients in unresolved clumps. Publication: The Astrophysical Journal Pub Date: December 1993 DOI: 10.1086/173521 Bibcode: 1993ApJ...419..707W Keywords: ISM: H II REGIONS; ISM: INDIVIDUAL MESSIER NUMBER: M17; ISM: MOLECULES; ISM: STRUCTURE; RADIO LINES: ISM full text sources ADS | data products SIMBAD (2)

A spatial domain Stokes flow model for the gravity and topography of the middle latitudes of Venus

A new modeling strategy is developed and applied to the long‐wavelength gravity, topography, and internal density structure of Venus. Geodynamic modeling of planetary scale phenomena is usually carried out in the wavenumber transform domain (spherical harmonics or Fourier transforms). However, because of limitations associated with the gravity and topography data available for Venus, a spatial domain approach is preferable. Smoothed representations of the gravity and topography of Venus are developed in terms of quadratic B splines on 10° centers in latitude and longitude, over the latitude interval from 45°S to 45°N. These models reproduce 83.6% and 98.3% of their respective data variances. A similarly constructed model is then presented for the dynamic support of gravity and topography on Venus. Internal mass anomalies are specified at two discrete depths (50 and 500 km), with lateral variations determined by two constraints: (1) that the slow viscous flow induced by the anomalies will distort the free surface into a form matching the observed topography and (2) that the sum of the gravitational effects of the internal anomalies plus that due to the surface distortion they cause will match the observed gravity. There are four major features evident in the gravity and topography data sets: Atla, Beta, Ovda, and Thetis regiones. All four have compensating mass patterns consistent with a mantle plume origin. The surficial flow pattern associated with this model does not resemble terrestrial plate tectonic patterns.

Forced nutations of the Earth: Influence of inner core dynamics: 3. Very long interferometry data analysis

We discuss the analysis of 798 very long baseline interferometry (VLBI) experiments carded out between July 1980 and February 1989, and the determination from this analysis of corrections to selected coefficients in the International Astronomical Union (IAU) 1980 theory of the nutations of the Earth. Our analysis confirms earlier VLBI results and indicates that most of these corrections can be explained by carefully accounting for (1) corrections to the IAU 1980 rigid‐Earth nutation series, (2) the presence of the Earth's inner core, (3) the difference between the dynamic flattening of the Earth inferred from the precession constant and that inferred from seismic models of the internal density structure of the Earth, and (4) the effects of mantle anelasticity and ocean tides. The standard deviations of the corrections to the coefficients are 0.04 milliarcseconds (mas) for terms with periods under 430 days, and 1.0 mas for the terms with a period of 18.6 years. The unresolved issues raised by our analysis are the origins of corrections to the out‐of‐phase retrograde annual(0.39 mas) and the in‐phase prograde 13.66 day (− 0.25 mas) nutations. Our analysis also yields a correction to the IAU 1976 value for the luni‐solar precession constant of −0.32±0.13 arc sec/century (cy).