The Earth's decelerated rotation and regularities in orientation of its surface lineaments and faults

The Earth's crust faults and lineaments group in clusters with predominant N-S and E-W (System I) and NW-SE and NE-SW (System II) directions. The earthquake epicenters of the Benioff seismofocal zones follow the same regularities. In other words, seismofocal zones (epicenters of earthquakes) constitute a part of the regular network of the Earth's crust and lithosphere faults and lineaments. Mathematical modeling of stress distribution in the lithosphere due to a change of the Earth's ellipsoid compression showed that the principal stresses σ₁ and σ₂ are oriented in N-S and E-W directions, while corresponding shear stresses τ are oriented in NE-SW and NW-SE directions. It is shown that the secular deceleration of the Earth's rotation can be a reasonable mechanism for the change of Earth's ellipsoid compression and, consequently, for the origin of the regular system of faults and lineaments described above.     

Testing geopotential models

The actual accuracy of the geopotential value on the geoid computed from satellite altimetry recently asW ₀ = (62 636 857.5 ± 1.0) m² s^–2 makes it possible to adopt this quantity as geopotential models testing (GMT) value. However, GMT network should be established consisting of points situated near the gauge stations and of other points at small sea level heights, globally distributed. As numerical example illustrating the GMT method suggested, the recent Satellite Laser Ranging network points have been used.     

Refinement of the geopotential scale factorR 0 on

Altimetric measurements of the GEOSAT satellite were used for the determination of geopotential scale factorR ₀. The geopotential valueW ₀ on the geoid surface was then computed (W ₀ =GM/R ₀).The GEOSAT Geophysical Data Records (GDR's) covering an initial period of the Exact Repeat Mission (ERM) were filtered and processed. The necessary corrections were made in order to allow a precise detection of the sea surface. Gravitational geopotential, rotation and permanent tides were taken into account and the equipotential surface which is the best approximation of the sea surface was found.The determination of the potential valueW ₀ on the mean geoid surface in this way is very promising. An associated value withW ₀ - the geopotential scale factorR ₀ - seems to be a very good Earth dimension defining quantity. Moreover, there are many possible applications ofW ₀ (R ₀) in modern geophysics.The incorporation of one of these parameters - we now recommendR ₀ - into the set of the Primary Geodetic Parameters (PGP) is discussed and suggested.     

Long-Term Stability Of Geoidal Geopotential FromTopex/Poseidon Satellite Altimetry 1993–1999

The TOPEX/POSEIDON (T/P) satellite altimeter data from January 1, 1993to October 24, 1999 (cycles 11–261) was used for investigating thelong-term variations in the geoidal geopotential W₀ and/orin the geopotential scale factor R₀ = GM/W₀ (GM is theadopted geocentric gravitational constant). The mean valuesdetermined for the whole period covered are: W₀ =(62 636 856.161 ± 0.002) m² s^-2, R₀ =(6 363 672.5448 ± 0.0002) m. The actual accuracy is limited bythe altimeter calibration error (2–3 cm) and it isestimated to be about ± 0.5 m² s^-2 (± 5 cm).The yearly variations of the above mean values are at the formalerror level. No long-term trend in W₀, representing the oceanvolume change, was found for the seven years period 1993–9 on thebasis of T/P altimeter (AVISO) data. No sea surface topography modelwas used in the solution. This revised version was published online in July 2006 with corrections to the Cover Date.     

Primary and derived parameters of common relevance of Astronomy,Geodesy, and Geodynamics

Problem of selecting primary parameters has been discussed. Primaries should be defined uniquely, as well as, physically. Since no unique definition for semimajor axis exists, it should be replaced by the geoidal geopotential valueW ₀ or by the geopotential scale factorR ₀ =GM/W ₀, geocentric gravitational constantGM be also primary parameter. Current best estimates of some parameters are given numerically.     

New optical measurements of planetary diameters— Part IV: Planet Mars

Optical measurements of the diameter of Mars were made using a double-image micrometer with large refractors from 1952 to 1971. Discussion of the 90 independent series of measurements gives nine determinations of radius with an accuracy of ±7–8km for different latitudes from pole to equator. The Mariner 4, 6 and 7 occultation results and the radar results availble in 1970 added seven further determinations of comparable accuracy. All these values, within the accuracy of measurement, fit an ellipsoid with R_eq=3398±3km and R_po1=3371±4km. The mean density of Mars is thus 3940±0.012g cm⁻³. The resulting optical oblateness of 0.0079, larger than the dynamical value of 0.0052, results in an equatorial radius excess of 9±5 km which presumably comes about by internal stresses.     

A New Reference Equipotential Surface, and Reference Ellipsoid for the Planet Mars

Using the shape model of Mars GTM090AA in terms of spherical harmonics complete to degree and order 90 and gravitational field model of Mars GGM2BC80 in terms of spherical harmonics complete to degree and order 80, both from Mars Global Surveyor (MGS) mission, the geometry (shape) and gravity potential value of reference equipotential surface of Mars (Areoid) are computed based on a constrained optimization problem. In this paper, the Areoid is defined as a reference equipotential surface, which best fits to the shape of Mars in least squares sense. The estimated gravity potential value of the Areoid from this study, i.e. W ₀ = (12,654,875 ± 69) (m²/s²), is used as one of the four fundamental gravity parameters of Mars namely, {W ₀, GM, ω, J ₂₀}, i.e. {Areoid’s gravity potential, gravitational constant of Mars, angular velocity of Mars, second zonal spherical harmonic of gravitational field expansion of Mars}, to compute a bi-axial reference ellipsoid of Somigliana-Pizzetti type as the hydrostatic approximate figure of Mars. The estimated values of semi-major and semi-minor axis of the computed reference ellipsoid of Mars are (3,395,428 ± 19) (m), and (3,377,678 ± 19) (m), respectively. Finally the computed Areoid is presented with respect to the computed reference ellipsoid.     

Kinematics of stellar populations with RAVE data

We study the kinematics of the Galactic thin and thick disk populations using stars from the RAVE survey’s second data release together with distance estimates from Breddels et al. (2010). The velocity distribution exhibits the expected moving groups present in the solar neighborhood. We separate thick and thin disk stars by applying the X (stellar-population) criterion of Schuster et al. (1993), which takes into account both kinematic and metallicity information. For 1906 thin disk and 110 thick disk stars classified in this way, we find a vertical velocity dispersion, mean rotational velocity and mean orbital eccentricity of (σ_W, 〈V_Φ〉, 〈e〉)_thin = (18 ± 0.3 km s⁻¹, 223 ± 0.4 km s⁻¹, 0.07 ± 0.07) and (σ_W, 〈V_Φ〉, 〈e〉)_thick = (35 ± 2 km s⁻¹, 163 ± 3 km s⁻¹, 0.31 ± 0.16), respectively. From the radial Jeans equation, we derive a thick disk scale length in the range 1.5-2.2 kpc, whose greatest uncertainty lies in the adopted form of the underlying potential. The shape of the orbital eccentricity distribution indicates that the thick disk stars in our sample most likely formed in situ with minor gas-rich mergers and/or radial migration being the most likely cause for their orbits. We further obtain mean metal abundances of 〈[M/H]〉_thin = +0.03 ± 0.17, and 〈[M/H]〉_thick = −0.51 ± 0.23, in good agreement with previous estimates. We estimate a radial metallicity gradient in the thin disk of −0.07 dex kpc⁻¹, which is larger than predicted by chemical evolution models where the disk grows inside-out from infalling gas. It is, however, consistent with models where significant migration of stars shapes the chemical signature of the disk, implying that radial migration might play at least part of a role in the thick disk’s formation.     

Prediction of satellites in Earth's gravitational field with axial symmetry using Burdet's regularized theory

In this paper, economical and stable recurrence formulae for the Earth's zonal potential and its gradient for Burdet's regularized theory will be established for any number N of the zonal harmonic coefficients. A general recursive computational algorithm based on these formulae is also established for the initial value problem of Burdet oscillator for the prediction of artificial satellites in the Earth's gravitational field with axial symmetry. Applications of the algorithm for the problem of the final state prediction are illustrated by numerical examples of three test orbits each for two geopotential models corresponding to N = 2 and N = 36.A final state of any desired accuracy is obtained for each case study, a result which shows the flexibility of the algorithm.Dept. of Astronomy, KAU     

Geoidal potential free of zero-frequency tidal distortion

It has been proved that the geoidal valueW ₀ is not dependent on the system used for defining the geoid surface. It is the same for the zero-frequency tidal system, mean system and tide-free system. It has been suggested,W ₀ be adopted as primary constant defining the length dimensions of celestial bodies.     

Prediction of satellite motions in the Earth's gravitational field with axial symmetry by the KS regularized theory

In this paper, economical and stable recurrence formulae for the Earth's zonal potential and its gradient for the KS regularized theory will be established for any numberN of the zonal harmonic coefficient. A general recursive computational algorithm based on these formulae is also established for the initial value problem of the KS theory for the prediction of artificial satellites in the Earth's gravitational field with axial symmetry. Applications of the algorithm for the problem of the final state prediction are illustrated by numerical examples of three test orbits each for two geopotential models corresponding toN=2 andN=36. A final state of any desired accuracy is obtained for each case study, a result which shows the flexibility of the algorithm.     

Rotating Stratified Heterogeneous Oblate Spheroid in Newtonian Physics

By solving the Euler hydrodynamical equations we have obtained closed form solutions for the angular velocities and pressures of a three stratified non-confocal heterogeneous oblate spheroid. Limiting and particular solutions cases, such as a spheroid with N layers, a stratified spheroid with the same eccentricities, as well as confocal layered spheroids are also explicitly written down. As an application, we have numerically estimated planet Earth's outer and inner cores' ellipticities to be _o=1/413.318 and _i=1/424.616, respectively. These Earth's ellipticities values are in good agreement with those found in the literature.     

On the CN (0, 0) spectrum of Comet Mrkos 1957d

We have carried out an analysis of the (0, 0) vibrational band of the CN molecule in Comet Mrkos 1957d, including the effect of collisions. We found that the sum of the squares of the residuals can be reduced by a factor of ten, if collisions account for 46±3% of the population of the lower level. A rotational temperature can be assigned to the cometary gas. The best value found was 410±40 K. The best fit for the constantR ₁ was (1.07±0.10)×10^–4. The velocity of the comet was left as a free parameter. We found for it a value of 34.38±0.10 km s^–1. This result is in disagreement with the nuclear orbital velocity of 34.74 km s^–1. The discrepancy can be explained, if the CN molecules are ejected from the cometary nucleus preferentially in the sunward direction, with a mean velocity that corresponds to the above temperature.     

The cosmic distance scale

Summary The status of the cosmic distance scale problem in early 1989 is reviewed. Internally consistent distances to Local Group galaxies are given in Tables 5 and 6. Within the Local Group the distance scale is found to be 11±5% smaller than that previously adopted by Sandage and Tammann. Distances to nearby galaxies are used as stepping stones to the Virgo cluster. The interpretation of the Tully-Fisher observations of Virgo spirals is found to be ambiguous because it is not yet clear which spirals are cluster members and which are background objects. Distance estimates of the Virgo cluster obtained by different techniques are listed in Table 11. The distance modulus of the Virgo cluster is found to be 31.5±0.2, corresponding to a distance of 20±2 Mpc. The elliptical galaxies in the core of the Virgo cluster haveV ₀=1200±46 kms^–1, which corresponds toV _LG=1082±48 km s^–1. With an infall velocity of 250±50 km s^–1 this yields a cosmological redshiftV=1332±69 km s^–1, from which a Hubble parameter H₀=67±8 km s^–1 Mpc^–1 is obtained. Space Telescope observations of distant Cepheids, Tully-Fisher observations of spirals in the Hercules eluster, and interference filter observations of Virgo planetary nebulae in the light of [O_III], should soon result in a major improvement in the accuracy with which H₀ is known.     

Spatially-resolved high-resolution spectroscopy of Venus 2. Variations of HDO, OCS, and SO2 at the cloud tops

While CO, HCl, and HF, that were considered in the first part of this work, have distinct absorption lines in high-resolution spectra and were detected four decades ago, the lines of HDO, OCS, and SO₂ are either very weak or blended by the telluric lines and have not been observed previously by ground-based infrared spectroscopy at the Venus cloud tops. The H₂O abundance above the Venus clouds is typically below the detection limit of ground-based IR spectroscopy. However, the large D/H ratio on Venus facilitates observations of HDO. Converted to H₂O with D/H ≈ 200, our observations at 2722 cm⁻¹ in the Venus afternoon show a H₂O mixing ratio of ∼1.2 ppm at latitudes between ±40° increasing to ±60° by a factor of 2. The observations in the early morning reveal the H₂O mixing ratio that is almost constant at 2.9 ppm within latitudes of ±75°. The measured H₂O mixing ratios refer to 74 km. The observed increase in H₂O is explained by the lack of photochemical production of sulfuric acid in the night time. The recent observations at the P-branch of OCS at 4094 cm⁻¹ confirm our detection of OCS. Four distributions of OCS along the disk of Venus at various latitudes and local times have been retrieved. Both regular and irregular components are present in the variations of OCS. The observed OCS mixing ratio at 65 km varies from ∼0.3 to 9 ppb with the mean value of ∼3 ppb. The OCS scale height is retrieved from the observed limb darkening and varies from 1 to 4 km with a mean value of half the atmospheric scale height. SO₂ at the cloud tops has been detected for the first time by means of ground-based infrared spectroscopy. The SO₂ lines look irregular in the observed spectra at 2476 cm⁻¹. The SO₂ abundances are retrieved by fitting by synthetic spectra, and two methods have been applied to determine uncertainties and detection limits in this fitting. The retrieved mean SO₂ mixing ratio of 350 ± 50 ppb at 72 km favors a significant increase in SO₂ above the clouds since the period of 1980-1995 that was observed by the SOIR occultations at Venus Express. Scale heights of OCS and SO₂ may be similar, and the SO₂/OCS ratio is ∼500 and may be rather stable at 65-70 km under varying conditions on Venus.     

The solar abundance of tungsten

Recent measurements of Wi oscillator strengths (Obbarius and Kock, 1982) lead to a solar photospheric abundance of tungsten, log _W = 1.06 ± 0.15 on the scale log _H = 12. The solar W/Si abundance ratio, 0.32 W atoms/10⁶ Si, coincides with that found in carbonaceous chrondrites. Implications for solar-system r-processes abundances are pointed out.     

The thermal and physical characteristics of the Gao-Guenie (H5) meteorite

Measurements of the bulk density, grain density, porosity, and magnetic susceptibility of 19 Gao-Guenie H5 chondrite meteorite samples are presented. We find average values of bulk density 〈ρ_bulk〉=3.46±0.07 g/cm³, grain density 〈ρ_grain〉=3.53±0.08 g/cm³, porosity 〈P(%)〉=2.46±1.39, and bulk mass magnetic susceptibility 〈log χ〉=5.23±0.11. Measurements of the specific heat capacity for a 3.01-g Gao-Guenie sample, a 61.37-g Gao-Guenie sample, a 62.35-g Jilin H5 chondrite meteorite sample, and a 51.37-g Sikhote-Alin IIAB Iron meteorite sample are also presented. Temperature interpolation formula are further provided for the specific heat capacity, thermal conductivity, and thermal diffusivity of the 3.01-g Gao-Guenie sample in the temperature range 300<T (K)<800. We briefly review the possible effects of the newly deduced specific heat and thermal conductivity values on the ablation of meteoroids within the Earth's atmosphere, the modeling of asteroid interiors and the orbital evolution of meteoroids through the Yarkovsky-O’Keefe-Radzievskii-Paddack (YORP) effect.     

Seasonal variations of diffuse solar radiation at Ilorin (8°32′N,4°46′E), Nigeria

Hourly diffuse solar irradiance (H_d) and the corresponding global irradiance (H) falling on a horizontal surface at Ilorin (8°32N,4°46E), Nigeria has been measured for a period of fifteen months commencing from February, 1993. As expected, each monthly mean diurnal variation of H_d exhibits a mid-day maximum, while that of the ratio H_d/H exhibits a minimum. The month to month variations of these parameters are consequent on the dominant atmospheric conditions observed in the months concerned. The monthly average daily total of diffuse radiation (H_dm) was found to be highest in February, 1994 with a value of (3347 ± 45) Wm^–2day^–1, mainly due to the effects of Harmattan haze and thin clouds, while it was found to be lowest in November, 1993 and January, 1994 with a value of about 2500 Wm^–2day^–1. Similarly, the ratio of the monthly average daily total of diffuse radiation to the monthly average daily total of global radiation (H_dm/H_m) had the lowest value of 0.49 in the relatively clear sky month of November, 1993 and the highest value of 0.74 in the mainly cloudy month of August, 1993. On an annual average, the diffuse component constituted about 60% of the global solar radiation arriving on the ground at Ilorin, Nigeria primarily due to clouds and Harmattan haze which are seasonal, in addition to the constant background of molecular scattering.     

Indirect experimental evidence against the tachyons

It is noted that the empirically confirmed existence of the massiveW ^± andZ ⁰ particles is in fact an indirect experimental evidence against the existence of tachyons.     

MM Herculis: An eclipsing binary of the RS CVn type

Differential photoelectric photometry inV, B, andU has been obtained for the eclipsing binary MM Her, a member of the RS Canum Venaticorum class. The light outside eclipse was Fourier-analyzed to study the wave. The migration and amplitude of the wave and the mean light level of the system now have been monitored from 1976 through 1980. The phase of wave minimum has decreased from 0 _. ^P 80 to 0 _. ^P 25, the wave amplitude has varied between 0 _. ^m 06 and 0 _. ^m 12, and the mean light level has fluctuated between 0.94 and 0.99. Observations within eclipse revealed that the eclipses are partial, not total as previously thought, and a new time of mid-eclipse was found to be JD (hel.)=2444 500.6665±0 _. ^d 0008. The Russell model was used to solve the 1980 light curve. Elements of the rectified light curve werei=86 _. ^° 35±0 _. ^° 09,r _h =0.070±0.002,r _c =0.125±0.001,L _h (V)=0.585±0.008 andL _h (B)=0.683±0.010. The geometric elements were forced on the pre-1980 light curves and found to be compatible. With these elements and previously obtained double-lined radial velocity curves, new absolute dimensions have been calculated: 1.18M and 1.58R for the hotter star and 1.27M and 2.83R for the cooler star. By plotting color indices on the color-color curve, spectral types of G2V and K21V were found, each uncertain by a couple of subclasses.Guest Observer Kitt Peak National Observatory, operated by the Association of Universities for Research in Astronomy, under contract with the National Science Foundation.