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.     

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.     

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.     

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.     

Tolerance of allogromiid Foraminifera to severely elevated carbon dioxide concentrations: Implications to future ecosystem functioning and paleoceanographic interpretations

Increases in the partial pressure of carbon dioxide (pCO₂) in the atmosphere will significantly affect a wide variety of terrestrial fauna and flora. Because of tight atmospheric–oceanic coupling, shallow-water marine species are also expected to be affected by increases in atmospheric carbon dioxide concentrations. One proposed way to slow increases in atmospheric pCO₂ is to sequester CO₂ in the deep sea. Thus, over the next few centuries marine species will be exposed to changing seawater chemistry caused by ocean–atmospheric exchange and/or deep-ocean sequestration. This initial case study on one allogromiid foraminiferal species (Allogromia laticollaris) was conducted to begin to ascertain the effect of elevated pCO₂ on benthic Foraminifera, which are a major meiofaunal constituent of shallow- and deep-water marine communities. Cultures of this thecate foraminiferan protist were used for 10–14-day experiments. Experimental treatments were executed in an incubator that controlled CO₂ (15 000; 30 000; 60 000; 90 000; 200 000 ppm), temperature and humidity; atmospheric controls (i.e., ~ 375 ppm CO₂) were executed simultaneously. Although the experimental elevated pCO₂ values are far above foreseeable surface water pCO₂, they were selected to represent the spectrum of conditions expected for the benthos if deep-sea CO₂ sequestration becomes a reality. Survival was assessed in two independent ways: pseudopodial presence/absence and measurement of adenosine triphosphate (ATP), which is an indicator of cellular energy. Substantial proportions of A. laticollaris populations survived 200 000 ppm CO₂ although the mean of the median [ATP] of survivors was statistically lower for this treatment than for that of atmospheric control specimens. After individuals that had been incubated in 200 000 ppm CO₂ for 12 days were transferred to atmospheric conditions for ~ 24 h, the [ATP] of live specimens (survivors) approximated those of the comparable atmospheric control treatment. Incubation in 200 000 ppm CO₂ also resulted in reproduction by some individuals. Results suggest that certain Foraminifera are able to tolerate deep-sea CO₂ sequestration and perhaps thrive as a result of elevated pCO₂ that is predicted for the next few centuries, in a high-pCO₂ world. Thus, allogromiid foraminiferal “blooms” may result from climate change. Furthermore, because allogromiids consume a variety of prey, it is likely that they will be major players in ecosystem dynamics of future coastal sedimentary environments.     

Dimension of the Earth's General Ellipsoid

The problem of specifying the Earth's mean (general)ellipsoid is discussed. This problem has been greatly simplified in the era of satellite altimetry, especially thanks to the adopted geoidal geopotential value, W₀ = (62 636 856.0 ± 0.5) m² s^-2.Consequently, the semimajor axis a of the Earth's mean ellipsoid can be easily derived. However, an a priori condition must be posed first. Two such a priori conditions have been examined, namely an ellipsoid with the corresponding geopotential that fits best W₀ in the least squares sense and an ellipsoid that has the global geopotential average equal to W₀. It has been demonstrated that both a priori conditions yield ellipsoids of the same dimension, with a–values that are practically identical to the value corresponding to the Pizzetti theory of the level ellipsoid: a = (6 378 136.68 ± 0.06) m.     

The significance of observed rotational magnetic hysteresis in lunar samples

Rotational Magnetic hysteresis (W _R ) curves for lunar soils 10084, 12070, 14259, and rock 14053, have been published. There is no adequate explanation to date for the observed largeW _R at high fields. Lunar rock magnetism researchers consider fine particle iron to be the primary source of stable magnetic remanence in lunar samples. Iron has cubic anisotropy with added shape anisotropy for extreme particle shapes. The observed high fieldW _R must have its source in uniaxial or unidirectional anisotropy. This implies the existence of minerals with uniaxial anisotropy or exchange coupled spin states. Therefore, the source of this observed high fieldW _R must be identified and understood before serious paleointensity studies are made. It is probable that the exchange coupled spin states and/or the source of uniaxial anisotropy responsible for the high fieldW _R might be influenced by the lunar surface diurnal temperature cycling. The possible sources of high fieldW _R in lunar samples are presented and considered.     

Astrophysical properties of red giants in three open clusters older than the hyades

Results fromCMT ₁T₂ 1T2 broad-band and DDO intermediate-band photometry are presented for G and K giants in the old open clusters NGC. 2482, NGC 3680, and IC 4651. Two independent photometric criteria have been used to separate red field stars from the physical members of the clusters. Recent calibrations of the DDO andCMT ₁T₂ systems have been used to derive reddening, distance moduli, metallicities, effective temperatures, and surface gravities. Rough estimates of masses have also been made. The giants of NGC 2482 and IC 4651 have CN strengths nearly identical to the Hyades giants, while those of NGC 3680 are slightly richer in CN than the nearby K giants.CMT1T2 abundance analysis in NGC 2482 and NGC 3680 yield [Fe/H]_MT = - 0.1 ± 0.1 as derived from the iron lines, while abundances derived from the CNO - contaminated (C - M) index are 0.4 dex higher. BothCMT ₁T₂ and DDO data support the conclusion that 1C 4651, with [Fe/H] = + 0.2 ± 0.1, is on the metalrich side of the distribution of intermediate and old open clusters. Finally, the mass results suggest that the clump stars in NGC 3680 and. IC 4651 could have undergone mass loss before reaching their helium core burning phase of evolution. Supported in part by the Consejo Nacional de Investigaciones Cientificas y Tecnicas (CONICET) of Argentina. Visiting astronomer of Cerro Tololo Inter-American Observatory supported by the National Science Foundation under contract No. AST 74-04128.     

Excess line broadening in various objects- a case for weak magnetic effects

I present updated compilations of both observational data and theoretical predictions concerning excess line width and sizes in astrophysical bodies. After removing two well-known broadening mechanisms (thermal width and width due to large scale motions such as expansion), I analyse statistically the excess line widthW _excess. The excess line width shows a changing behavior with object sizeR, of the formW _excess ~R ^q. Taking all objects together, I find thatq = 0.55 with s.d. = 0.05. This resultextends previous studies to cover 5 decades in sizes, from 0.01 pc up to 1000 pc. Taking only objects withR < 1 pc, I find thatq = 0.7 with s.d.=0.1, while taking only objects withR > 1 pc givesq = 0.5 with s.d.=0.1; thus a steeper (not flatter) value ofq at smallR may be possible. Previous claims to derive a law for objects of sizesR > 1 kpc are discussed, in relation to the problem of removing obvious large scale motions from the observed line width. Thus several models with predictedq values between 0 and 1 can be eliminated, and the remaining ones could allow weak magnetic effects on the line widths.     

The Phase Space Structure Around L4 in the Restricted Three-Body Problem

The phase space structure around L ₄ in the restricted three-body problem is investigated. The connection between the long period family emanating from L ₄ and the very complex structure of the stability region is shown by using the method of Poincarés surface of section. The zero initial velocity stability region around L ₄ is determined by using a method based on the calculation of finite-time Lyapunov characteristic numbers. It is shown that the boundary of the stability region in the configuration space is formed by orbits suffering slow chaotic diffusion.     

Quasi-critical orbits for artificial lunar satellites

We study the problem of critical inclination orbits for artificial lunar satellites, when in the lunar potential we include, besides the Keplerian term, the J ₂ and C ₂₂ terms and lunar rotation. We show that, at the fixed points of the 1-D averaged Hamiltonian, the inclination and the argument of pericenter do not remain both constant at the same time, as is the case when only the J ₂ term is taken into account. Instead, there exist quasi-critical solutions, for which the argument of pericenter librates around a constant value. These solutions are represented by smooth curves in phase space, which determine the dependence of the quasi-critical inclination on the initial nodal phase. The amplitude of libration of both argument of pericenter and inclination would be quite large for a non-rotating Moon, but is reduced to <0°.1 for both quantities, when a uniform rotation of the Moon is taken into account. The values of J ₂, C ₂₂ and the rotation rate strongly affect the quasi-critical inclination and the libration amplitude of the argument of pericenter. Examples for other celestial bodies are given, showing the dependence of the results on J ₂, C ₂₂ and rotation rate.     

The effect of ground ice on the Martian seasonal CO2 cycle

The mostly carbon dioxide (CO₂) atmosphere of Mars condenses and sublimes in the polar regions, giving rise to the familiar waxing and waning of its polar caps. The signature of this seasonal CO₂ cycle has been detected in surface pressure measurements from the Viking and Pathfinder landers. The amount of CO₂ that condenses during fall and winter is controlled by the net polar energy loss, which is dominated by emitted infrared radiation from the cap itself. However, models of the CO₂ cycle match the surface pressure data only if the emitted radiation is artificially suppressed suggesting that they are missing a heat source. Here we show that the missing heat source is the conducted energy coming from soil that contains water ice very close to the surface. The presence of ice significantly increases the thermal conductivity of the ground such that more of the solar energy absorbed at the surface during summer is conducted downward into the ground where it is stored and released back to the surface during fall and winter thereby retarding the CO₂ condensation rate. The reduction in the condensation rate is very sensitive to the depth of the soil/ice interface, which our models suggest is about 8 cm in the Northern Hemisphere and 11 cm in the Southern Hemisphere. This is consistent with the detection of significant amounts of polar ground ice by the Mars Odyssey Gamma Ray Spectrometer and provides an independent means for assessing how close to the surface the ice must be. Our results also provide an accurate determination of the global annual mean size of the atmosphere and cap CO₂ reservoirs, which are, respectively, 6.1 and 0.9 hPa. They also indicate that general circulation models will need to account for the effect of ground ice in their simulations of the seasonal CO₂ cycle.     

The Non-Linear Stability of L4 in the Restricted Three-Body Problem when the Bigger Primary is a Triaxial Rigid Body

The non-linear stability of L ₄ in the restricted three-body problem has been studied when the bigger primary is a triaxial rigid body with its equatorial plane coincident with the plane of motion. It is found that L ₄ is stable in the range of linear stability except for three mass ratios:

Long-chain alkenones and U37′ variability along a south–north transect in the Western Pacific Ocean

In this paper, we present 50 surface water samples collected during the IMAGES III cruise (June–July 1997) along a transect from New Zealand to the China Sea (42°S–178°E, 21°N–120°E) covering a temperature range from 13.3 to 30.4 °C. A very worthwhile aspect of this study is a coupling of both biomarker (alkenone) and coccolithophorid counting. We show that the U₃₇^k′–temperature relationship is very similar to the Prahl et al. [Geochim. Cosmochim. Acta 52 (1988) 2203] culture calibration and to the global core top calibration of Müller et al. [Geochim. Cosmochim. Acta 62 (1998) 1757]. However, in the warmest surface waters of the Western Pacific ocean (>26.4 °C) where Gephyrocapsa oceanica is likely the most widespread species, the associated U₃₇^k′ has a constant value of 1.0. The consequence is that above this temperature threshold, U₃₇^k′ cannot be used as an accurate paleothermometer.     

Electronic Sputtering Analysis of Astrophysical Ices

Experimental results on fast ion collision with icy surfaces having astrophysical interest are presented. ²⁵²Cf fission fragments projectiles were used to induce ejection of ionized material from H₂O, CO₂, CO, NH₃, N₂, O₂ and Ar ices; the secondary ions were identified by time-of-flight mass spectrometry. It is observed that all the bombarded frozen gas targets emit cluster ions which have the structure X_nR^±, where X is the neutral ice molecule and R^± is either an atomic or a molecular ion. The shape of the positive or negative ion mass spectra is characterized by a decreasing yield as the emitted ion mass increases and is generally described by the sum of two exponential functions. The positive ion water ice spectrum is dominated by the series (H₂O)_nH₃O⁺ and the negative ion spectrum by the series (H₂O)_nOH⁻ and (H₂O)_nO⁻. The positive ion CO₂ ice spectrum is characterized by R⁺ = C⁺, O⁺, CO⁺, O₂⁺ or CO₂⁺ and the negative one by R⁻ = CO₃⁻. The dominant series for ammonia ice correspond to R⁺ = NH₄⁺ and to R⁻ = NH₂⁻. The oxygen series are better described by (O₃)_nO_m⁺ secondary ions where m = 1, 2 or 3. Two positive ion series exist for N₂ ice: (N₂)_nN₂⁺ and (N₂)_nN⁺. For argon positive secondary ions, only the (Ar)_nAr⁺ series was observed. Most of the detected molecular ions were formed by one-step reactions. Ice temperature was varied from ∼20 K to complete sublimation.     

Preliminary Analysis of Photometric Variations of the Central Star of the Planetary Nebula Sh 2-71

We confirm the presence of regular UBV(RI)_C light variations of the object in the center of the planetary nebula Sh 2-71, with an improved period of P = 68.132 ± 0.005 days. The shapes and amplitudes of light curves, in particular colours, are briefly discussed.     

The problem of the maximum volumes and particle horizon in the Friedmann universe model

The maximum volume of the closed Friedmann universe is further investigated and is shown to be 2² R ³ (t), instead of ² R ³ (t) as found previously. This discrepancy comes from the incomplete use of the volume formula of 3-dimensional spherical space in the astronomical literature. Mathematically, there exists the maximum volume at any cosmic timet in a 3-dimensional spherical case. However, the Friedmann closed universe in expansion reaches its maximum volume only at the timet _m of the maximum scale factorR(t _m ). The particle horizon has no limitation for the farthest objects in the closed Friedmann universe if the proper distance of objects is compared with the particle horizon as it should be. It will lead to absurdity if the luminosity distance of objects is compared with the proper distance of the particle horizon.     

Existence and uniqueness of stellar equilibrium models

The stellar equilibrium equations for given surface pressureP _* and temperatureT _*, and in the absence of convection, are translated into a nonlinear integral equation, in which the radiusR of the star enters as an eigenvalue. We show that under broad mathematical assumptions on the constitutive equations (equation of state, opacity and energy generation) a global existence and uniqueness property can be formulated. If a valueP _M is selected, which restricts the allowed pressure and temperature range |P(r)–P _*|+E|T(r)–T _*P _M (E, arbitrary constant of dimensions of a pressure over temperature), thenat least one solutionP(r),T(r) exists in the pressure-temperature range chosen, for anyR<R _E . This solution isunique forR<R _c .R _E andR _c are expressed in terms of the constitutive equations, and of the pressure-temperature range adopted. A physical argument in favour of the stability of this solution is presented.     

GEOS-II and 13th order terms of the geopotential

The resonance of GEOS-II (1968-002A) with 13th-order terms of the geopotential is analyzed. The odd-degree geopotential coefficients (13, 13), (15, 13), and (17, 13) given by Yionoulis most accurately model the resonance effects on GEOS-II of any of the published sets of 13th-order coefficients. However, this set is not adequate for precision orbit determination; additional even-degree coefficients are required.Values ofC _14,13(=0.57×10^–21) andS _14,13(=6.5×10^–21) to be used with the odd-degree set of Yionoulis were obtained from an analysis of the observed along-track position variation of GEOS-II. These coefficients, when used with those of Yionoulis, yield greatly improved fits to the data and orbital prediction capability. However, further refinement is possible because the small effects of the remaining even-degree resonant terms were not modeled.The composite coefficientsC _13,13(=1.7×10^–20) andS _13,13(=+2.7×10^–20) were obtained under the assumption that the (13, 13) spherical harmonic of the geopotential is responsible for all of the observed along-track variation of GEOS-II due to resonance. The good agreement of these deliberately composite values with some published values ofC _13,13 andS _13,13 suggests that some of the published values may also be composite to some extent.These coefficients are hereinafter referred to as the APL coefficients.     

Analytical short-term orbit predictions withJ 3 andJ 4 in terms of KS elements

Analytical theory for short-term orbit motion of satellite orbits with Earth's zonal harmonicsJ ₃ andJ ₄ is developed in terms of KS elements. Due to symmetry in KS element equations, only two of the nine equations are integrated analytically. The series expansions include terms of third power in the eccentricity. Numerical studies with two test cases reveal that orbital elements obtained from the analytical expressions match quite well with numerically integrated values during a revolution. Typically for an orbit with perigee height, eccentricity and inclination of 421.9 km, 0.17524 and 30 degrees, respectively, maximum differences of 27 and 25 cm in semimajor axis computation are noted withJ ₃ andJ ₄ term during a revolution. For application purposes, the analytical solutions can be used for accurate onboard computation of state vector in navigation and guidance packages.