On a transformation of the differential equations of the lunar theory

This work contains a transformation of Hill-Brown differential equations for the coordinates of the satellite to a type which can be integrated in a literal form using an analytical programming language. The differential equation for the parallax of the satellite is also established. Its use facilitates the computation of Hill's periodic intermediary orbit of the satellite and provides a good check for the expansion of the coordinates and frequencies. The knowledge of the expansion of the parallax facilitates the formation of differential equations for terms with a given characteristic. These differential equations are put into a form which favors the solution by means of iteration on the computer. As in the classical theory we obtain the expansions of the coordinates and of the parallax in the form of trigonometric series in four arguments and in powers of the constants of integration. We expand the differential operators into series in squares of the constants of integration. Only the terms of order zero in these expansions are employed in the integration of the differential equations. The remaining terms are responsible for producing the cross-effects between the perturbations of different order. By applying the averaging operator to the right sides of the differential equations we deduce the expansion of the frequencies in powers of squares of the constants of integration.Basic Notations f the gravitational constant - E the mass of the planet - M the mass of the satellite - t dynamical time - x, y, z planetocentric coordinates of the satellite - u x+y–1 - s x–y–1 - the planetocentric distance of the satellite - w 1/ - ₀ the variational part of - w ₀ the variational part ofw, - n the mean daily sidereal motion of the satellite - a the mean semi-major axis of the satellite defined by means of the Kepler relation:a ³ n ²=f(E+M) - a the mean semi-major axis defined as the constant factor attached to the variational solution - e the constant of the eccentricity of the satellite - the sine of one half the orbital inclination of the satellite relative to the orbit of the sun - c(n–n) the anomalistic frequency of the satellite - c ₀ the part ofc independent frome,e, and - g(n–n) the draconitic frequency of the satellite, - g ₀ the part ofg independent frome,e, and - exp (n–n)t–1 - D d/d - e the eccentricity of the solar planetocentric orbit - a the semi-major axis of the solar orbit - n the mean daily motion of the sun in its orbit around the planet - m n/(n–n) - a/a-the parallactic factor - the disturbing function     

Law of the sea and ASW: National security versus arms control

The law of the sea has always been open to the charge of being a ‘covenant without a sword’ and its effectiveness when challenged by the perceived national security of a superpower is questionable. Attempts to limit and control antisubmarine warfare (ASW) have demonstrated that neither superpower is prepared to risk its second-strike capability for what may be an illusory legal protection. This article reviews developments relevant to ASW in the law of the sea and describes the significance of ASW to the superpowers' strategic objectives. The authors conclude by stressing the urgent need for effective arms control.     

THE SUPERIORITY OF LOW-GRADE IRON ORE*

At the mine, pelletized low-grade taconite iron ore requires more energy and labor than rich hematite. In blast furnaces, however, taconite pellets are much more efficient than hematite. Overall, pellets save energy and labor. Attempts to pelletize hematite have not worked well. Therefore, many hematite mines have closed and miners have relocated to taconite plants. Also, some jobs, capital investments, and pollution have decreased at steel mills while increasing in the sparsely populated mining regions as a result of pelletizing.     

Morphological relationships in the chromospheric Hα fine structure

A continuous relationship is proposed between the basic elements of the dark fine structure of the quiet and active chromosphere. A progression from chromospheric bushes to fibrils, then to chromospheric threads and active region filaments, and finally to diffuse quiescent filaments, is described. It is shown that the horizontal component of the field on opposite sides of an active region quiescent filament can be in the same direction and closely parallel to the filament axis. Consequently, it is unnecessary to postulate twisted or otherwise complex field configurations to reconcile the support mechanism of filaments with the observed motion along their axis.     

The influence of the great inequality on the secular disturbing function of the planetary system

This paper derives the contributionF ₂ ^* by the great inequality to the secular disturbing function of the principal planets. Andoyer's expansion of the planetary disturbing function and von Zeipel's method of eliminating the periodic terms is employed; thereby, the corrected secular disturbing function for the planetary system is derived. An earlier solution suggested by Hill is based on Leverrier's equations for the variation of elements of Jupiter and Saturn and on the semi-empirical adjustment of the coefficients in the secular disturbing function. Nowadays there are several modern methods of eliminating periodic terms from the Hamiltonian and deriving a purely secular disturbing function. Von Zeipel's method is especially suitable. The conclusion is drawn that the canonicity of the equations for the secular variation of the heliocentric elements can be preserved if there be retained, in the secular disturbing function, terms only of the second and fourth order relative to the eccentricity and inclinations.The Krylov-Bogolubov method is suggested for eliminating periodic terms, if it is desired to include the secular perturbations of the fifth and higher order in the heliocentric elements. The additional part of the secular disturbing functionF ₂ ^* derived in this paper can be included in existing theories of the secular effects of principal planets. A better approach would be to preserve the homogeneity of the theory and rederive all the secular perturbations of principal planets using Andoyer's symbolism, including the part produced by the great inequality.     

A critique of the internal tracer method for estimating contaminant degradation rates

The internal tracer method for estimating contaminant degradation rates separates the attenuation effects not associated with degradation by using a codisposed recalcitrant internal tracer to normalize the degrading contaminant concentration. The remaining attenuation between the internal tracer and degrading contaminant is attributed to degradation and the degradation rate half-life is estimated from the first-order decay equation. An analytical solution of the advection- dispersion equation was used to evaluate flow-and-transport conditions that could result in incorrect estimates of contaminant degradation rate constants. Flow-and-transport characteristics that result in overestimating degradation rates were of particular interest because the internal tracer method often used to demonstrate natural attenuation can achieve remedial objectives. The analytical solution was also used to estimate the magnitude of error associated with using the internal tracer method at an example site and to explain different degradation rates estimated using tracers with different decay rate constants.     

Volumetric characteristics of lava flows from interferometric radar and multispectral satellite data: the 1995 Fernandina and 1998 Cerro Azul eruptions in the western Galápagos

We have used a suite of remotely sensed data, numerical lava flow modeling, and field observations to determine quantitative characteristics of the 1995 Fernandina and 1998 Cerro Azul eruptions in the western Galápagos Islands. Flank lava flow areas, volumes, instantaneous effusion rates, and average effusion rates were all determined for these two eruptions, for which only limited syn-eruptive field observations are available. Using data from SPOT, TOPSAR, ERS-1, and ERS-2, we determined that the 1995 Fernandina flow covers a subaerial area of 6.5×10⁶ m² and has a subaerial dense rock equivalent (DRE) volume of 42×10⁶ m³. Field observations, ATSR satellite data, and the FLOWGO numerical model allow us to determine that the effusion rate declined exponentially from a high of ~60–200 m³ s^-1 during the first few hours to <5 m³ s^-1 prior to ceasing after 73 days, with a mean effusion rate of 4–16 m³ s^-1. Integrating the ATSR-derived, exponentially declining effusion rate over the eruption duration produces a total (subaerial + submarine) DRE volume of between 27 and 100×10⁶ m³, the range in values being due to differing assumptions about heat loss characteristics; only values in the higher part of this range are consistent with the independently derived subaerial volume. Using SPOT, TOPSAR, ERS-1, and ERS-2 data, we determine that the 1998 Cerro Azul flow is 16 km long, covers 16 km², and has a DRE volume of 54×10⁶ m³. FLOWGO produces at-vent velocity and effusion rate values of 11 m s^-1 and ~600 m³ s^-1, respectively. The velocity value agrees well with the 12 m s^-1 estimated in the field. The mean effusion rate (total DRE volume/duration) was 7–47 m³ s^-1. Dike dimensions, fissure lengths, and pressure gradients along the conduit based on magma chamber depth estimates of 3–5 km produce mean effusion rates for the two eruptions that range over nearly four orders of magnitude, the range being due to uncertainty in the magma viscosity, dike dimensions, and pressure gradient between magma chamber and vent. Although somewhat consistent with mean effusion rates from other techniques, their wide range makes them less useful. The exponentially declining effusion rates during both eruptions are consistent with release of elastic strain being the driving mechanism of the eruptions. Our results provide independent input parameters for previously published theoretical relationships between magma chamber pressurization and eruption rates that constrain chamber volumes and increases in volume prior to eruption, as well as time constants of exponential decay during the eruption. The results and theoretical relationships combine to indicate that at both volcanoes probably 25–30% of the volumetric increase in the magma chamber erupted as lava onto the surface. In both eruptions the lava flow volumes are less than 1% of the magma chamber volume.     

Efstadalsvatn – a multi-proxy study of a Holocene lacustrine sequence from NW Iceland

Multi-proxy data, both lithostratigraphic and biostratigraphic, are presented from Efstadalsvatn, a lake in NW Iceland. The sequence covers the period 10,000 to 3500 ¹⁴C yr B.P. The biostratgraphic data include the first Icelandic chironomid-based reconstruction of Holocene mean July air temperatures, using a Norwegian training set in the absence of modern Icelandic data. The results show that deglaciation and ecosystem development probably began before 10,000 ¹⁴C yr B.P. and that July temperatures were around 4°C at ca. 9500 ¹⁴C yr B.P. Temperatures then rose to ca. 8°C at the time of the deposition of the Saksunarvatn tephra (9100 ¹⁴C yr B.P.), reaching ca. 10°C by 8500 ¹⁴C yr B.P., high enough for the growth of tree birch, although successful birch colonisation did not take place until 6750 ¹⁴C yr B.P. There is some evidence for cooling immediately preceding 9100 ¹⁴C yr B.P. There is little firm biostratigraphic evidence for the 8200 cal. B.P. event, although this may be due to a relatively low resolution pollen sampling interval, but there are changes at this time in the total carbon (TC) and mass susceptibility (MS) data. Optimal temperatures and relative vegetation stability may have occurred between 8000–6100 ¹⁴C yr B.P. but the chironomid assemblages indicate higher temperatures after 5000 ¹⁴C yr B.P. This latter interpretation may, however, reflect delayed colonisation of thermophilous taxa and requires further investigation. There is evidence in the lithostratigraphy for greater local terrestrial instability after 6100 ¹⁴C yr B.P. but it seems unlikely that this led to the redevelopment of ice in the catchment. The biostratigraphic records appear to show a degree of resistence to climate forcing throughout the early and middle Holocene. The new chironomid-based temperature reconstruction needs to be refined by further studies in Iceland, particularly the development of an Icelandic training set, but has already demonstrated the problems of paleoclimatic interpretations based on pollen and/or macrofossil evidence alone.