The restricted problem of n+ν bodies

The simplest, conventional, and original form of the circular restricted problem of three bodies is briefly described in sidereal and synodic systems using dimensional and non-dimensional variables. This dynamical system is generalized to n2 primary bodies (from n=2) with masses M_i, 1in, interacting with arbitrary force laws (instead of only gravitational forces). The number of bodies of small mass mM_i not perturbing the primaries is increased from =1 to 1 where 1 and the minor bodies are allowed to interact with one another under arbitrary force laws. While the minor bodies (m) do not affect the motions of the primaries (M_i), the primaries influence the motions of the minor bodies with arbitrary force laws.For the case where n=2, 1, and only gravitational forces act on the system, an integral of the system is derived. It is shown that the energy integral of the general problem of N bodies and the Jacobian integral of the classical restricted problem of three bodies are limiting cases of this integral. The role of the integral in bounding the motion of the minor bodies is discussed. Several applications of this system are given.     

Temperature fluctuations in interstellar dust grains

Temperature fluctuations in interstellar dust grains caused by absorption of ultraviolet photons are discussed. Temperature probability distributions are presented for various assumptions about the grain specific heat and far infrared emissivity. Grains smaller than or about 0.01 may suffer large temperature fluctuations and would spend most of their time at very low temperatures. The equilibrium temperature is not a good measure for most average temperatures of such grains. It is shown that, although small grains spend only a small fraction of their time at the higher temperatures, the emitted far infrared spectrum is significantly shifted towards shorter wavelengths than predicted for grains assumed to be at the equilibrium temperature.Invited contribution to the Proceedings of a Workshop onThermodynamics and Kinetics of Dust Formation in the Space Medium held at the Lunar and Planetary Institute, Houston, 6–8 September, 1978.     

A study of the background corona near solar minimum

The white light coronagraph data from Skylab is used to investigate the equatorial and polarK andF coronal components during the declining phase of the solar cycle near solar minimum. Measurements of coronal brightness and polarization brightness product between 2.5 and 5.5R during the period of observation (May 1973 to February 1974) lead to the conclusions that: (1) the equatorial corona is dominated by either streamers or coronal holes seen in projections on the limb approximately 50% and 30% of the time, respectively; (2) despite the domination by streamers and holes, two periods of time were found which were free from the influences of streamers or holes (neither streamers nor holes were within 30° in longitude of the limb); (3) the derived equatorial background density model is less than 15% below the minimum equatorial models of Newkirk (1967) and Saito (1970); (4) a spherically symmetric density model for equatorial coronal holes yields densities one half those of the background density model; and (5) the inferred brightness of theF-corona is constant to within ±10% and ±5% for the equatorial and polar values, respectively, over the observation period. While theF-corona is symmetric at 2R it begins to show increasing asymmetry beyond this radius such that at 5R the equatorialF-coronal brightness is 25% greater than the polar brightness.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Petrogenesis and paleotectonic history of the Wild Bight Group,an Ordovician rifted island arc in central Newfoundland

The Wild Bight Group (WBG) is a sequence of early and middle Ordovician volcanic, subvolcanic and epiclastic rocks, part of the Dunnage Tectonostratigraphic Zone of the Newfoundland Appalachians. A detailed geochemical and Nd-isotopic study of the volcanic and subvolcanic rocks has been carried out to determine the geochemical characteristics of the rocks, interpret their palcotectonic environments and constrain their petrogenetic history. The lower and central stratigraphic levels of the WBG contain mafic volcanic rocks with island-arc geochemical signatures, including LREE-enriched are tholeiites with _Nd(t) =-0.1 to +2.2 (type A-I), LREE-depleted arc tholeiites with _Nd(t) =+5.6 to +7.1 (type A-II) and an unusual suite of strongly incompatible-element depleted tholeiites in which _Nd(t) ranges from-0.9 to +4.6 and is negatively correlated with¹⁴⁷Sm/¹⁴⁴Nd (type A-III). High-silica, low-K rhyolites occur locally in the central part of the stratigraphy, associated with mafic rocks of arc affinity, and have _Nd(t) =+4.7 to +5.4. The upper stratigraphic levels of the WBG dominantly contain rocks with non-arc geochemical signatures, including alkalic basalts with _Nd(t) =+4.6 to +5.5 (type N-I), strongly LREE- and incompatible element-enriched tholeiites that are transitional between alkalic and non-alkalic rocks with _Nd(t) =+4.4 to +7.0 (type N-II) and rocks with flat to slightly LREE-enriched patterns and _Nd(t) =+5.1 to +7.4 (type N-III). Rocks with non-arc and arc signatures are locally interbedded near the stratigraphic type of the WBG. Nd-isotopic data in the type A-I and A-II rocks are generally compatible with mixing/partial melting models involving depleted mantle, variably contaminated by a subducted crustally-derived sediment. The petrogenesis of type A-III rocks must involve source mixing and multi-stage partial melting, but the details are not clear. The geochemistry and Nd isotope data for types N-I, N-II and N-III rocks are compatible with petrogenetic models involving variable partial melting of a source similar to that postulated for modern oceanic island basalts. Comparison of the WBG with modern analogues suggests a 3-stage developmental model: stage 1) island-arc volcanism (eruption of type mafic volcancs); stage 2) arc-rifting (continued eruption of type A-I, A-I, eruption of types A-II and A-III mafic volcanics and high-silica, low-K rhyolites); and stage 3) back-arc basin volcanism (continued minor eruption of type A-I basalts, eruption of types N-I, N-II, N-III basalts). Stages 1 and 2 volcanism involved partial melting of subduction contaminated mantle, while stage 3 volcanism utilized depleted-mantle sources not affected by the subducting slab. This model provides a basis for interpreting coeval sequences in central Newfoundland and a comparative framework for some early Paleozoic oceanic volcanic sequences elsewhere in the Appalachian orogen.     

Primary fractionation of elements among iron meteorites

The primary fractionation process in iron meteorites is that responsible for the distribution of elements between the groups, most notably Ga and Ge, which show concentration ranges of 10³ and 10⁴ respectively. To investigate the cause of the primary fractionation, concentrations of 16 elements were converted to relative abundances by dividing the element/Ni ratio by the CI chondrite ratio. These abundances were plotted on logarithmic graphs with data for each group (except IB and IIICD) and each cluster of closely related anomalous irons averaged.Co, P, Au, As, Cu, Sb, Ge and Zn are positively correlated with Ga. For most groups (except IA, IC and IIAB) relative abundances of these elements tend to decrease from about 1 in approximately the order listed above. This is the expected order in which these elements will condense into Fe, Ni during equilibrium nebular condensation. Mean relative abundances of refractory elements in groups generally lie within a narrow range of 0.5–2, and are uncorrelated with Ga. Although the equilibrium model may be only a gross approximation, it suggests that most primary fractionation did occur during nebular condensation.The anomalous irons are essential for defining many of the primary fractionation trends. On several element-Ga graphs the displacements of the anomalous irons from the primary curves indicate that these irons experienced the same secondary fractionation process (probably fractional crystallization) that produced the trends within most groups. The anomalous irons appear to be samples from over 50 minor groups, which have similar histories to the 12 major groups.     

Relationship of intertidal surface sediment chlorophyll concentration to hyperspectral reflectance and chlorophyll fluorescence

Estimating biomass of microphytobenthos (MPB) on intertidal mud flats is extremely difficult due to their patchy occurrence, especially at the scale of an entire mud flat. We tested two optical approaches that can be applied in situ: spectral reflectance and chlorophyll fluorescence. These two approaches were applied in 4 European estuaries with different sediment characteristics. At each site, paired replicate measurements of hyperspectral reflectance, chlorophyll fluorescence (after 15 min dark adaptation, F_o ¹⁵), sediment water content, and chlorophylla concentrations were taken (including breakdown products: [chla+phaeo]). Sediments were further characterized by grain size and organic content analysis. The spectral signatures of tidal flats dominated by benthic microalgae, mainly diatoms, could be easily distinguished from sites dominated by macrophytes; we present a 3 waveband algorithm that can be used to detect the presence of macrophytes. The normalized difference vegetation index (NDVI) was found to be most strongly correlated to sediment [chla+phaeo], except for the predominantly sandy Sylt stations. F_o ¹⁵ was also significantly correlated to sediment [chla+phaeo] in all but one grid (Sylt grid A). Our results suggest that the functional relationships (i.e., the slopes) between NDVI or fluorescence and [chla+ phaeo] were not significantly different in the muddier grids, although the intercepts could differ significantly, especially for F_o ¹⁵. This suggests a mismatch of the optical depth seen by the reflectometer or fluorometer and the depth sampled for pigment analysis. NDVI appears to be a robust proxy for sediment [chla+phaeo] and can be used to quantify MPB biomass in muddy sediments of mid latitude estuaries.     

Displacement-length scaling relations for faults on the terrestrial planets

Displacement-length (D/L)scaling relations for normal and thrust faults from Mars, and thrust faults from Mercury, for which sufficiently accurate measurements are available, are consistently smaller than terrestrial D/L ratios by a factor of about 5, regardless of fault type (i.e. normal or thrust). We demonstrate that D/L ratios for faults scale, to first order, with planetary gravity. In particular, confining pressure modulates: (1) the magnitude of shear driving stress on the fault; (2) the shear yield strength of near-tip rock; and (3) the Young's (or shear) modulus of crustal rock. In general, all three factors decrease with gravity for the same rock type and pore-pressure state (e.g. wet conditions). Faults on planets with lower surface gravities, such as Mars and Mercury, demonstrate systematically smaller D/L ratios than faults on larger planets, such as Earth. Smaller D/L ratios of faults on Venus and the Moon are predicted by this approach, and we infer still smaller values of D/L ratio for faults on icy satellites in the outer solar system. Collection of additional displacement-length and down-dip height data from terrestrial normal, strike-slip, and thrust faults, located within fold-and-thrust belts, plate margins, and continental interiors, is required to evaluate the influence of fault shape and progressive deformation on the scaling relations for faults from Earth and elsewhere.     

Net Energy Payback and CO2 Emissions from Three Midwestern Wind Farms: An Update

This paper updates a life-cycle net energy analysis and carbon dioxide emissions analysis of three Midwestern utility-scale wind systems. Both the Energy Payback Ratio (EPR) and CO₂ analysis results provide useful data for policy discussions regarding an efficient and low-carbon energy mix. The EPR is the amount of electrical energy produced for the lifetime of the power plant divided by the total amount of energy required to procure and transport the materials, build, operate, and decommission the power plants. The CO₂ analysis for each power plant was calculated from the life-cycle energy input data. A previous study also analyzed coal and nuclear fission power plants. At the time of that study, two of the three wind systems had less than a full year of generation data to project the life-cycle energy production. This study updates the analysis of three wind systems with an additional four to eight years of operating data. The EPR for the utility-scale wind systems ranges from a low of 11 for a two-turbine system in Wisconsin to 28 for a 143-turbine system in southwestern Minnesota. The EPR is 11 for coal, 25 for fission with gas centrifuge enriched uranium and 7 for gaseous diffusion enriched uranium. The normalized CO₂ emissions, in tonnes of CO₂ per GW_eh, ranges from 14 to 33 for the wind systems, 974 for coal, and 10 and 34 for nuclear fission using gas centrifuge and gaseous diffusion enriched uranium, respectively.