Delaunay variables approach to the elimination of the perigee in Artificial Satellite Theory

Analytical integration in Artificial Satellite Theory may benefit from different canonical simplification techniques, like the elimination of the parallax, the relegation of the nodes, or the elimination of the perigee. These techniques were originally devised in polar-nodal variables, an approach that requires expressing the geopotential as a Pfaffian function in certain invariants of the Kepler problem. However, it has been recently shown that such sophisticated mathematics are not needed if implementing both the relegation of the nodes and the parallax elimination directly in Delaunay variables. Proceeding analogously, it is shown here how the elimination of the perigee can be carried out also in Delaunay variables. In this way the construction of the simplification algorithm becomes elementary, on one hand, and the computation of the transformation series is achieved with considerable savings, on the other, reducing the total number of terms of the elimination of the perigee to about one third of the number of terms required in the classical approach.     

Shatter cones and planar deformation features confirm Santa Marta in Piauí State,Brazil, as an impact structure

A total of 184 confirmed impact structures are known on Earth to date, as registered by the Earth Impact Database . The discovery of new impact structures has progressed in recent years at a rather low rate of about two structures per year. Here, we introduce the discovery of the approximately 10 km diameter Santa Marta impact structure in Piauí State in northeastern Brazil. Santa Marta is a moderately sized complex crater structure, with a raised rim and an off‐center, approximately 3.2 km wide central elevated area interpreted to coincide with the central uplift of the impact structure. The Santa Marta structure was first recognized in remote sensing imagery and, later, by distinct gravity and magnetic anomalies. Here, we provide results obtained during the first detailed ground survey. The Bouguer anomaly map shows a transition from a positive to a negative anomaly within the structure along a NE–SW trend, which may be associated with the basement signature and in parts with the signature developed after the crater was formed. Macroscopic evidence for impact in the form of shatter cones has been found in situ at the base around the central elevated plateau, and also in the interior of fractured conglomerate boulders occurring on the floor of the surrounding annular basin. Planar deformation features (PDFs) are abundant in sandstones of the central elevated plateau and at scattered locations in the inner part of the ring syncline. Together, shatter cones and PDFs provide definitive shock evidence that confirms the impact origin of Santa Marta. Crystallographic orientations of PDFs occurring in multiple sets in quartz grains are indicative of peak shock pressures of 20–25 GPa in the rocks exposed at present in the interior of the crater. In contrast to recent studies that have used additional, and sometimes highly controversial, alleged shock recognition features, Santa Marta was identified based on well‐understood, traditional shock evidence.     

On the preferential electrification of some dusts Part III: Rates of electrical charging of alumina upon desorption of nitrous oxide

Summary Electrification of monodisperse powders of activated alumina is investigated, following adsorption of nitrous oxide. It is found that rates of electrical charging of porous particulates examined depend on rates of release of gas from the solid.     

Formation and disruption of aquifers in southwestern Chryse Planitia, Mars

We present geologic evidence suggesting that after the development of Mars' cryolithosphere, the formation of aquifers in southwestern Chryse Planitia and their subsequent disruption led to extensive regional resurfacing during the Late Hesperian, and perhaps even during the Amazonian. In our model, these aquifers formed preferentially along thrust faults associated with wrinkle ridges, as well as along fault systems peripheral to impact craters. The characteristics of degraded wrinkle ridges and impact craters in southwestern Chryse Planitia indicate a profound role of subsurface volatiles and especially liquid water in the upper crust (the upper one hundred to a few thousands of meters). Like lunar wrinkle ridges, the martian ones are presumed to mark the surface extensions of thrust faults, but in our study area the wrinkle ridges are heavily modified. Wrinkle ridges and nearby plains have locally undergone collapse, and in other areas they are associated with domical intrusions we interpret as mud volcanoes and mud diapirs. In at least one instance, a sinuous valley emanates from a modified wrinkle ridge, further indicating hydrological influences on these thrust-fault-controlled features. A key must be the formation of volatile-rich crust. Primary crustal formation and differentiation incorporated juvenile volatiles into the global crust, but the crustal record here was then strongly modified by the giant Chryse impact. The decipherable rock record here begins with the Chryse impact and continues with the resulting basin's erosion and infilling, which includes outflow channel activity. We propose that in Simud Vallis surface flow dissection into the base of the cryolithosphere-produced zones where water infiltrated and migrated along SW-dipping strata deformed by the Chryse impact, thereby forming an extensive aquifer in southwestern Chryse Planitia. In this region, compressive stresses produced by the rise of Tharsis led to the formation of wrinkle ridges. Zones of high fracture density within the highly strained planes of the thrust faults underlying the wrinkle ridges formed regions of high permeability; thus, groundwater likely flowed and gathered along these tectonic structures to form zones of elevated permeability. Volatile depletion and migration within the upper crustal materials, predominantly along fault systems, led to structurally controlled episodic resurfacing in southwestern Chryse Planitia. The erosional modification of impact craters in this region is linked to these processes. This erosion is scale independent over a range of crater diameters from a few hundred meters to tens of kilometers. According to our model, pressurized water and sediment intruded and locally extruded and caused crustal subsidence and other degradational activity across this region. The modification of craters across this wide range of sizes, according to our model, implies that there was intensive mobilization of liquid water in the upper crust ranging from about one hundred to several thousand meters deep.     

Glacial to Holocene climate changes in the SE Pacific. The Raraku Lake sedimentary record (Easter Island, 27°S)

Easter Island (SE Pacific, 27°S) provides a unique opportunity to reconstruct past climate changes in the South Pacific region based on terrestrial archives. Although the general climate evolution of the south Pacific since the Last Glacial Maximum (LGM) is coherent with terrestrial records in southern South America and Polynesia, the details of the dynamics of the shifting Westerlies, the South Pacific Convergence Zone and the South Pacific Anticyclone during the glacial–interglacial transition and the Holocene, and the large scale controls on precipitation in tropical and extratropical regions remain elusive. Here we present a high-resolution reconstruction of lake dynamics, watershed processes and paleohydrology for the last 34 000 cal yrs BP based on a sedimentological and geochemical multiproxy study of 8 cores from the Raraku Lake sediments constrained by 22 AMS radiocarbon dates. This multicore strategy has reconstructed the sedimentary architecture of the lake infilling and provided a stratigraphic framework to integrate and correlate previous core and vegetation studies conducted in the lake. High lake levels and clastic input dominated sedimentation in Raraku Lake between 34 and 28 cal kyr BP. Sedimentological and geochemical evidences support previously reported pollen data showing a relatively open forest and a cold and relatively humid climate during the Glacial period. Between 28 and 17.3 cal kyr BP, including the LGM period, colder conditions contributed to a reduction of the tree coverage in the island. The coherent climate patterns in subtropical and mid latitudes of Chile and Eastern Island for the LGM (more humid conditions) suggest stronger influence of the Antarctic circumpolar current and an enhancement of the Westerlies. The end of Glacial Period occurred at 17.3 cal kyr BP and was characterized by a sharp decrease in lake level conducive to the development of major flood events and erosion of littoral sediments. Deglaciation (Termination 1) between 17.3 and 12.5 cal kyr BP was characterized by an increase in lake productivity, a decrease in the terrigenous input and a rapid lake level recovery, inaugurating a period of intermediate lake levels, dominance of organic deposition and algal lamination. The timing and duration of deglaciation events in Easter Island broadly agree with other mid- and low-latitude circum South Pacific terrestrial records. The transition to the Holocene was characterized by lower lake levels. The lake level dropped during the early Holocene (ca 9.5 cal kyr BP) and swamp and shallow lake conditions dominated till mid Holocene, partially favored by the infilling of the lacustrine basin. During the mid- to late-Holocene drought phases led to periods of persistent low water table, subaerial exposure and erosion, generating a sedimentary hiatus in the Raraku sequence, from 4.2 to 0.8 cal kyr BP. The presence of this dry mid Holocene phase, also identified in low Andean latitudes and in Patagonian mid latitudes, suggests that the shift of storm tracks caused by changes in the austral summer insolation or forced by “El Niño-like” dominant conditions have occurred at a regional scale. The palm deforestation of the Easter Island, attributed to the human impact could have started earlier, during the 4.2–0.8 cal kyr BP sedimentary gap. Our paleoclimatic data provides insights about the climate scenarios that could favor the arrival of the Polynesian people to the island. If it occurred at ca AD 800 it coincided with the warmer conditions of the Medieval Climate Anomaly, whereas if it took place at ca AD 1300 it was favored by enhanced westerlies at the onset of the Little Ice Age. Changes in land uses (farming, intensive cattle) during the last century had a large impact in the hydrology and limnology (eutrophication) of the lake.     

The imprint of massive black hole formation models on the LISA data stream

The formation, merging and accretion history of massive black holes (MBHs) along the hierarchical build-up of cosmic structures leaves a unique imprint on the background of gravitational waves (GWs) at mHz frequencies. We study here, by means of dedicated simulations of black hole build-up, the possibility of constraining different models of black hole cosmic evolution using future GW space-borne missions, such as LISA . We consider two main scenarios for black hole formation, namely, one where seeds are light (  ≃10² M_⊙  , remnant of Population III stars) and one where seeds are heavy (  ≳10⁴ M_⊙  , direct collapse). In all the models we have investigated, MBH binary coalescences do not produce a stochastic GW background, but rather, a set of individual resolved events. Detection of several hundreds merging events in a 3-yr LISA mission will be the sign of a heavy seed scenario with efficient formation of black hole seeds in a large fraction of high-redshift haloes. At the other extreme, a low event rate, about a few tens in 3 yr, is peculiar of scenarios where either the seeds are light, and many coalescences do not fall into the LISA band, or seeds are massive, but rare. In this case a decisive diagnostic is provided by the shape of the mass distribution of detected events. Light binaries  ( m < 10⁴ M_⊙)  are predicted in a fairly large number in Population III remnant models, but are totally absent in direct collapse models. Finally, a further, helpful diagnostic of black hole formation models lies in the distribution of the mass ratios in binary coalescences. While heavy seed models predict that most of the detected events involve equal-mass binaries, in the case of light seeds, mass ratios are equally distributed in the range 0.1–1.     

The theory of canonical perturbations applied to attitude dynamics and to the Earth rotation. Osculating and nonosculating Andoyer variables

In the method of variation of parameters we express the Cartesian coordinates or the Euler angles as functions of the time and six constants. If, under disturbance, we endow the “constants” with time dependence, the perturbed orbital or angular velocity will consist of a partial time derivative and a convective term that includes time derivatives of the “constants”. The Lagrange constraint, often imposed for convenience, nullifies the convective term and thereby guarantees that the functional dependence of the velocity on the time and “constants” stays unaltered under disturbance. “Constants” satisfying this constraint are called osculating elements. Otherwise, they are simply termed orbital or rotational elements. When the equations for the elements are required to be canonical, it is normally the Delaunay variables that are chosen to be the orbital elements, and it is the Andoyer variables that are typically chosen to play the role of rotational elements. (Since some of the Andoyer elements are time-dependent even in the unperturbed setting, the role of “constants” is actually played by their initial values.) The Delaunay and Andoyer sets of variables share a subtle peculiarity: under certain circumstances the standard equations render the elements nonosculating. In the theory of orbits, the planetary equations yield nonosculating elements when perturbations depend on velocities. To keep the elements osculating, the equations must be amended with extra terms that are not parts of the disturbing function [Efroimsky, M., Goldreich, P.: J. Math. Phys. 44, 5958–5977 (2003); Astron. Astrophys. 415, 1187–1199 (2004); Efroimsky, M.: Celest. Mech. Dyn. Astron. 91, 75–108 (2005); Ann. New York Acad. Sci. 1065, 346–374 (2006)]. It complicates both the Lagrange- and Delaunay-type planetary equations and makes the Delaunay equations noncanonical. In attitude dynamics, whenever a perturbation depends upon the angular velocity (like a switch to a noninertial frame), a mere amendment of the Hamiltonian makes the equations yield nonosculating Andoyer elements. To make them osculating, extra terms should be added to the equations (but then the equations will no longer be canonical). Calculations in nonosculating variables are mathematically valid, but their physical interpretation is not easy. Nonosculating orbital elements parameterise instantaneous conics not tangent to the orbit. (A nonosculating i may differ much from the real inclination of the orbit, given by the osculating i.) Nonosculating Andoyer elements correctly describe perturbed attitude, but their interconnection with the angular velocity is a nontrivial issue. The Kinoshita–Souchay theory tacitly employs nonosculating Andoyer elements. For this reason, even though the elements are introduced in a precessing frame, they nevertheless return the inertial velocity, not the velocity relative to the precessing frame. To amend the Kinoshita–Souchay theory, we derive the precessing-frame-related directional angles of the angular velocity relative to the precessing frame. The loss of osculation should not necessarily be considered a flaw of the Kinoshita–Souchay theory, because in some situations it is the inertial, not the relative, angular velocity that is measurable [Schreiber, K. U. et al.: J. Geophys. Res. 109, B06405 (2004); Petrov, L.: Astron. Astrophys. 467, 359–369 (2007)]. Under these circumstances, the Kinoshita–Souchay formulae for the angular velocity should be employed (as long as they are rightly identified as the formulae for the inertial angular velocity).     

Simple procedure to simulate karstic aquifers

A procedure to simulate karstic aquifers is presented. It is based on a simulation of spring discharge using precipitation and, where necessary, temperature as input data. The karstic aquifer system is considered to be divided into three zones: the surface zone, the unsaturated zone (UZ) and the saturated zone (SZ). Each of these is described by a transfer function that determines the water supplied from the overlying zone. Water loss through evapotranspiration is calculated empirically and subtracted from the total precipitation in order to obtain the effective infiltration into the UZ. The transfer function characterizing the UZ can be expressed as a convolution function. The UZ acts as a buffer, delaying effective infiltration into the SZ. Water discharge from the SZ is described by the recession function of the spring, and this becomes the transfer function that characterizes the emergence of water from the SZ. The model permits the simulation of the influence of pumped abstractions from the system by a simple modification of the transfer functions involved. Copyright © 2007 John Wiley & Sons, Ltd.     

Cosmological models in the scalar-tetradic theory a

Exact cosmological solutions in the scalar-tetradic theory A are obtained by the assumption of a power relation between the scalar field and the expansion factor of the Universe. Among them there is an inflationary solution.     

Deep Hubble Space Telescope imaging surveys and the formation of spheroidal galaxies

We have extended our previous analysis of morphologically selected elliptical and S0 galaxies in the Hubble Deep Field (HDF) North to include Hubble Space Telescope ( HST ) data in the HDF South and the HDFS–NICMOS areas. Our final sample amounts to 69 E/S0 galaxies with K <20.15 over an area of 11 arcmin². Although a moderately small number over a modest sky area, this sample benefits from the best imaging and photometric data available on high-redshift galaxies. Multi-waveband photometry allows us to estimate with good accuracy the redshifts for the majority of these galaxies, which lack a spectroscopic measure. We confirm our previous findings that massive E/S0s tend to disappear from flux-limited samples at z >1.4. This adds to the evidence that the rest-frame colours and spectral energy distributions (SEDs) of the numerous objects found at 0.8< z <1.2 are inconsistent with a very high redshift of formation for the bulk of stars, while they are more consistent with protracted (either continuous or episodic) star formation down to z ≤1. These results based on high-quality imaging on a small field can be complemented with data from colour-selected extremely red objects (EROs) on much larger sky areas: our claimed demise of E/S0s going from z =1 to z =1.5 is paralleled by a similarly fast decrease in the areal density of EROs when the colour limit is changed from ( R − K )=5 to ( R − K )=6 (corresponding to z ≃1 and z ≃1.3 respectively). Altogether, the redshift interval from 1 to 2 seems to correspond to a very active phase for the assembly of massive E/S0 galaxies in the field, and also probably one where a substantial fraction of their stars are formed.