Non-Continuation of Integrals of the Rotating Two-body Problem in Hill's Lunar Problem

We consider Hill's lunar problem as a perturbation of the integrable two-body problem. For this we avoid the usual normalization in which the angular velocity of the rotating frame of reference is put equal to unity and consider as the perturbation parameter. We first express the Hamiltonian H of Hill's lunar problem in the Delaunay variables. More precisely we deduce the expressions of H along the orbits of the two-body problem. Afterwards with the help of the conserved quantities of the planar two-body problem (energy, angular momentum and Laplace–Runge–Lenz vector) we prove that Hill's lunar problem does not possess a second integral of motion, independent of H, in the sense that there exist no analytic continuation of integrals, which are linear functions of in the rotating two-body problem. In connection with the proof of this main result we give a further restrictive statement to the nonintegrability of Hill's lunar problem.     

Analytical solutions for the equations of motion of a space vehicle during the atmospheric re-entry phase on a 2-D trajectory

A practical and important problem encountered during the atmospheric re-entry phase is to determine analytical solutions for the space vehicle dynamical equations of motion. The author proposes new solutions for the equations of trajectory and flight-path angle of the space vehicle during the re-entry phase in Earth’s atmosphere. Explicit analytical solutions for the aerodynamic equations of motion can be effectively applied to investigate and control the rocket flight characteristics. Setting the initial conditions for the speed, re-entering flight-path angle, altitude, atmosphere density, lift and drag coefficients, the nonlinear differential equations of motion are linearized by a proper choice of the re-entry range angles. After integration, the solutions are expressed with the Exponential Integral, and Generalized Exponential Integral functions. Theoretical frameworks for proposed solutions as well as, several numerical examples, are presented.     

Numerical simulation of colour equations for the uvby system

The results of numerical simulation of colour equations of uvby photometry for filter-defined bandpasses are presented. It is shown that linear transformation equations to the standard system are valid for instrumental systems deviating by no more than 2.5 nm in peak transmission wavelengths. The comparison with the results of observations is satisfying. Im Ergebnis einer numerischen Farbgleichungssimulation im uvby-System wird nachgewiesen, daß für Instrumentensysteme mit Abweichungen der Wellenlängen maximaler Transmission bis zu 2.5 nm gegenüber den Standardwerten eine lineare Transformation möglich ist. Der Vergleich mit Beobachtungsresultaten zeigt eine gute Übereinstimmung.     

Covariant formulation of the dynamical equations of quantum vortices in type II superconductors

We have derived the closed system of covariant equations which describe the motion of quantum vortices regarded as a two-2dimensional polarized liquid. We have obtained the covariant expressions of the forces acting on the vortices; from the equilibrium condition of these forces we have deduced the equation satisfied by the velocity field of the fluid. It is shown that this velocity field depends on the friction coefficient, the density of vortices and the superconducting current. From this closed system of equations we derived the relaxation equation when a variable magnetic field is applied. Published in Astrofizika, Vol. 50, No. 3, pp. 381–391 (August 2007).     

Tetrad formulation of the basic equations of type II superconductors in curved space-time

The basic equations of type II superconductors have been obtained by adopting London’s phenomenological approach. The generation of the electromagnetic field in a superconductor at rest in a stationary universe has been investigated using the method of anholonomic frames. The Newtonian formulation of the problem has also been studied. __________ Translated from Astrofizika, Vol. 51, No. 1, pp. 99–107 (February 2008).     

吸积盘随机振荡光度功率谱密度中低频准周期振荡现象的研究

采用含有频率涨落噪声和指数形式关联随机力作用的广义朗之万(Langevin)方程模型描述黑洞吸积盘的垂向振荡,推导出吸积盘随机振荡光度功率谱密度的解析表达式,并讨论了系统参数对功率谱密度中低频准周期振荡(Low Frequency Quasi-Periodic Oscillations,LFQPOs)现象的影响。研究结果发现选取合适的系统参数时,功率谱密度曲线上出现了一个基频和一个二次谐频的共振双峰低频准周期振荡,基频峰对应的中心频率为吸积盘振荡的特征频率;随机力关联时间决定了基频峰的高度和宽度,频率噪声强度和粘滞阻尼只对二次谐频峰产生影响。结果说明吸积盘的随机振荡模型可以作为低频准周期振荡起源的一种解释。     

The fifth-order analytical solution of the equations of motion of a satellite in orbit around a non-spherical planet

A high-precise analytical theory of a satellite in orbit around a non-spherical planet has been developed. The Poisson's small parameter method has been used. All secular and short-periodic perturbations proportional up to and including a product of five arbitrary harmonic coefficients of the planetary potential expansion are calculated. Long-periodic perturbations are derived with the accuracy of up to the fourth-order, inclusive. The influence of the high-order perturbations on the motion of ETALON-1 satellite has been investigated. The results of comparison of the numerical and analytical integration of the equations of its motion over a five year interval are as follows:

Experimental study on the rheological properties of polycrystalline solid nitrogen and methane: Implications for tectonic processes on Triton

To investigate the evolution of any processes on planetary surfaces in the outer Solar System, the rheological properties of non-water ices were studied by means of a sound velocity measurement system and a uniaxial deformation apparatus. A pulse transmission method was used to obtain longitudinal (V_p) and transverse (V_s) wave velocities through solid nitrogen and methane at temperatures ranging from 5 to 64 K and from 5 to 90 K, respectively. The measured velocities confirmed that the solid methane and solid nitrogen samples were non-porous polycrystalline samples without any cracks and bubbles inside. Compression tests at constant strain-rate were performed for solid nitrogen and methane at temperatures of 5-56 K and 5-77 K, respectively, at strain-rates of 10⁻⁴-10⁻² s⁻¹. Both brittle and ductile behavior was observed for solid nitrogen and methane under these conditions. The maximum strength of solid nitrogen was observed to be 9 MPa in the brittle failure mode, and that of solid methane was 10 MPa. These low strengths cannot support cantaloupe structures with the topographic undulation larger than several kilometers found on Triton’s surface, suggesting that other materials such as H₂O ice could underlay solid methane and nitrogen and support these structures.     

Experimental study on the impact fragmentation of core-mantle bodies: Implications for collisional disruption of rocky planetesimals with sintered core covered with porous mantle

Impact experiments of inhomogeneous targets such as layered bodies consisting of a dense core and porous mantle were conducted to clarify the effect of the layered structure on impact strength. The layered structure of small bodies could be the result of the thermal evolution of planetesimals in the solar nebula. So, the impact disruption of thermally evolved bodies with core-mantle structure is important for the origin of small bodies such as asteroids. We investigated the impact strength of rocky-layered bodies with porous mantle-sintered cores, which could be formed at an initial stage of thermal evolution. Spherical targets composed of soda-lime glass or quartz core and porous gypsum mantle were prepared as an analog of small bodies with a core-mantle structure, and the internal structure was changed. A nylon projectile was impacted at the impact velocity from 1 to 5 km/s. The impact strength of the core-mantle targets decreases with the increase of the core/target mass ratio (RCM) in the specific energy range from 1×¹⁰³ to 4×¹⁰⁴ J/kg. We observed two distinct destruction modes characterized by the damage to the core: one shows a damaged core and fractured mantle, and the other shows an intact core and broken mantle. The former mode was usually observed with increasing RCM, and the boundary condition of the core destruction () was experimentally found to be , where is the specific energy required to disrupt a glass core. From this empirical equation, it might be possible to discuss the destruction conditions of a thermally evolved body with a porous mantle-sintered core structure. We speculate that the impact strength of the body could be significantly reduced with the progress of internal evolution at the initial stage of thermal evolution.     

Flow patterns of lobate debris aprons and lineated valley fill north of Ismeniae Fossae, Mars: Evidence for extensive mid-latitude glaciation in the Late Amazonian

A variety of Late Amazonian landforms on Mars have been attributed to the dynamics of ice-related processes. Evidence for large-scale, mid-latitude glacial episodes existing within the last 100 million to 1 billion years on Mars has been presented from analyses of lobate debris aprons (LDA) and lineated valley fill (LVF) in the northern and southern mid-latitudes. We test the glacial hypothesis for LDA and LVF along the dichotomy boundary in the northern mid-latitudes by examining the morphological characteristics of LDA and LVF surrounding two large plateaus, proximal massifs, and the dichotomy boundary escarpment north of Ismeniae Fossae (centered at 45.3°N and 39.2°E). Lineations and flow directions within LDA and LVF were mapped using images from the Context (CTX) camera, the Thermal Emission Imaging Spectrometer (THEMIS), and the High Resolution Stereo Camera (HRSC). Flow directions were then compared to topographic contours derived from the Mars Orbiter Laser Altimeter (MOLA) to determine the down-gradient components of LDA and LVF flow. Observations indicate that flow patterns emerge from numerous alcoves within the plateau walls, are integrated over distances of up to tens of kilometers, and have down-gradient flow directions. Smaller lobes confined within alcoves and superposed on the main LDA and LVF represent a later, less extensive glacial phase. Crater size-frequency distributions of LDA and LVF suggest a minimum (youngest) age of 100 Ma. The presence of ring-mold crater morphologies is suggestive that LDA and LVF are formed of near-surface ice-rich bodies. From these observations, we interpret LDA and LVF within our study region to result from formerly active debris-covered glacial flow, consistent with similar observations in the northern mid-latitudes of Mars. Glacial flow was likely initiated from the accumulation and compaction of snow and ice on plateaus and in alcoves within the plateau walls as volatiles were mobilized to the mid-latitudes during higher obliquity excursions. Together with similar analyses elsewhere along the dichotomy boundary, these observations suggest that multiple glacial episodes occurred in the Late Amazonian and that LDA and LVF represent significant reservoirs of non-polar ice sequestered below a surface lag for hundreds of millions of years.     

Valley formation on martian volcanoes in the Hesperian: Evidence for melting of summit snowpack, caldera lake formation, drainage and erosion on Ceraunius Tholus

Ceraunius Tholus, a Hesperian-aged volcano in the Tharsis region, is characterized by small radial valleys on its flanks, and several larger valleys originating near its summit caldera. All of these large valleys drain from near the lowest present portion of the caldera rim and down the flanks of the volcano. The largest valley debauches into Rahe Crater (an oblique impact crater), forming a depositional fan. Recent study of climate change on Mars suggests that many low-latitude regions (especially large volcanic edifices) were periodically the sites of snow accumulation, likely triggered by variations in spin orbital parameters. We apply a conductive heat flow model to Ceraunius Tholus that suggests that following magmatic intrusion, sufficient heating would be available to cause basal melting of any accumulated summit snowpack and produce sufficient meltwater to cause the radial valleys. The geometry of the volcano summit caldera suggests that meltwater would also accumulate in a volumetrically significant caldera lake. Analysis of the morphology and volumes of the largest valley, as well as depositional features at its base, suggest that fluvial erosion due to drainage of this summit caldera lake formed the large valleys, in a manner analogous to how valleys were formed catastrophically from a lake in Aniakchak caldera in Alaska. Moreover, the event which carved the largest valley on Ceraunius Tholus appears to have led to the formation of a temporary lake within Rahe Crater, at its base. The more abundant, small valleys on the flanks are interpreted to form by radial drainage of melted ice or snow from the outside of the caldera rim. Comparison of Ceraunius Tholus with the volcano-capping Icelandic ice sheet Myrdalsjokull provides insight into the detailed mechanisms of summit heating, ice-cap accumulation and melting, and meltwater drainage. These observations further underline the importance of a combination of circumstances (i.e., climate change to produce summit snowpack and an active period of magmatism to produce melting) to form the valley systems on some martian volcanoes and not on others.     

Geologic context of in situ rocky exposures in Mare Serpentis, Mars: Implications for crust and regolith evolution in the cratered highlands

Global acquisition of infrared spectra and high-resolution visible and infrared imagery has enabled the placement of compositional information within stratigraphic and geologic context. Mare Serpentis, a low albedo region located northwest of Hellas Basin, is rich in spectral and thermophysical diversity and host to numerous isolated exposures of in situ rocky material. Most martian surfaces are dominated by fine-grained particulate materials that bear an uncertain compositional and spatial relationship to their source. Thus location and characterization of in situ rock exposures is important for understanding the origin of highland materials and the processes which have modified those materials. Using spectral, thermophysical and morphologic information, we assess the local and regional stratigraphy of the Mare Serpentis surface in an effort to reconstruct the geologic history of the region. The martian highlands in Mare Serpentis are dominated by two interspersed surface units, which have distinct compositional and thermophysical properties: (1) rock-dominated surfaces relatively enriched in olivine and pyroxene, and depleted in high-silica phases, and (2) sediment or indurated material depleted in olivine and pyroxene, with relatively higher abundance of high-silica phases. This is a major, previously unrecognized trend which appears to be pervasive in the Mare Serpentis region and possibly in other highland areas. The detailed observations have led us to form two hypotheses for the relationship between these two units: either (1) they are related through a widespread mechanical and/or chemical alteration process, where less-mafic plains materials are derived from the mafic bedrock, but have been compositionally altered in the process of regolith formation, or (2) they are stratigraphically distinct units representing separate episodes of upper crust formation. Existing observations suggest that the second scenario is more likely. In this scenario, plains materials represent older, degraded, and possibly altered, “basement” rock, whereas the rocky exposures represent later additions to the crust and are probably volcanic in origin. These hypotheses should be further testable with decimeter-resolution imagery and meter-resolution short wavelength infrared spectra.     

Constraints on mechanisms for the growth of gully alcoves in Gasa crater, Mars, from two-dimensional stability assessments of rock slopes

The value of slope stability analyses for gaining insight into the geologic conditions that would facilitate the growth of gully alcoves on Mars is demonstrated in Gasa crater. Two-dimensional limit equilibrium methods are used in conjunction with high-resolution topography derived from stereo High Resolution Imaging Science Experiment (HiRISE) imagery. These analyses reveal three conditions that may produce observed alcove morphologies through slope failure: (1) a ca. >10 m thick surface layer that is either saturated with H₂O ground ice or contains no groundwater/ice at all, above a zone of melting H₂O ice or groundwater and under dynamic loading (i.e., seismicity), (2) a 1-10 m thick surface layer that is saturated with either melting H₂O ice or groundwater and under dynamic loading, or (3) a >100 m thick surface layer that is saturated with either melting H₂O ice or groundwater and under static loading. This finding of three plausible scenarios for slope failure demonstrates how the triggering mechanisms and characteristics of future alcove growth would be affected by prevailing environmental conditions. HiRISE images also reveal normal faults and other fractures tangential to the crowns of some gully alcoves that are interpreted to be the result of slope instability, which may facilitate future slope movement. Stability analyses show that the most failure-prone slopes in this area are found in alcoves that are adjacent to crown fractures. Accordingly, crown fractures appear to be a useful indicator of those alcoves that should be monitored for future landslide activity.     

Modeling the formation of bright slope deposits associated with gullies in Hale Crater, Mars: Implications for recent liquid water

Our study investigates possible formation mechanisms of the very recent bright gully deposits (BGDs) observed on Mars in order to assess if liquid water was required. We use two models in our assessment: a one-dimensional (1D) kinematic model to model dry granular flows and a two-dimensional (2D) fluid-dynamic model, FLO-2D (O’Brien et al., 1993, FLO Engineering), to model water-rich and wet sediment-rich flows. Our modeling utilizes a high-resolution topographic model generated from a pair of images acquired by the High Resolution Imaging Science Experiment (HiRISE) aboard the Mars Reconnaissance Orbiter. For the 1D kinematic modeling of dry granular flows, we examine a range of particle sizes, flow thicknesses, initial velocities, flow densities, and upslope initiation points to examine how these parameters affect the flow run-out distances of the center of mass of a flow. Our 1D modeling results show that multiple combinations of realistic parameters could produce dry granular flows that travel to within the observed deposits’ boundaries. We run the 2D fluid-dynamic model, FLO-2D, to model both water-rich and wet sediment-rich flows. We vary the inflow volume, inflow location, discharge rate, water-loss rate (water-rich models only), and simulation time and examine the resulting maximum flow depths and velocities. Our 2D modeling results suggest that both wet sediment-rich and water-rich flows could produce the observed bright deposits. Our modeling shows that the BGDs are not definitive evidence of recent liquid water on the surface of Mars.     

Large-scale transport of plasma in the Earth's plasma sheet: comparative analysis for adiabatic and non-adiabatic cases

A system of multi-fluid MHD-equations is used to compare adiabatic and non-adiabatic transport of the energetic particles in the magnetospheric plasma sheet. A “slow-flow” approximation is considered to study large-scale transport of the anisotropic plasma consisting of energetic electrons and protons. Non-adiabatic transport of the energetic plasma is caused by scattering of the particles in the presence of both wave turbulence and arbitrary time-varying electric fields penetrating from the solar wind into the magnetosphere. The plasma components are devided into particle populations defined by their given initial effective values of the magnetic moment per particle. The spatial scales are also given to estimate the non-uniformity of the geomagnetic field along the chosen mean path of a particle. The latters are used to integrate approximately the system of MHD-equations along each of these paths. The behaviour of the magnetic moment mentioned above and of the parameter which characterizes the pitch-angle distribution of the particles are studied self-consistently in dependence on the intensity of non-adiabatic scattering of the particles. It is shown that, in the inner magnetosphere, this scattering influences the particles in the same manner as pitch-angle diffusion does. It reduces the pitch-angle anisotropy in the plasa. The state of the plasma may be unstable in the current sheet of the magnetotail. If the initial state of the plasma does not correspond to the equilibrium one, then, in this case, scattering influences the particles so as to remove the plasma further from the equilibrium state. The coefficient of the particle diffusion across the geomagnetic field lines is evaluated. This is done by employing the Langevin approach to take the stochastic electric forces acting on the energetic particles in the turbulent plasma into account. The behaviour of the energy density of electrostatic fluctuations in the magnetosphere is estimated.     

Evidence for and implications of sedimentary diapirism and mud volcanism in the southern Utopia highland-lowland boundary plain, Mars

Several types of spatially associated landforms in the southern Utopia Planitia highland-lowland boundary (HLB) plain appear to have resulted from localized geologic activity, including (1) fractured rises, (2) elliptical mounds, (3) pitted cones with emanating lobate materials, and (4) isolated and coalesced cavi (depressions). Stratigraphic analysis indicates these features are Hesperian or younger and may be associated with resurfacing that preferentially destroyed smaller (<8 km diameter) impact craters. Based on landform geomorphologies and spatial distributions, the documented features do not appear to be specifically related to igneous or periglacial processes or the back-wasting and erosion of the HLB scarp. We propose that these features are genetically related to and formed by sedimentary (mud) diapirs that ascended from zones of regionally confined, poorly consolidated, and mechanically weak material. We note morphologic similarities between the mounds and pitted cones of the southern Utopia boundary plain and terrestrial mud volcanoes in the Absheron Peninsula, Azerbaijan. These analogs provide a context for understanding the geological environments and processes that supported mud diapir-related modification of the HLB. In southern Utopia, mud diapirs near the Elysium volcanic edifice may have resulted in laccolith-like intrusions that produced the fractured rises, while in the central boundary plain mud diapirs could have extruded to form pitted cones, mounds, and lobate flows, perhaps related to compressional stresses that account for wrinkle ridges. The removal of material a few kilometers deep by diapiric processes may have resulted in subsidence and deformation of surface materials to form widespread cavi. Collectively, these inferences suggest that sedimentary diapirism and mud volcanism as well as related surface deformations could have been the dominant Hesperian mechanisms that altered the regional boundary plain. We discuss a model in which detritus would have accumulated thickly in the annular spaces between impact-generated structural rings of Utopia basin. We envision that these materials, and perhaps buried ejecta of Utopia basin, contained volatile-rich, low-density material that could provide the source material for the postulated sedimentary diapirs. Thick, water-rich, low-density sediments buried elsewhere along the HLB and within the lowland plains may account for similar landforms and resurfacing histories.     

Martian gullies in the southern mid-latitudes of Mars: Evidence for climate-controlled formation of young fluvial features based upon local and global topography

A new survey of Mars Orbiter Camera (MOC) narrow-angle images of gullies in the 30°-45° S latitude band includes their distribution, morphology, local topographic setting, orientation, elevation, and slopes. These new data show that gully formation is favored over a specific range of conditions: elevation (−5000 to +3000 m), slope (>10°), and orientation (83.8% on pole-facing slopes). These data, and the frequent occurrence of gullies on isolated topographic highs, lead us to support the conclusion that climatic-related processes of volatile accumulation and melting driven by orbital variations are the most likely candidate for processes responsible for the geologically recent formation of martian gullies.     

Cratering of icy targets by different impactors: Laboratory experiments and implications for cratering in the Solar System

Studies of impacts (impactor velocity about 5 km s⁻¹) on icy targets were performed. The prime goal was to study the response of solid CO₂ targets to impacts and to find the differences between the results of impacts on CO₂ targets with those on H₂O ice targets. The crater dimensions in CO₂ ice were found to scale with impact energy, with little dependence on projectile density (which ranged from nylon to copper, i.e., 1150-8930 kg m⁻³). At equal temperatures, craters in CO₂ ice were the same diameter as those in water ice, but were shallower and smaller in volume. In addition, the shape of the radial profiles of the craters was found to depend strongly on the type of ice and to change with impact energy. The impact speed of the data is comparable to that for impacts on many types of icy bodies in the outer Solar System (e.g., the satellites of the giant planets, the cometary nuclei and the Kuiper Belt objects), but the size and thus energy of the impactors is lower. Scaling with impact energy is demonstrated for the impacts on CO₂ ice. The issue of impact disruption (rather than cratering) is discussed by analogy with that on water ice. Expressions for the critical energy density for the onset of disruption rather than cratering are established for water ice as a function of porosity and silicate content. Although the critical energy density for disruption of CO₂ ice is not established, it is argued that the critical energy to disrupt a CO₂ ice body will be greater than that for a (non-porous) water ice body of the similar mass.     

Unraveling the patterns of late Holocene debris-flow activity on a cone in the Swiss Alps: Chronology, environment and implications for the future

Debris-flow activity on the forested cone of the Ritigraben torrent (Valais, Swiss Alps) was assessed from growth disturbances in century-old trees, providing an unusually complete record of past events and deposition of material. The study of 2246 tree-ring sequences sampled from 1102 Larix decidua Mill., Picea abies (L.) Karst. and Pinus cembra ssp. sibirica trees allowed reconstruction of 123 events since AD 1566. Geomorphic mapping permitted identification of 769 features related to past debris-flow activity on the intermediate cone. The features inventoried in the study area covering 32 ha included 291 lobes, 465 levées and 13 well-developed debris-flow channels. Based on tree-ring records of disturbed trees growing in or next to the deposits, almost 86% of the lobes identified on the present-day surface could be dated. A majority of the dated material was deposited over the last century. Signs of pre-20th century events are often recognizable in the tree-ring record of survivor trees, but the material that caused the growth anomaly in trees has been completely overridden or eroded by more recent debris-flow activity.Tree-ring records suggest that cool summers with frequent snowfalls at higher elevations regularly prevented the release of debris flows between the 1570s and 1860s; the warming trend combined with greater precipitation totals in summer and autumn between 1864 and 1895 provided conditions that were increasingly favorable for releasing events from the source zone. Enhanced debris-flow activity continued well into the 20th century and reconstructions show a clustering of events in the period 1916–1935 when warm–wet conditions prevailed during summer in the Swiss Alps. In contrast, very low activity is observed for the last 10-yr period (1996–2005) with only one debris-flow event recorded on August 27, 2002. Since sediment availability is not a limiting factor, this temporal absence of debris-flow activity is due to an absence of triggering events, which not only shifted from June and July to August and September over the 20th century, but also seemed to be initiated primarily by persistent precipitation rather than summer thunderstorms. From the reconstructions, based on RCM simulations, there are indications that debris-flow frequencies might continue to decrease in the future, as precipitation events are projected to occur less frequently in summer but become more common in spring or autumn.