Expansion of the principal functions of Keplerian motion using complex variables

A special system of canonical variables is considered. An algorithm for expanding the principal functions of Keplerian motion in new elements is presented. The advantage of the proposed system is a relatively small number of terms in the classical expansions of the unperturbed two-body problem. A method for expanding the time derivatives of the rectangular coordinates is proposed. Some estimates of the number of terms in the presented expansions have been obtained through numerical experiments.     

Modulation of ion acoustic waves

The multiple scales perturbation theory is applied to a system of dispersive waves including plasma waves (ion-acoustic waves). Assuming the amplitudes of waves are slowly varying function of space and time, we find that long-time slow modulation of the complex amplitude can be described by the non-linear Schrödinger equation. This result agrees with that obtained by Shimizu and Ichikawa using the reductive perturbation theory, and agrees exactly with the nonrelativistic limit of the nonlinear Schrödinger equation obtained by Nejoh using the stretching method.     

Analysis of the hyades giant stars ε and γ Tau

Two hyades giant stars, and Tau, have been studied from an analysis of strong line profiles. We get for Tau,T _e =4750K and logg=2.7, and for Tau,T _e =4700K and logg=2.8. Hydrogen-to-metal ratio for the two stars is nearly the same as that of solar value.     

Incorporating Spatial Dependence in Predictive Vegetation Models: Residual Interpolation Methods*

Predictive vegetation modeling can be used statistically to relate the distribution of vegetation across a landscape as a function of important environmental variables. Often these models are developed without considering the spatial pattern that is inherent in biogeographical data, resulting from either biotic processes or missing or misspecified environmental variables. Including spatial dependence explicitly in a predictive model can be an efficient way to improve model accuracy with the available data. In this study, model residuals were interpolated and added to model predictions, and the resulting prediction accuracies were assessed. Adding kriged residuals improved model accuracy more often than adding simulated residuals, although some alliances showed no improvement or worse accuracy when residuals were added. In general, the prediction accuracies that were not increased by adding kriged residuals were either rare in the sample or had high nonspatial model accuracy. Regression interpolation methods can be an important addition to current tools used in predictive vegetation models as they allow observations that are predicted well by environmental variables to be left alone, while adjusting over‐ and underpredicted observations based on local factors.     

Comparing Solar Minimum 23/24 with Historical Solar Wind Records at 1 AU

Based on the variations of sunspot numbers, we choose a 1-year interval at each solar minimum from the beginning of the acquisition of solar wind measurements in the ecliptic plane and at 1 AU. We take the period of July 2008??C?June 2009 to represent the solar minimum between Solar Cycles 23 and 24. In comparison with the previous three minima, this solar minimum has the slowest, least dense, and coolest solar wind, and the weakest magnetic field. As a result, the solar wind dynamic pressure, dawn?Cdusk electric field, and geomagnetic activity during this minimum are the weakest among the four minima. The weakening trend had already appeared during solar minimum 22/23, and it may continue into the next solar minimum. During this minimum, the galactic cosmic ray intensity reached the highest level in the space age, while the number of solar energetic proton events and the ground level enhancement events were the least. Using solar wind measurements near the Earth over 1995??C?2009, we have surveyed and characterized the large-scale solar wind structures, including fast-slow stream interaction regions (SIRs), interplanetary coronal mass ejections (ICMEs), and interplanetary shocks. Their solar cycle variations over the 15 years are studied comprehensively. In contrast with the previous minimum, we find that there are more SIRs and they recur more often during this minimum, probably because more low- and mid-latitude coronal holes and active regions emerged due to the weaker solar polar field than during the previous minimum. There are more shocks during this solar minimum, probably caused by the slower fast magnetosonic speed of the solar wind. The SIRs, ICMEs, and shocks during this minimum are generally weaker than during the previous minimum, but did not change as much as did the properties of the undisturbed solar wind.     

The OSIRIS‐REx target asteroid (101955) Bennu: Constraints on its physical,geological, and dynamical nature from astronomical observations

We review the results of an extensive campaign to determine the physical, geological, and dynamical properties of asteroid (101955) Bennu. This investigation provides information on the orbit, shape, mass, rotation state, radar response, photometric, spectroscopic, thermal, regolith, and environmental properties of Bennu. We combine these data with cosmochemical and dynamical models to develop a hypothetical timeline for Bennu's formation and evolution. We infer that Bennu is an ancient object that has witnessed over 4.5 Gyr of solar system history. Its chemistry and mineralogy were established within the first 10 Myr of the solar system. It likely originated as a discrete asteroid in the inner Main Belt approximately 0.7–2 Gyr ago as a fragment from the catastrophic disruption of a large (approximately 100‐km), carbonaceous asteroid. It was delivered to near‐Earth space via a combination of Yarkovsky‐induced drift and interaction with giant‐planet resonances. During its journey, YORP processes and planetary close encounters modified Bennu's spin state, potentially reshaping and resurfacing the asteroid. We also review work on Bennu's future dynamical evolution and constrain its ultimate fate. It is one of the most Potentially Hazardous Asteroids with an approximately 1‐in‐2700 chance of impacting the Earth in the late 22nd century. It will most likely end its dynamical life by falling into the Sun. The highest probability for a planetary impact is with Venus, followed by the Earth. There is a chance that Bennu will be ejected from the inner solar system after a close encounter with Jupiter. OSIRIS‐REx will return samples from the surface of this intriguing asteroid in September 2023.     

Mean crustal velocity: a critical parameter for interpreting crustal structure and crustal growth

Mean crustal velocity is a critical parameter for genesis of continental crystalline crust because it is a function of mean crustal composition and therefore may be used to resolve continental crustal growth in space and time. Although the best values of mean crustal velocity are determined from wide-angle reflection measurements, most studied here necessarily come from vertical averages in crustal refraction determinations. The mode of 158 values of mean crustal velocity is 6.3 km/s, a velocity which corresponds to a mean crustal composition of granodiorite to felsic quartz diorite; Archean crust may be slightly more mafic. Mean crustal velocities range from 5.8 to 7.0 km/s. The lowest values invariably are found in thermally disturbed rift zones and the highest values correspond to velocities in gabbro. Velocities in island arcs may be as low as 6.0 km/s but are typically 6.5–6.9 km/s which corresponds to andesitic composition; estimates of island arc composition are andesitic. If values of mean crustal velocity are not biased, this observation suggests that continental crust did not grow simply by addition of island arc material. Possibilities are that crust formed from fusion of island arcs and was later changed to more felsic composition by addition of material from the mantle or that the late Archean episode of major crustal growth did not involve processes similar to younger island arcs. Some crustal blocks might be changed in composition and thickness by such processes as underplating, interthrusting, necking and sub-crustal erosion. Specially designed experiments are suggested to determine this parameter so critical for understanding genesis of continental crust.     

Paleolimnological investigations of anthropogenic environmental change in Lake Tanganyika: V. Palynological evidence for deforestation and increased erosion

Pollen spectra from seven short cores taken from deltaic sites in the central and northern parts of Lake Tanganyika provide information about vegetation changes around the lake during the last 5000 years. Pollen analysis was undertaken to understand the history and timing of catchment deforestation and its causal linkage to excess sedimentation and ecosystem change in Lake Tanganyika. The spectra are dominated by grass pollen at all levels in every core. Grass pollen percentage values range between 40 and 80%. Low values of arboreal pollen taxa (1–20%) were documented from most cores except core LT-98-2M. Core LT-98-2M represents the longest duration vegetation record of this study (close to 5000 years BP), and records the onset of increasingly arid conditions in the Late Holocene, especially after 500 A.D., with the probable replacement of forest by open grassland in the Mahale Mountains region. The pollen/spore content for other cores showed a consistent trend of a decrease in grass pollen and an increase in pteridophyte and forest indicator pollen taxa during the last few centuries, contemporaneous with other indications of increased watershed disturbance from forest clearing (especially isotopes and lake faunal change). The timing or strength of this trend is not tied to specific levels of watershed disturbance. However, increasing fern spore abundance does occur progressively later towards the south, where modern human population densities are lower. Although increasing fern spore abundance is consistent with a land-clearing hypothesis, the rising arboreal pollen percentages are seemingly counterintuitive. One possible explanation is that increasing arboreal pollen proportions reflects the recycling of abundant pollen of this type from rapidly eroding soils. Another likely explanation for this finding is that land clearing involved the replacement of miombo woodland, with its mixture of trees producing little pollen and understory grasses producing large amounts of pollen, by the present day cassava, banana, and legume agricultural systems, all of which are poor pollen producers. This shift in catchment vegetation would increase the relative contribution of Afromontane pollen transported long distances from the surrounding highland regions. This hypothesis is consistent with both the lack of correlation of palynological history with specific watershed deforestation attributes, as well as the broader historical record of human habitation in the Lake Tanganyika region. This study also highlights the need for both modern pollen transect data from the region and comparative cores from low elevation swamps or ponds (wetlands) in the region with smaller catchment areas.