Collisions of stars by oscillating orbits of the second kind

Ordinary estimations of the number of star collisions in our galaxy—by simple kinematic considerations—lead to a very small number of such collisions: about one or even less every millions of years. However star collisions can occur through the following indirect way which has a much higher probability. (a) Binary stars are very common in our galaxy, about 30–50% of the stars. (b) If two binary stars meet a triple system can be formed by an ordinary exchange type motion. (c) A triple system is generally decomposed into the “inner orbit” (i.e. the relative orbit of the two nearest stars) and the “outer orbit” (i.e. the relative orbit of the third star with respect to the center of mass of the two nearest stars). The major axes of these two orbits have generally small perturbations and it is the same for the eccentricity of the outer orbit. On the contrary, if the relative inclination of the two orbits is large, the perturbations of the eccentricity of the inner orbit are important and can even in some cases lead to an eccentricity equal to one, that is to a collision of the two stars of the inner orbit.Such orbits can be called “oscillating orbits of the second kind”, indeed the first oscillating orbits—conceived by Khilmi and described for the first time in an example by Sitnikov—have unbounded mutual distances r_ij, but the system always come back to small sizes, it has an infinite number of very large expansions followed by strong contractions and, in the three-body case, an upper bound of lim inf (r_1.2 + r_1.3 + r_2.3) can be given in terms of the three masses and the integrals of motion. For the oscillating orbits of the second kind the mutual distances r_ij are bounded, but the velocities are unbounded (i.e. lim inf r_ij = 0 for at least one r_ij) and the system goes to a collision if the bodies have non-zero radius even small. The analytical study of the oscillating orbits of the second kind is a part of the general analytical study of the three-body problem, a part which must be valid for large eccentricities and large inclinations. The use of Delaunay's variables and of a Von Zeipel transformation lead to a first order integrable approximation, valid for any eccentricities and any inclinations, and giving the following results: (a) The oscillating orbits of the second kind occur when the angular momentum of the outer orbit has a modulus sufficiently close to the modulus of the total angular momentum of the three-body system. Hence these orbits occur for inclinations in the vicinity of 90°. (b) The oscillating orbits represent a set of positive measure of phase space and the first order study allows to give a rough estimation of the probability of collisions—even for stars of infinitely small radius. This probability, for given initial major axes and eccentricities and for isotropic arbitrary initial orientations, is generally of the order of m₃$\text{R}\text{M}$ (m₃ being the mass of the outer star, M the total mass and R the ratio of the period of the inner orbit to that of outer orbit).One question remains to be solved: how many collisions of stars are due to that phenomenon? That question is difficult because the probability of formation of a triple system by a random meeting of two binaries is very uneasy to estimate. However it seems that, compared to the usual evaluations based on pure kinematic considerations without gravitational effects, the number of collisions must be multiplied by a factor between one thousand and one million.     

Multipole Models of the Earth's Magnetic Field

To develop a mathematical model of rotational motion of an artificial satellite about its center of mass under the action of various forces (magnetic, Lorentz, etc.) caused by the geomagnetic field, it is necessary to know the induction of the Earth's magnetic field (EMF) as a function of the radius vector of a given point in the near-Earth space. Because the EMF possesses a complex structure and the above-mentioned functional dependence is unavailable in explicit analytic form, a set of approximate models of the EMF should be used. The simplest such model—a right dipole (aligned with the axis of rotation)—does not enable one to reveal in detail the influence of diurnal EMF rotation on the rotational motion of a satellite. The next EMF approximation—an inclined magnetic dipole—does not suffer from the above-mentioned drawback. However, it is shown that not all corrections to the magnetic induction of the EMF of the same order of magnitude are taken into account in the course of transformation from the model of aligned dipole to the model of inclined dipole. So, to develop the EMF model accurately accounting for the absence of axial symmetry of the EMF with respect to the axis of diurnal rotation of the Earth, in general, the effect of the quadrupole component of the geomagnetic potential on the EMF induction (and, probably, even the components of higher orders) must be taken into consideration. By using the International Geomagnetic Reference Field IGRF-2000, the multipole models of the EMF, corresponding to quadrupole, octupole, and higher-order approximations, were constructed and studied in this work. The EMF potential is expressed in terms of its multipole tensors. As a result, projections of the induction and induction gradient of EMF in the center of mass of the satellite onto the axes of the orbital coordinate system can be written in convenient and concise form. The expressions for the first four multipole tensors through the known geomagnetic constants are found. A method for estimating the reliability of these models is put forward, and the regions of applicability of the quadrupole and octupole models are drawn on the plane of orbital parameters.     

Cardiac arrhythmias in space. Role of vagotonia.

Rhythm disorders observed in space have always been minor but they are not unfrequent. They include: ventricular or supra-ventricular extrasystoles, nodal arrhythmias, auriculo-ventricular conduction disorders. There are several etiopathogenetic hypotheses: a strict selection must permit its elimination of an underlying heart disease; the potassium deficiency is often advanced but its role is not certain; the role of catecholamines is also discussed; the role of hypervagotony is extensively analysed as great clinical and electro-cardiographic evidence speaks for it. It can induce disorders which are more serious than those observed so far, particularly fibrillation or intermittent atrial flutter; weightlessness itself could partly condition the vagotonic state; and the effects of fluid shifts are also discussed from this point of view. The possible therapies for various atrial, nodal, ventricular disorders are reviewed, with greater detail for vagal atrial arrhythmias.     

Mining Spatial Associations with Limited Sensory Information

Abstract

Human navigation in an unknown environment requires an understanding of the spatial relationships of the terrain. For example, a soldier who is on a reconnaissance mission in a new city needs to “know” the spatial layout of the surroundings with high confidence. Oftentimes, this understanding must be acquired within a very short amount of time and with limited sensory inputs. The soldier would benefit from a digital avatar that draws inferences about the spatial layout of the city based on an initial set of observations and guides the soldier either in further exploring the environment or in making decisions based on these inferences. In this paper, we present and evaluate an inductive approach to learning spatial associations using sensory data that is available from the simulation environment of a computer game, Unreal Tournament. We study two kinds of spatial relationships between nodes on a level of a game map: nodes that are placed near each other to satisfy some spatial requirement and nodes that are placed near each other to satisfy the design preferences of a level architect. We show that we can infer both kinds of relationships using an association rule mining algorithm. Furthermore, we show how to use an ontology to distinguish between these relationships in order to discover different types of spatial arrangements on a specific map. We discuss how the inferred associations can be used to control an avatar that makes recommendations for navigating unexplored areas on a map. We conclude with some thoughts on the applicability of our methods to scenarios in the real world, beyond the simulation environment of a game, and on how the learned associations can be represented and queried by a simple question-answer type system.     

Archaeal genome organization and stress responses: implications for the origin and evolution of cellular life

For DNA to be used as an informational molecule it must exist in the cell on the edge of stability because all genomic processes require local controlled melting. This presents mechanistic opportunities and problems for genomic DNA from hyperthermophilic organisms, whose unpackaged DNA could melt at optimal temperatures for growth. Hyperthermophiles are suggested to employ the novel positively supercoiling topoisomerase enzyme reverse gyrase (RG) to form positively supercoiled DNA that is intrinsically resistant to thermal denaturation. RG is presently the only archaeal gene that is uniquely found in hyperthermophiles and therefore is central to hypotheses suggesting a hypothermophilic origin of life. However, the suggestion that RG has evolved by the fusion of two pre-existing enzymes has led to hypotheses for a lower temperature for the origin of life. In addition to the action of topoisomerases, DNA packaging and the intracellular ionic environment can also manipulate DNA topology significantly. In the Euryarchaeota, nucleosomes containing minimal histones can adopt two alternate DNA topologies in a salt-dependent manner. From this we hypothesize that since internal salt concentrations are increased following an increase in temperature, the genomic effects of temperature fluctuations could also be accommodated by changes in nucleosome organization. In addition, stress-induced changes in the nucleoid proteins could also play a role in maintaining the genome in the optimal topological state in changing environments. The function of these systems could therefore be central to temperature adaptation and thus be implicated in origin of life scenarios involving hyperthermophiles.     

Overview of the legal and policy challenges of orbital debris removal

Much attention has been paid recently to the issue of removing human-generated space debris from Earth orbit, especially following conclusions reached by both NASA and ESA that mitigating debris is not sufficient, that debris-on-debris and debris-on-active-satellite collisions will continue to generate new debris even without additional launches, and that some sort of active debris removal (ADR) is needed. Several techniques for ADR are technically plausible enough to merit further research and eventually operational testing. However, all ADR technologies present significant legal and policy challenges which will need to be addressed for debris removal to become viable. This paper summarizes the most promising techniques for removing space debris in both LEO and GEO, including electrodynamic tethers and ground- and space-based lasers. It then discusses several of the legal and policy challenges posed, including: lack of separate legal definitions for functional operational spacecraft and non-functional space debris; lack of international consensus on which types of space debris objects should be removed; sovereignty issues related to who is legally authorized to remove pieces of space debris; the need for transparency and confidence-building measures to reduce misperceptions of ADR as anti-satellite weapons; and intellectual property rights and liability with regard to ADR operations. Significant work on these issues must take place in parallel to the technical research and development of ADR techniques, and debris removal needs to be done in an environment of international collaboration and cooperation.     

Orbital manoeuvres of free flying platforms for retrieval by space shuttle

In a typical future mission a free flying platform will be released to space by Space Shuttle. After performing its active mission, it will have to wait for a suitable later Shuttle flight for retrieval at its original orbital altitude. To allow for the orbital descent during the total mission time of typically several months, one or several orbit raise manoeuvres have to be performed with the platform's own propulsion system. In the paper, the velocity-requirements Δv for these orbital transfers, depending on Sun activity, rendezvous-altitude, ballistic coefficient and longest expected mission time are treated.The simplest manoeuvre, consisting of one initial ascent transfer and one descent transfer at the actual retrieval date, is shown to be not optimal. Up to 25% of Δv can be saved, if several orbit raising transfers in a certain sequence are applied. A straightforward analytical treatment is presented for the optimization, while a computer program with the CIRA-atmosphere model is used for actual mission planning.     

Qualitative Spatial Reasoning for Topological Map Learning

Abstract

In this paper we investigate the application of qualitative spatial reasoning methods for learning the topological map of an unknown environment. We develop a topological mapping framework that achieves robustness against ambiguity in the available information by tracking all possible graph hypotheses simultaneously. We then exploit spatial reasoning to reduce the space of possible hypotheses. The considered constraints are qualitative direction information and the assumption that the map is planar. We investigate the effects of absolute and relative direction information using two different spatial calculi and combine the approach with a real mapping system based on Voronoi graphs.     

Study of singular surfaces of systems of unsupported gyrodynes by the parameter continuation method

A system of two-degree-of-freedom force gyroscopes (gyrodynes) is considered to be used for spacecraft attitude control. Possible values of its total angular momentum form some finite region P in the frame of reference rigidly connected with the spacecraft. Near the boundary of this region and singular surfaces located inside it the control of the angular momentum is complicated or impossible. The program angular momentum of the gyrodynes, realizing the law of variation of the spacecraft orientation, should lie inside P and outside some singular surfaces, and due to this fact the boundary and internal singular surfaces should be studied. This work is dedicated to the numerical construction of region P and its internal singular surfaces by the method of parameter continuation. Using the results by E.N. Tokar’ we formalize sufficient conditions which in some cases allow one to determine the type of the singular surface. As an example, a system of six gyrodynes is considered, for which the regions of variations of the intrinsic angular momentum and singular surfaces are constructed. The possibilities of the system are demonstrated for the case when one gyrodyne fails.     

Studies of substorm on March 12, 1991: 2. Auroral electrons. Acceleration,injection, and dynamics

In the first part of this study of the substorm of March 12, 1991, the space-time structure of substrorm disturbance and dynamics of auroral ions were considered. This second part presents an analysis of measurements of auroral electrons onboard the CRRES satellite. It is demonstrated that enhancements of the electron flux (injections) during large-scale and local dipolarizations of the magnetic field are determined by a combination of field-aligned, induction, and betatron mechanisms of acceleration with an effect of displacement of the drift shells of particles. The relative contributions of these mechanisms in relation to the energy of auroral electrons are determined.     

Order of magnitude analysis of convective effects in dendritic solidification

The different types of convective phenomena which may occur during the dendritic solidification of metallic alloys are discussed from an order of magnitude analysis. Bulk thermal convection and/or interdendritic solutal convection have to be considered according to the values of the experimental data. Scaling laws for the solute boundary layer resulting from bulk thermal convection have already been derived. It is shown here that the interdendritic flow depends on a solutal Grashof number Gr based on the horizontal density gradient and a characteristic length L_s which is of the order of the liquid channels width. For Gr < 1, which is generally verified in practical cases, the interdendritic flow velocity U_r is proportional to the Grashof number. This a priori law compares favorably with the results of horizontal solidification experiments where the mean interdendritic flow velocity has been estimated from the resulting measured macrosegregation. In these experiments, as well as for most horizontal dendritic solidifications of metallic alloys at 1 g, the ratio $\text{U}{}_{\mathrm{r}}\text{R}$ (R is the growth rate) is of order one. In order to cancel the interdendritic flow effects, this ratio has to be lowered by one order of magnitude. According to our analysis, this can be obtained by performing the experiments either at a slightly reduced g level (～10^?1 g), or at 1 g in a vertical stable configuration with a sufficiently low residual horizontal thermal gradient.     

地磁场中卫星不侧置态下磁矩测试方法

对地磁场中卫星不倒置状态下分离卫星Z分量磁矩的测试及数据处理方法进行了研究。利用地球磁场方向特征、卫星剩磁矩与感磁矩在不同测量状态和测量过程中的变化,确定卫星Z分量磁矩含地磁垂直向感磁影响与不含地磁垂直向感磁影响的比例关系,基于积累的不同卫星水平和垂直向的磁测试数据,用近场法计算,获得了卫星Z分量的感磁系数。试验表明:用该法测得的Z分量磁矩测量相对误差不大于30%,工程上有较高的实用价值。     

Specific features of solar cosmic ray fluxes and geomagnetic conditions on December 5–18, 2006

Results of the analysis of specific features of solar activity, dynamics of solar cosmic ray fluxes, and state of the interplanetary medium are presented for the period December 5–18, 2006. The data analysis is based on new model concepts on coronal and interplanetary propagation of solar cosmic rays: partial capture into the magnetic field traps and oscillations at reflections from magnetic mirrors. Some new hypotheses about possible relations of the features of the interplanetary medium with processes in the Earth’s magnetosphere are put forward: the influence of the discrete interplanetary medium on processes in the Earth’s magnetosphere does exist always and, in this sense, it is a fundamental phenomenon; the discreteness of the inter-planetary medium can be one of the causes of geomagnetic substorms.     

Using radiation risk for assessment of space radiation hazard

Radiation hazard caused by exposure during a spaceflight is characterized by radiobiological consequences at all levels of organism. These consequences have a stochastic nature. Even deterministic effects are basically random quantity having all attributes of such mathematical values. The radiation risk is defined in this case as an additional probability of health damage or as a death probability in extreme case. For the manned spaceflight additional peculiarity of a human’s exposure is added. A natural space radiation environment has a stochastic character because solar particle events and crew of a spacecraft can be exposed to dose from background level up to lethal one.The report presents a procedure of radiation risk assessment for quantitative expression of radiation hazard level during a flight and using this value for developing protection recommendations. It is emphasized that the risk value is connected specifically with the time interval of possible hazard’s existent. The form of risk representation must be chosen depending on a time scale of radiobiological processes induced by the exposure (expressing in fact the radiation hazard model). Surviving function specified for the crewmember mortality rate changed by the professional exposure must be used for risk calculation. Solar particle events determine a stochastic character of radiation environment in space that must be taken into account for a risk assessment. The reliability of radiation risk assessment can be used for this goal.     

On some spacecraft fatigue-crack propagation problems

For thin-gauge sheet structures the effective critical range of stress-intensity factor ΔK_c can be calculated by curve fitting to the results of the crack propagation tests. A new, more exact, coordinate transformation method based on the Forman formula has been developed for this purpose.The method can be extended to cover the determination of the threshold stress-intensity range ΔK_th as well. There are two candidate transportation formulae for this purpose. The correct one of them will be singled out on the base of practical experience.Recent test data may indicate that even pure atmospheric air can exert a corrosion-like influence on the crack-growth rate of certain light-metal alloys. Should this prove to be true, then respective tests will have to be run in the proper environment and/or corrections will have to be applied for the corrosion influence.     

Optimal aeroassisted return from high earth orbit with plane change

This paper gives a complete analysis of the problem of aeroassisted return from a high Earth orbit to a low Earth orbit with plane change. A discussion of pure propulsive maneuver leads to the necessary change for improvement of the fuel consumption by inserting in the middle of the trajectory an atmospheric phase to obtain all or part of the required plane change. The variational problem is reduced to a parametric optimization problem by using the known results in optimal impulsive transfer and solving the atmospheric turning problem for storage and use in the optimization process. The coupling effect between space maneuver and atmospheric maneuver is discussed. Depending on the values of the plane change i, the ratios of the radii, $\text{n =}\text{r}{}_1\text{r}{}_2$ between the orbits and $\text{a =}\text{r}{}_2\text{R}$ between the low orbit and the atmosphere, and the maximum lift-to-drag ratio E1 of the vehicle, the optimal maneuver can be pure propulsive or aeroassisted. For aeroassisted maneuver, the optimal mode can be parabolic, which requires only drag capability of the vehicle, or elliptic. In the elliptic mode, it can be by one-impulse for deorbit and one or two-impulse in postatmospheric flight, or by two-impulse for deorbit with only one impulse for final circularization. It is shown that whenever an impulse is applied, a plane change is made. The necessary conditions for the optimal split of the plane changes are derived and mechanized in a program routine for obtaining the solution.     

Ultralight deployable booms for solar sails and other large gossamer structures in space

Future solar sail spacecraft which do not need any rocket motors and propellants are a promising option for long-term exploration missions in the solar system. However, they will require ultralight reflective foils and deployable booms which will allow for the unfolding of huge sails. The achievement of an acceptable ratio of reflective sail area and structural mass, which results in a still small, but significant acceleration under the photon pressure of sunlight, is extremely challenging. The same challenging deployment technique is required for the unfolding of large reflector membranes or antennas (gossamer structures). The key elements are the booms which must be stowable in a very small envelope before they reach their destination in space. Such booms were developed by DLR and have been successfully tested under zero-g-conditions during a parabolic flight campaign in February 2009. It could be convincingly demonstrated that the unfolding process is both controllable and reproducible. The booms consisted of two co-bonded omega-shaped carbonfiber half shells with 0.1 mm wall thickness each and had a weight of only 62 g per meter. Two different deployment technologies were tested, one based upon an inflatable 12 μm thick polymer hose inside the boom, the other one using an electromechanical uncoiling device at the tip of each boom. In the latter case, the uncoiling devices will radially fly away from the spacecraft, such that they become “expendable deployment mechanisms” and their mass does not count any more for the spacecraft mass that needs to be accelerated or actively controlled.