One optimization problem for trajectories of spacecraft rendezvous mission to a group of asteroids

The optimization problem is considered for the trajectory of a spacecraft mission to a group of asteroids. The ratio of the final spacecraft mass to the flight time is maximized. The spacecraft is controlled by changing the value and direction of the jet engine thrust (small thrust). The motion of the Earth, asteroids, and the spacecraft proceeds in the central Newtonian gravitational field of the Sun. The Earth and asteroids are considered as point objects moving in preset elliptical orbits. The spacecraft departure from the Earth is considered in the context of the method of a point-like sphere of action, and the excess of hyperbolic velocity is limited. It is required sequentially to have a rendezvous with asteroids from four various groups, one from each group; it is necessary to be on the first three asteroids for no less than 90 days. The trajectory is finished by arrival at the last asteroid. Constraints on the time of departure from the Earth, flight duration, and final mass are taken into account in this problem.     

Generalized restricted circular three-body problem as a model for dynamics of binary asteroids

Exploration of the Solar System has recently revealed the existence of a large number of asteroids with satellites, which has stimulated interest in studying the dynamics of such systems. This paper is dedicated to the analysis of the relative motion of a binary asteroid. The conditions of existence of such a system (i.e., when its components do not run away) are derived in the Introduction. Then it is assumed that the satellite has no significant effect on the motion of the main asteroid, the latter being modeled as a dumbbell-like precessing solid body. The equations of motion of this system are a two-parameter generalization of the corresponding equations of the restricted circular three-body problem. It is demonstrated that in the system under consideration there exist steady-state motions in which the small asteroid is equidistant from attracting centers at the ends of the dumbbell (an analog to triangle libration points). The conditions of existence of such motions are derived, and the positions with respect to the dumbbell are analyzed in detail. Examination of the stability of the triangle libration points is reduced to investigation of a characteristic equation of the sixth degree. The stability conditions are derived in the case when the main asteroid executes near-planar motion.     

On a possibility of delivery of samples of primordial matter from asteroids of the main belt by a spacecraft with electric propulsion

The possibilities of an expedition to asteroids of the Main belt with the goal of obtaining samples of their matter using a spacecraft with a small-thrust electric propulsion, which is under development as a part of the Fobos-Grunt project, are considered. Obtaining matter from different regions of the Solar system is necessary in order to understand its origin and the structure of the Earth. Approximate estimates are made for the flights of spacecraft with electric propulsion and different power of solar batteries, and with perturbation maneuver near Mars for expeditions to the Main asteroid belt, including its middle part.     

On the arc length of observations of a small solar system body sufficient to classify it as hazardous

This paper analyzes the accuracy of orbit determination calculated by observations of short arcs. In this case, we imposed the condition that the arc length and/or the distribution of arc observations should provide a confident classification of the orbit of a small celestial body allowing one to distinguish a potentially hazardous body, also including a threat of collision.     

Application of a Multiple Hypothesis Filter to near GEO high area-to-mass ratio space objects state estimation

Optical surveys have identified a class of high area-to-mass ratio (HAMR) objects in the vicinity of the Geostationary Earth Orbit (GEO) regime. The nature of these objects is not well known, though their proximity to the GEO belt implies origins from space objects (SOs) near GEO. These HAMR objects pose a collision hazard as they transit through the vicinity of active GEO satellites. Due to their high area-to-mass ratios (AMRs), ranging from 0.1 to 20 m²/kg and higher, the effective solar radiation pressure perturbs their orbits significantly. Improvements in detection sensitivity will result in large numbers of uncorrelated tracks from surveys. A Multiple Hypothesis Filter (MHF) approach to the initial state estimation and track association provides a potentially automated and efficient approach to the processing of multiple un-correlated tracks.The availability of long-term optical angles data collected for a set of near GEO HAMR objects provides the means for testing candidate estimation processes such as the MHF. A baseline orbit determination (OD) process uses an Extended Kalman Filter/Smoother to manually estimate the 6 orbital elements and the effective area-to-mass ratio (AMR) which drives the solar radiation pressure perturbations on the orbital trajectories. In addition to allowing the characterization of the long-term behavior of the AMR, this process establishes a pseudo-truth trajectory to which the MHF analysis can be compared. An Unscented Kalman Filter (UKF) is applied in the MHF estimation process to estimate the 6 orbital elements and AMR, with no a priori state assumptions, and the results are compared to the pseudo-truth results for validation.The work to be presented summarizes the UKF/MHF process and assesses state estimation performance based on selected data for selected near GEO HAMR objects having a range of AMR value and variations. The prediction accuracy is also assessed by comparing predictions derived from filter updates to segments of the pseudo-truth trajectory determined from data not included in the updates.     

Applying international space station (ISS) and solar-sail technology to the exploration and diversion of small,dark near earth objects (NEO's)

Space-Station technology, micron-thick 100-m solar sails, and a near-Earth propulsion system allow exploration of small, dark Near-Earth-Objects (NEO's) of cometary origin. Early crewed missions to NEO's could analyze the objects' properties and evaluate resource-mining possibilities. Later missions to Earth-threatening 100-m radius NEO's could deploy NEO-centered, high-area, low-mass reflective structures. The solar gravitational parameter (GM_sun) on a NEO is slightly reduced by increased radiation pressure. The central-force-field equations reveal that NEO eccentricity and average solar distance are thereby slightly increased. Given decades of warning and long-lived reflective canopies, such structures can convert Earth-impacts into near-misses. Although not suitable for NEO mining, such structures are superior to nuclear detonations because (as revealed by the 1994 Jupiter-comet interaction) NEO calving may be a consequence of explosions. NEO despinning is not required.     

Physical-chemical treatment of wastes: a way to close turnover of elements in LSS.

"Man-plants-physical-chemical unit" system designed for space stations or terrestrial ecohabitats to close steady-state mineral, water and gas exchange is proposed. The physical-chemical unit is to mineralize all inedible plant wastes and physiological human wastes (feces, urine, gray water) by electromagnetically activated hydrogen peroxide in an oxidation reactor. The final product is a mineralized solution containing all elements balanced for plants' requirements. The solution has been successfully used in experiments to grow wheat, beans and radish. The solution was reusable: the evaporated moisture was replenished by the phytotron condensate. Sodium salination of plants was precluded by evaporating reactor-mineralized urine to sodium saturation concentration to crystallize out NaCl which can be used as food for the crew. The remaining mineralized product was brought back for nutrition of plants. The gas composition of the reactor comprises O2, N2, CO2, NH3, H2. At the reactor's output hydrogen and oxygen were catalyzed into water, NH3 was converted in a water trap into NH4 and used for nutrition of plants. A special accessory at the reactor's output may produce hydrogen peroxide from intrasystem water and gas which makes possible to close gas loops between LSS components.     

Solving Optimization Problems for the Flight Trajectories of a Spacecraft with a High-Thrust Jet Engine in Pulse Formulation for an Arbitrary Gravitational Field in a Vacuum

A mathematically well-posed technique is suggested to obtain first-order necessary conditions of local optimality for the problems of optimization to be solved in a pulse formulation for flight trajectories of a spacecraft with a high-thrust jet engine (HTJE) in an arbitrary gravitational field in vacuum. The technique is based on the Lagrange principle of derestriction for conditional extremum problems in a function space. It allows one to formalize an algorithm of change from the problems of optimization to a boundary-value problem for a system of ordinary differential equations in the case of any optimization problem for which the pulse formulation makes sense. In this work, such a change is made for the case of optimizing the flight trajectories of a spacecraft with a HTJE when terminal and intermediate conditions (like equalities, inequalities, and the terminal functional of minimization) are taken in a general form. As an example of the application of the suggested technique, we consider in this work, within the framework of a bounded circular three-point problem in pulse formulation, the problem of constructing the flight trajectories of a spacecraft with a HTJE through one or several libration points (including the case of going through all libration points) of the Earth–Moon system. The spacecraft is launched from a circular orbit of an Earth's artificial satellite and, upon passing through a point (or points) of libration, returns to the initial orbit. The expenditure of mass (characteristic velocity) is minimized at a restricted time of transfer.     

The use of solutions to problems of spacecraft trajectory optimization in impulse formulation when solving the problems of optimal control of trajectories of a spacecraft with limited thrust engine: I

In this first part of our paper, it is suggested to use solutions to boundary value problems in the optimization problems (in impulse formulation) for spacecraft trajectories in order to obtain the initial approximation, when boundary value problems of the maximum principle are solved numerically by the shooting method. The technique suggested is applied to the problems of optimal control over motion of the center of mass of a spacecraft controlled by the thrust vector of jet engine with limited thrust in an arbitrary gravitational field in a vacuum. The method is based on a modified (in comparison to the classic scheme) shooting method computation together with the method of continuation along a parameter (maximum reactive acceleration, initial thrust-to-weight ratio, or any other parameter equivalent to them). This technique allows one to obtain the initial approximation with a high precision, and it is applicable to a wide range of optimal control problems solved using the maximum principle, if the impulse formulation makes sense for these problems.     

The use of solutions to problems of spacecraft trajectory optimization in impulse formulation when solving the problems of optimal control of trajectories of a spacecraft with limited thrust engine: II

As examples of application of the technique suggested in the first part of this work, the problems of optimizing the trajectories of spacecraft transfers between circular coplanar orbits are considered in this second part. During the transfer the spacecraft is controlled by the vector of thrust of a limited-thrust jet engine. The mass consumption is minimized for a limited time of transfer. Extreme trajectories with two and three powered sections (Homan-type and bi-elliptic transfer trajectories) are numerically determined. The solution of these well-studied problems allows one to compare the results of applying the suggested technique with the results of application of other previously used techniques.     

以推行质量管理体系为契机 促进各项工作再上新台阶

内蒙古空管分局从ISO9001宣贯至今,已有两年时间,两年来,分局经历了宣贯、编写、内审、试行、外审、运行并改进,年度复审等贯标各阶段工作,我们深切感受到ISO9001质量体系是我们空管行业行之有效的基础管理工具,对切实提高单位管理水平,规范运行,保证持续安全有极大的促进作用。通过建立与实施ISO9001质量管理体系,并与分局实际有效地结合,我们以优异的成绩完成了呼和浩特机场不停航施工、     

Variation of the orbital elements for parabolic trajectories due to a small impulse using Gauss equations

Firstly we derive Gauss’ perturbation equation for parabolic motion using Murray–Dermott and Kovalevsky procedures. Secondly, we easily deduce the variations of the orbital elements for the parabolic trajectories due to a small impulse at any point along the path and at the vertex of the parabola.     

Guidance of a spacecraft with low lift-to-drag ratio to a landing point

The problem of terminal control over a deorbiting spacecraft at the stage of its flight after leaving plasma (altitude of ∼40 km) is considered, the aim being to guide it to a preset landing point. The algorithm is based on a modification of the well-known method of proportional navigation, when a fixed point is the target. It is suggested to use satellite navigation systems (of the GLONASS or GPS types) and/or radio beacons, which should allow one to determine the spacecraft trajectory parameters with high precision. Single-channel control is performed by changing the roll angle according to current parameters of the trajectory, which ensures adaptability of the method. Examples of three-dimensional trajectories of flight are presented for a manned spacecraft with low lift-to-drag ratio (∼0.5), currently under design in Russia. The results of statistical modeling taking into account initial deviations of the trajectory parameters and wind disturbances are presented. A method of statistical choice of a reference trajectory for the guidance stage is suggested. A theoretical possibility of using the algorithm of spacecraft guidance (in case of in-light accident with a carrier launcher) to preset regions in the vicinity of launching route is demonstrated. A qualitative analysis of proportional navigation with a fixed target is presented.     

Rats in a transparent morris water maze use elemental and configural geometry of landmarks as well as distance to the pool wall

The aim of this study is to evaluate whatare the dimensions of a panorama of discretelandmarks that a rodent will store in order toreturn to a previously visited target. Ratswere trained to locate a hidden platform in acircular pool of clouded water set within aquasi-spherical enclosure. In order to find theplatform, they had to learn the geometricrelations between the platform and asurrounding set of three discrete landmarks,highly visible through the transparent wall ofthe pool. In test trials without a platform,the array of landmarks was so manipulated as todissociate the effect of actual distance to thelandmarks, of their angular separation, and oftheir apparent dimension. Animals were shown torely equally on angular separation and apparentdimension. The role of actual distance couldnot be definitely ascertained, as animals wereshown to additionally rely on the distance tothe pool wall in order to locate theplatform.     

From initial ideas to a European plan: GMES as an exemplar of European space strategy

Global Monitoring for Environment and Security (GMES) is an idea which originated during a meeting in Baveno, Italy, in May 1998, which generated a call for Europe to get its act together in the field of environmental monitoring from space, to define a well articulated strategy in this area and to build upon its excellent scientific research community, its proven technical prowess in Earth observation from space and its nascent political will to express its objectives in international fora related to climate change and other global environment topics. While Europe was already active in the most advanced areas of global monitoring, its rather uncoordinated efforts (even within the European Commission) lacked visibility and did not appear to fit into a clearly established strategy. The ‘Baveno initiative’ was an attempt to remedy this situation and find a place within a developing ‘European Strategy for Space’, which requires ESA and the European Union to work more closely together. GMES was extended to include the ‘security’ (in its wider sense) aspects of global monitoring, a move that produced a number of questions and misunderstandings, but which allowed many in Europe to realize that monitoring the activities of the Earth’ land masses, oceans and atmosphere do include a security dimension. GMES will eventually incorporate an implementation plan which will call upon various monitoring techniques, ambitious modelling projects and connections with society's more urgent requirements with respect to environmental protection and prevention or reduction of risks related to natural hazards. This will entail significant efforts to inform the user communities and to convince them of the relevance and usefulness of this initiative. It will also provide a sound basis for the European contribution to the new initiative for improved coordination of strategies and systems for Earth observations called for by the July 2003 Earth Observation Summit.     

Optimization of the Flight of a Spacecraft with a Solar Sail from the Earth to Mars with a Perturbation Maneuver near Venus

The trajectories of the fastest flight of a spacecraft (SC) with a solar sail from the Earth's sphere of activity to the Martian sphere of activity including the section of a perturbation maneuver near Venus are investigated. The planetary spheres of activity are assumed to be point-like; i.e., the maneuver section and the initial and final positions of the SC coincide with the corresponding positions of the planets. The initial velocity of the SC is assumed to be equal to the Earth's velocity, so that no leveling of the velocities of the SC and Mars in the final point of the flight is required. The perturbation maneuver is considered as a jump of the heliocentric velocity of the SC at the point of its contact with Venus, which does not change the magnitude of its Venus-centric velocity. The orbits of planets are assumed to be circular and coplanar; the SC trajectory lies at the plane of these orbits. The sail is planar with a specularly reflecting surface. The trajectories of optimum flights are determined as a result of solving the boundary value problem of the Pontryagin maximum principle. The families of solutions to this problem depending on the initial angular positions of Venus and Mars are constructed by the method of continuation over a parameter.     

Effectiveness of centrifuge-induced artificial gravity with ergometric exercise as a countermeasure during simulated microgravity exposure in humans

To test the effectiveness of centrifuge-induced artificial gravity with ergometric exercise, 12 healthy young men (20.7 +/- 1.9 yr) were exposed to simulated microgravity for 14 days of -6 degrees head-down bedrest. Half the subjects were randomly selected and loaded 1.2 G artificial gravity with 60 W (four out of six subjects) or 40 W (two out of six subjects) of ergometric workload on days 1, 2, 3, 5, 7, 9, 11, 12, 13, 14 (CM group). The rest of the subjects served as the control. Anti-G score, defined as the G-load x running time to the endpoint, was significantly elongated by the load of the centrifuge-ergometer. Plasma volume loss was suppressed (-5.0 +/- 2.4 vs. -16.4 +/- 1.9%), and fluid volume shift was prevented by the countermeasure load. Elevated heart rate and muscle sympathetic nerve activity after bedrest were counteracted, and exaggerated response to head-up tilt was also suppressed. Centrifuge-induced artificial gravity with exercise is effective in preventing cardiovascular deconditioning due to microgravity exposure, however, an effective and appropriate regimen (magnitude of G-load and exercise workload) should be determined in future studies.     

Sequences of Solar Events with Identical Decays as a Tool for Isolating Quasistationary States in the Interplanetary Space

Time profile of the fluxes of energetic solar particles generated by solar flares (including their phase of decline) is formed to a large extent by the structure of the interplanetary magnetic field and its irregularities that move away from the Sun with the solar wind velocity. When propagation is a pure diffusion, the solar particle fluxes decay after the maximum in a power-law manner. At the same time in many cases this decay is exponential, which is indicative of a considerable role played by the convective sweep of particles and their adiabatic deceleration in the expanding solar wind. In this paper we consider the events with long exponential decays and newly discovered series of successive events with identical exponential decays lasting for one to two weeks or more. They allow us to assume that the interplanetary space is stable and homogeneous during this period.     

Net electric power of concentrating solar mirror systems for application in space as a function of the distance to the sun

The use of solar radiation by means of concentrating solar mirror systems, such as parabolic and spheric configurations, mainly is an engineering problem. A decisive characteristic for the optimisation of a complete system with turboelectric power conversion is the thermal cycle applied. Besides the Carnot process, here taken up into the study as an ideal comparative process, suitable processes for the technological realisation are the Brayton process and the Rankine process. The Brayton process is a typical gas turbine process using only the gaseous phase. The Rankine process is a steam engine process using liquid and gaseous phase.The work in hand shows how such solar systems with turboelectric conversion are optimised with respect to their specific weight (kg/kW_e) and how the distance to the sun as well as technological data enter into the analysis.As expected, the Carnot cycle as an ideal comparative process for both types of systems shows the best results for the optimum specific mass of the system. Regarding the real processes, the Rankine cycle shows more favourable characteristics than the Brayton cycle. The difference of the specific masses of the real processes mainly results from the different thermal conditions at the radiator.The influence of the distance to the sun is as expected. The nearer to the sun the solar power system operates, the better is the optimum specific mass of the system. For distances to the sun between 0.3 and 1.0 AU the spheric system shows a better behaviour than the parabolic system. For distances to the sun greater than 2.0 AU the parabolic system shows better behaviour of the specific weight. In the region between 1 and 2 AU the better optimum specific mass of the system belongs to the technological data used in the analysis.