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.     

Optimization of Flight Trajectories of a Spacecraft with Electric Propulsion Using the Gravitational Maneuver

Necessary conditions of optimality of the use of a gravitational maneuver during a flight are obtained, and a mathematical model for its study is proposed. With the help of the developed method of optimization of a trajectory of an interplanetary flight using a favorable gravitational maneuver, estimations of a spacecraft's transport capabilities are made for flights to Mercury and for the delivery of a solar probe into the near vicinity of the Sun.     

Work and rest planning as a way of crew member error management.

Human error prevention is very important to support the safety and efficiency of human-machine systems. The approach to space crew member management error is considered in this paper. The data collected during 14 "Mir" station missions were analyzed to substantiate this approach. As a result of data processing, the significant (p<0.05) correlation of crew member errors with work and rest schedule tensity has been revealed. This finding was used to work out the mathematical model describing the dependence between the frequency (the probability) of crew member errors and work and rest schedule tensity. Based on the model, the algorithm of error management by means of efficient planning of crew members' work has been developed. The suggested approach may be used equally with other methods to raise the reliability of human-operator performance. Grant numbers: NAS-15-10110.     

Reachable domain of spacecraft with a single tangent impulse considering trajectory safety

The reachable domain of the two-body transfer orbit with a single upper-bounded tangent impulse is studied. Three cases are analyzed for either the magnitude of the tangent impulse or the initial impulse point being free, or both being free. For a fixed impulse magnitude and a free initial impulse point, the initial orbit is proved to be one of the envelopes of the reachable domain. Moreover, the trajectory safety for the transfer orbit requires a lower bound on the perigee altitude and an upper bound on the apogee altitude. Then the ranges of the impulse magnitude and the initial true anomaly can be obtained by solving quadratic and cubic inequalities, respectively. If both constraints are required for an arbitrary impulse point, the range of the impulse magnitude is obtained with impulses at the perigee and the apogee. Several numerical examples with different eccentricities are provided to show the geometry of the reachable domain and to verify the proposed method.     

Parabolic maneuvers of the Swiss Air Force fighter jet F-5E as a research platform for cell culture experiments in microgravity

Long-term sensitivity of human cells to reduced gravity has been supposed since the first Apollo missions and was demonstrated during several space missions in the past. However, little information is available on primary and rapid gravi-responsive elements in mammalian cells. In search of rapid-responsive molecular alterations in mammalian cells, short-term microgravity provided by parabolic flight maneuvers is an ideal way to elucidate such initial and primary effects. Modern biomedical research at the cellular and molecular level requires frequent repetition of experiments that are usually performed in sequences of experiments and analyses. Therefore, a research platform on Earth providing frequent, easy and repeated access to real microgravity for cell culture experiments is strongly desired. For this reason, we developed a research platform onboard the military fighter jet aircraft Northrop F-5E “Tiger II”. The experimental system consists of a programmable and automatically operated system composed of six individual experiment modules, placed in the front compartment, which work completely independent of the aircraft systems. Signal transduction pathways in cultured human cells can be investigated after the addition of an activator solution at the onset of microgravity and a fixative or lysis buffer after termination of microgravity. Before the beginning of a regular military training flight, a parabolic maneuver was executed. After a 1 g control phase, the parabolic maneuver starts at 13,000 ft and at Mach 0.99 airspeed, where a 22 s climb with an acceleration of 2.5g is initiated, following a free-fall ballistic Keplerian trajectory lasting 45 s with an apogee of 27,000 ft at Mach 0.4 airspeed. Temperature, pressure and acceleration are monitored constantly during the entire flight. Cells and activator solutions are kept at 37 °C during the entire experiment until the fixative has been added. The parabolic flight profile provides up to 45 s of microgravity at a quality of 0.05g in all axes. Access time is 30 min before take-off; retrieval time is 30 min after landing. We conclude that using military fighter jets for microgravity research is a valuable tool for frequent and repeated cell culture experiments and therefore for state-of-the art method of biomedical research.     

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.     

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.     

辅导员如何实现与学生的有效沟通

辅导员的教育功能是高校人才培养与校园和谐建设的重要工作之一。辅导员教育功能的实现关键在于师生之间进行有效的思想沟通。论文分析了目前高职高专院校学生的外部环境和内在特点,从换位思考,尊重学生等几个方面入手,就辅导员与学生之间的各种沟通方式进行了分析阐述。实践证明,师生间的有效沟通,对人才培养与校园和谐建设起着十分重要的作用。     

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.     

Performance of a small and low-cost chamber to simulate lunar surface environment

The performance of a small and low-cost metal chamber built to simulate the pressure and temperature conditions of lunar surface was assessed and the results are presented. This chamber is intended for studying the physical properties of lunar surface and subsurface (using soil simulants) and also to validate the technology readiness of certain newly developed payloads planned for future lunar surface missions (Lander/Rover). It is possible to reach down to ∼10⁻⁷ Pa under specific conditions and maintain the temperature of the sample under investigation to lunar day and night temperatures. The designed system has been subjected to various tests to evaluate its performance and suitability for carrying out experiments in a simulated lunar environment.     

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.     

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.     

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、