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.     

Internal Gravitational Field of a Thin Homogeneous Ring

The potential of gravity forces is found inside a thin homogeneous ring when the ring’s mean radius is much larger than the diameter of its cross section. Rings with elliptic and almost circular cross sections are considered.__________Translated from Kosmicheskie Issledovaniya, Vol. 43, No. 4, 2005, pp. 260–268.Original Russian Text Copyright © 2005 by Kasatkin.     

Observation of Mercury’s sodium tail using Fabry–Perot Interferometer

We observed sodium emission from Mercury’s atmosphere using a Fabry–Perot Interferometer at Haleakala Observatory on June 14, 2006. The Fabry–Perot Interferometer was used as a wavelength-tunable filter. The spectra of the surface reflection were subtracted from the observed spectra because sodium emission is contaminated by the surface reflection of Mercury. The image obtained in our observation shows the sodium exosphere extended to the anti-solar direction. The lifetime of a sodium atom was estimated to be 1.6 × 10⁴ to 1.9 × 10⁵ s with an error by a factor of 3–4.     

Efficient fault tolerant estimation using the IMM methodology

Space systems are characterized by a low-intensity process noise resulting from uncertain forces and moments. In many cases, their scalar measurement channels can be assumed to be independent, with one-dimensional internal dynamics. The nominal operation of these systems can be severely damaged by faults in the sensors. A natural method that can be used to yield fault tolerant estimates of such systems is the interacting multiple model (IMM) filtering algorithm, which is known to provide very accurate results. However, having been derived for a general class of systems with switching parameters, the IMM filter does not utilize the independence of the measurement errors in different channels, nor does it exploit the fact that the process noise is of low intensity. Thus, the implementation of the IMM in this case is computationally expensive. A new estimation technique is proposed herein, that explicitly utilizes the aforementioned properties. In the resulting estimation scheme separate measurement channels are handled separately, thus reducing the computational complexity. It is shown that, whereas the IMM complexity is exponential in the number of fault-prone measurements, the complexity of the proposed technique is polynomial. A simulation study involving spacecraft attitude estimation is carried out. This study shows that the proposed technique closely approximates the full-blown IMM algorithm, while requiring only a modest fraction of the computational cost.     

Parameters of a creasing-bending machine as applied to the scheme of transverse rotary shaping of chevron structures

Based on the topological representation and transformation of the elementary chevron structure module, we propose the dependences that relate the geometrical parameters of rollers with the chevron structure element sizes for the transverse scheme of rotary creasing and bending. The calculation scheme is realized in the form of the parametrized geometrical model using CAD SolidWorks aids.     

An algorithm for solving three-dimensional problem of elasticity theory for transversally isotropic medium

An algorithm for solving a boundary-value problem of deforming structures made of composite materials is considered. The polynomial solutions of the equation system for the linear theory of elasticity for the anisotropic medium in displacements are used in this algorithm.     

Bursts of geomagnetic pulsations in the frequency range 0.2-5 Hz excited by large changes of the solar wind pressure

We present the results of studying the magnetospheres’s response to sharp changes of the solar wind flow (pressure) based on observations of variations of the ions flux of the solar wind onboard the Inreball-1 satellite and of geomagnetic pulsations (the data of two mid-latitude observatories and one auroral observatory are used). It is demonstrated that, when changes of flow runs into the magnetosphere, in some cases short (duration ~ < 5 min) bursts of geomagnetic pulsations are excited in the frequency range Δf~ 0.2–5 Hz. The bursts of two types are observed: noise bursts without frequency changes and wide-band ones with changing frequency during the burst. A comparison is made of various properties of these bursts generated by pressure changes at constant velocity of the solar wind and by pressure changes on the fronts of interplanetary shock waves at different directions of the vertical component of the interplanetary magnetic field.     

Relative occurrence rate and geoeffectiveness of large-scale types of the solar wind

We investigate the relative occurrence rate for various types of the solar wind and their geoeffectiveness for magnetic storms with Dst < —50 nT. Both integrated effect for the entire time 1976–2000 and variations during this period of 2.5 cycles of solar activity are studied As raw data for the analysis we have used the catalog of large-scale types of the solar wind for the period 1976-2000 (see ftp://ftp.iki.rssi.ru/omni/) created by us with the use of the OMNI database (http://omni.web.gsgc.nasa.gov) [1] and described in detail in [2]. The average annual numbers of different type of events are as follows: 124 ±81 for the heliospheric current sheet (HCS), 8 ±6 for magnetic clouds (MC), 99 ±38 for Ejecta, 46 ±19 for Sheath before Ejecta, 6 ±5 for Sheath before MC, and 63 ±15 for CIR. The measurements that allowed one to determine a source in the solar wind were available only for 58% of moderate and strong magnetic storms (with index Dst < —50 nT) during the period 1976–2000. Magnetic clouds (MC) are shown to be the most geoeffective (~61%). The CIR events and Ejecta with Sheath region are three times less geoeffective (~20–21 %). Variations of occurrence rate and geoeffectiveness of various types of the solar wind in the solar cycle are discussed.     

Statistical properties of the most powerful solar and heliospheric disturbances

We present and discuss here the first version of a data base of extreme solar and heliospheric events. The data base contains now 87 extreme events mostly since 1940. An event is classified as extreme if one of the three critical parameters passed a lower limit. The critical parameters were the X-ray flux (parameter R), solar proton flux (parameter S) and geomagnetic disturbance level (parameter G). We find that the five strongest extreme events based on four variables (X-rays SEP, Dst, Ap) are completely separate except for the October 2003 event which is one the five most extreme events according to SEP, Dst and Ap. This underlines the special character of the October 2003 event, making it unique within 35 years. We also find that the events based on R and G are rather separate, indicating that the location of even extreme flares on the solar disk is important for geomagnetic effects. We also find that S = 3 events are not extreme in the same sense as R > 3 and G > 3 events, while S = 5 events are missing so far. This suggests that it might be useful to rescale the classification of SEP fluxes.     

An Overview of Ionosphere—Thermosphere Models Available for Space Weather Purposes

Our objective is to review recent advances in ionospheric and thermospheric modeling that aim at supporting space weather services. The emphasis is placed on achievements of European research groups involved in the COST Action 724. Ionospheric and thermospheric modeling on time scales ranging from a few minutes to several days is fundamental for predicting space weather effects on the Earth’s ionosphere and thermosphere. Space weather affects telecommunications, navigation and positioning systems, radars, and technology in space. We start with an overview of the physical effects of space weather on the upper atmosphere and on systems operating at this regime. Recent research on drivers and development of proxies applied to support space weather modeling efforts are presented, with emphasis on solar radiation indices, solar wind drivers and ionospheric indices. The models are discussed in groups corresponding to the physical effects they are dealing with, i.e. bottomside ionospheric effects, trans-ionospheric effects, neutral density and scale height variations, and spectacular space weather effects such as auroral emissions. Another group of models dealing with global circulation are presented here to demonstrate 3D modeling of the space environment. Where possible we present results concerning comparison of the models’ performance belonging to the same group. Finally we give an overview of European systems providing products for the specification and forecasting of space weather effects on the upper atmosphere, which have implemented operational versions of several ionospheric and thermospheric models.