Refinement of the Oblique Dipole Model in the Evolution of Rotary Motion of a Charged Body in the Geomagnetic Field

When solving problems related to the induction of the Earth's magnetic field, the potential of which is expressed in the form of a series of spherical harmonic functions, it is necessary to use an approximate model of the geomagnetic field that satisfies the two conflicting requirements of simplicity and accuracy. As is noted in [3, p. 10], at the stage of design of satellites, especially at the stage of preliminary analysis of their dynamics, simple models of the geomagnetic field are usually employed. This offers additional possibilities for theoretical analysis of the problem. The averaged model and the model of a right dipole are just such simple models. The quadrupole model of the geomagnetic field developed in [4] is more accurate, but also more complex. The model of an oblique or skewed dipole is intermediate. The quadrupole model generalizes the simpler models mentioned above, and its analysis allows estimation of the accuracy of each model. It turns out that the oblique dipole model, which differs from the model of a right dipole by small correcting terms, does not take into account other correcting terms caused by the quadrupole part of the geomagnetic field, which are greater in magnitude. The evolution of the rotary motion of a charged rigid body in the geomagnetic field is considered, and the incorrectness of the oblique dipole model is demonstrated. The effect of the quadrupole component of the geomagnetic field on the body dynamics is revealed.     

Secular evolution of rotary motion of a charged satellite in a decaying orbit

An electrostatically charged Earth satellite whose orbit is decaying due to the Earths oblateness is considered. Secular perturbations of the orbit are taken into account: they are caused by the second zonal harmonic of the geopotential. These perturbations represent deviations of the longitude of the ascending node and perigee argument, the orbit form being invariable and the orbit inclination to the equatorial plane being constant. The attitude rotary motion of the satellite under the action of perturbing moments of the gravitational and Lorentz forces is studied. The magnetic field of the Earth is taken in a quadrupole approximation. The evolution of the satellites rotary motion is investigated on the basis of new differential equations in s-parameters specially constructed for this purpose. Using the method of averaging, basic regularities of the secular evolution of rotary motion of a screened satellite are revealed. It is found that the rotary motion of a charged satellite essentially depends on the quadrupole component of the geomagnetic potential.__________Translated from Kosmicheskie Issledovaniya, Vol. 43, No. 2, 2005, pp. 111–125.Original Russian Text Copyright © 2005 by Tikhonov.     

Determination of the Attitude Motion of a Satellite Based on a Kinematical Model of Motion and Using Data of Measurements of Its Angular Velocity and the Earth’s Magnetic Field Strength

An integral statistical procedure of determination of the attitude motion of a satellite using the data of onboard measurements of angular velocity vectors and the strength of the Earth’s magnetic field (EMF) is suggested. The procedure uses only the equations of kinematics of a solid body and is applicable to determining both controlled and uncontrollable motions of a satellite at any external mechanical moments acting upon it. When applying this procedure, the data of measurements of both types, accumulated during a certain interval of time, are processed jointly. The data of measuring the angular velocity are smoothed by discrete Fourier series, and these series are substituted into kinematical Poisson equations for elements of the matrix of transition from a satellite-fixed coordinate system to the orbital coordinate system. The equations thus obtained represent a kinematical model of the satellite motion. The solution to these equations (which approximate the actual motion of a satellite) is found from the condition of the best (in the sense of the least squares method) fit of the data of measuring the EMF strength vector to its calculated values. The results of testing the suggested procedure using the data of measurements of the angular velocity vectors onboard the Foton-12 satellite and measurements of EMF strengths are presented.__________Translated from Kosmicheskie Issledovaniya, Vol. 43, No. 4, 2005, pp. 295–305.Original Russian Text Copyright © 2005 by Abrashkin, Volkov, Voronov, Egorov, Kazakova, Pankratov, Sazonov, Semkin.     

Attitude control system of the first Russian nanosatellite <Emphasis Type="Italic">TNS-0 no. 1</Emphasis>

The results of designing the attitude control system of the first Russian nanosatellite TNS-0 no. 1 providing orientation of its longitudinal axis along the local geomagnetic field induction vector are presented. The system consists of a permanent magnet and two sets of hysteresis rods. The magnetic and geometric parameters of the magnet and rods are calculated. The influence of the permanent magnet field on the hysteresis rods and mutual influence of the rods in the case of compact satellite packaging are analyzed. Examples of calculations of transient processes and steady-state angular satellite motion are presented.     

Empirical model of the high-latitude boundary of the Earth’s outer radiation belt at altitudes of up to 1000 km

An empirical model of the high-latitude boundary of the outer Earth’s radiation belt (ERB) has been presented, which is based on the measurement data of electron fluxes on the polar low-orbit CORONAS-Photon, Meteor-M1, and Meteor-M2 satellites. The boundary was determined by a sharp decrease to the background level of the flux of trapped electrons with energies of 100 or 200 keV in the polar part of the profile of the outer radiation belt. A numerical algorithm has been implemented to determine the time moment, when the fastest flux changes are recorded. The primary search was carried out, first, on 30 s averaged data, then repeated on data with a higher resolution. A functional dependence was obtained in order to approximate the obtained set of intersections of the boundary by elliptical curve. The empirical model constructed using the CORONAS-Photon measurement data in the epoch of anomalously low geomagnetic activity reflects the longitude structure of the high-latitude boundary of the outer radiation belt associated with the internal Earth’s magnetic field (MF), as well as its dependence on the universal time. Based on the data of intersections of the high-latitude boundary of the outer ERB (OERB) in the epoch of 2014–2016, the latitudinal shift of the boundary to the equator dependent on geomagnetic activity has been determined, as well as the nightside shift of the boundary due to the diurnal rotation of the Earth.     

Statistical Relationships between Solar,Interplanetary, and Geomagnetic Disturbances, 1976–2000: 3

In this paper we continue the analysis of the influence of solar and interplanetary events on magnetic storms of the Earth that was started in [9, 10]. Different experimental results on solar-terrestrial physics are analyzed in the study and the effects are determined that arise due to differences in the methods used to analyze the data. The classifications of magnetic storms by the K _p and D _st indices, the solar flare classifications by optical and X-ray observations, and the classifications of different geoeffective interplanetary events are compared and discussed. It is demonstrated that quantitative estimations of the relationships between two types of events often depend on the direction in which the events are compared. In particular, it was demonstrated that the geoeffectiveness of halo CMEs (that is, the percentage of Earth-directed coronal mass ejections that result in geomagnetic storms) is 40–50%. Higher values given in some papers were obtained by another method, in which they were defined as the probability of finding candidates for a source of geomagnetic storms among CMEs, and, strictly speaking, these values are not true estimates of the geoeffectiveness. The latter results are also in contrast with the results of the two-stage tracing of the events: first a storm—an interplanetary disturbance, and then an interplanetary disturbance—a CME.     

Effect of orientation of the solar wind magnetic clouds on the seasonal variation of geomagnetic activity

An analysis is made of the causes of seasonal dependence of geomagnetic activity, taking into account orientation of large-scale plasma structures (of the magnetic cloud type) of the solar wind. The contribution of magnetic clouds of different orientation in the periods of equinoxes and solstices is demonstrated. It is established that in equinox periods the geomagnetic activity increases due to ejections with small angles of inclination of their axis to the ecliptic plane, most frequently detected in near-Earth space. In solstice periods, such clouds are not geoeffective structures because of a decreased magnitude of projection of the magnetic field of cloud axis onto the Earth’s magnetic dipole during such intervals. This effect reveals itself in a reduced level of geomagnetic activity in summer and winter.     

The Earth's Magnetosphere Response to Solar Wind Events according to the INTERBALL Project Data

The results of studying the interaction of two types of the solar wind (magnetic clouds and solar wind of extremely low density) with the Earth's magnetosphere are discussed. This study is based of the INTERBALL space project measurements and on the other ground-based and space observations. For moderate variations of the solar wind and interplanetary magnetic field (IMF) parameters, the response of the magnetosphere is similar to its response to similar changes in the absence of magnetic clouds and depends on a previous history of IMF variations. Extremely large density variations on the interplanetary shocks, and on leading and trailing edges of the clouds result in a strong deformation of the magnetosphere, in large-scale motion of the geomagnetic tail, and in the development of magnetic substorms and storms. The important consequences of these processes are: (1) the observation of regions of the magnetosphere and its boundaries at great distances from the average location; (2) density and temperature variations in the outer regions of the magnetosphere; (3) multiple crossings of geomagnetic tail boundaries by a satellite; and (4) bursty fluxes of electrons and ions in the magnetotail, auroral region, and the polar cap. Several polar activations and substorms can develop during a single magnetic cloud arrival; a greater number of these events are accompanied, as a rule, by the development of a stronger magnetic storm. A gradual, but very strong, decrease of the solar wind density on May 10–12, 1999, did not cause noticeable change of geomagnetic indices, though it resulted in considerable expansion of the magnetosphere.     

小卫星磁场分布测量方法研究

文章通过分析卫星磁场与地磁场的关系,确立了磁场分布的测量方法,并对测量误差进行了分析.     

On dynamics of a plasma ring rotating in the magnetic field of a central body: Magneto-gyroscopic waves. Problems of stability and quantization

Based on a mathematical model described in [1], some new aspects of the dynamics of a thin planar plasma ring rotating in the magnetic field of a central body are considered. The dipole field is considered assuming that the dipole has a small eccentricity, and the dipole axis is inclined at a small angle to the central body’s axis of rotation. Emphasis is placed on the problem of stability of the ring’s stationary rotation. Unlike [1], the disturbed motion is considered which has a character of eddy magneto-gyroscopic waves. The original mathematical model is reduced to a system of finite-difference equations whose asymptotic analytical solution is obtained. It is demonstrated that some “elite” rings characterized by integral quantum numbers are long-living, while “lethal” or unstable rings (antirings) are associated with half-integer quantum numbers. As a result, an evolutionally rife rotating ring of magnetized plasma turns out to be stratified into a large number of narrow elite rings separated by gaps whose positions correspond to antirings. The regions of possible existence of elite rings in near-central body space are considered. Quantum numbers determining elite eigenvalues of the mean sector velocity (normalized in a certain manner) of a ring coincide with the quantum numbers appearing in the solution to the Schrödinger equation for a hydrogen atom. Perturbations of elite orbits corresponding to these quantum numbers satisfy the de Brogli quantum-mechanical condition. This is one more illustration of the isomorphism of quantization in microcosm and macrocosm.     

基于IGRF地磁场模型的航天器地磁干扰力矩数值仿真

航天器长期在轨运行期间,空间磁场与其自身磁矩相互作用的累积,会对航天器的姿态造成较大影响,加重姿态控制系统负担,降低航天器的可靠性。文章分别针对航天器轨道计算及地磁场模型的使用,对航天器地磁干扰力矩数值的仿真进行了系统的研究,最终得到航天器在轨运行时地磁干扰力矩计算仿真方法。     

地球磁场对带电赤道卫星的轨道半长轴和偏心率的摄动影响

本文利用摄动理论研究了带电的赤道卫星在地球磁场中做椭圆轨道运动时地磁摄动力对轨道半长径和偏心率的摄动影响。研究结果表明：地磁场对带电赤道卫星的轨道半长径没有摄动影响，既无周期摄动，也无长期摄动，但对轨道偏心率有摄动影响，且只有周期性摄动，而无长期摄动。当卫星自身带电量较大时，这种摄动影响必须予以考虑     

Attitude stabilization of a satellite by magnetic coils

Stabilization problem for a satellite is considered. The only measurement is of the geomagnetic field in the satellite coordinates. The control is carried out by a magnetic moment of current coils (magnetorquers) mounted on the satellite body. The stabilizer constructed in this work solves the problems of magnetic and gravitational stabilization. Qualitative analysis and results of numerical simulation are presented. The results of simulation show that the proposed stabilization system is reliable, and has an appropriate accuracy and does not need powerful sources of energy, and therefore can be used for attitude control of small satellites.     

三轴稳定微小卫星主动磁阻尼姿态控制

针对三轴稳定微小卫星,用四元数法建立了速率阻尼阶段的动力学和运动学模型.根据地磁场强度矢量投影到轨道坐标系的简便旋转关系,设计了采用主动磁控的拟比例微分控制器,同时分析了磁力矩器的磁偶极矩.速率阻尼仿真结果表明:该控制法有效可行,具有一定的应用价值.     

利用地磁场测量的小卫星自主导航设计

地磁场矢量是卫星所在位置的函数 ,通过对地磁场的测量 ,即可实现对近地小卫星的自主导航。本文采用卡尔曼滤波技术设计了小卫星基于地磁场测量的导航方法 ,在采用地磁场模型时选取磁偶极子模型 ,以此使设计算法的计算量大大减少。最后利用数字仿真验证了系统性能。     

Storm deviations of the geomagnetic trap core from dipole configuration deduced from data on relativistic electrons

Satellite data on the position of maximum L _m of the belt of relativistic electrons during strong storms, obtained at low altitudes (∼500 km) and at high altitudes (near the geomagnetic equator plane), are compared (L is the McIlwain parameter). Both at low and high altitudes the maximum of the storm belt of relativistic electrons is formed on the outer edge of the ring current. It is shown that the geomagnetic field can substantially deviate from dipole configuration not only at the geomagnetic trap periphery, but at its core as well (at L ∼ 2.5–3.5), and these deviations are nonlinear. Simultaneous measurements of the fluxes of relativistic electrons at low and high altitudes can serve for estimation of the real shape of magnetic field lines at L < 4 during geomagnetic disturbances.     

Magnetic Storms in October 2003

Preliminary results of an analysis of satellite and ground-based measurements during extremely strong magnetic storms at the end of October 2003 are presented, including some numerical modeling. The geosynchronous satellites Ekspress-A2and Ekspress-A3, and the low-altitude polar satellites Coronas-F and Meteor-3M carried out measurements of charged particles (electrons, protons, and ions) of solar and magnetospheric origin in a wide energy range. Disturbances of the geomagnetic field caused by extremely high activity on the Sun were studied at more than twenty magnetic stations from Lovozero (Murmansk region) to Tixie (Sakha-Yakutia). Unique data on the dynamics of the ionosphere, riometric absorption, geomagnetic pulsations, and aurora observations at mid-latitudes are obtained.     

Satellite communications' role in national development : Policy and regulatory aspects

This paper examines the way in which satellite communication can assist development in the Third World — through improvement of access to education, integration, especially of remote areas, increased market opportunities and as a tool to attract investment — with particular reference to Indinesia. Future trends, eg the expansion of satellite capability, introduction of new services, liberalization and a shift in satellite utilization towards broadcasting, are discussed, as are the regulatory reforms that will be needed to accommodate them.     

Large and sharp changes of solar wind dynamic pressure and disturbances of the magnetospheric magnetic field at geosynchronous orbit caused by these variations

The large and sharp changes of solar wind dynamic pressure, found from the INTERBALL-1 satellite and WIND spacecraft data, are compared with simultaneous magnetic field disturbances in the magnetosphere measured by geosynchronous GOES-8, GOES-9, and GOES-10 satellites. For this purpose, about 200 events in the solar wind, associated with sharp changes of the dynamic pressure, were selected from the INTERBALL-1 satellite data obtained during 1996–1999. The large and sharp changes of the solar wind dynamic pressure were shown to result in rapid variations of the magnetic field strength in the outer magnetosphere, the increase (drop) of the solar wind dynamic pressure always lead to an increase (drop) of the geosynchronous magnetic field magnitude. The value of the geomagnetic field variation strongly depends on the local time of the observation point, reaching a maximum value near the noon meridian. It is shown that the direction of the B _z component of the interplanetary magnetic field has virtually no effect on the geomagnetic field variation because of a sharp jump of pressure. The time shift between an event in the solar wind and its response in the magnetosphere at a geosynchronous orbit essentially depends on the inclination of the front of a solar wind disturbance to the Sun-Earth line.     

用地球磁场和重力场成功挽救风云一号（B）卫星的控制技术

风云一号气象卫星是我国最早成功发射的太阳同步三轴稳定对地遥感卫星，由于早期的技术和器件原因，星上计算机因空间辐照而失控，造成星上贮气耗尽、卫星高速翻滚。本文详细介绍了了在卫星面临失败的情况下，作者利用地球磁场和重力场与卫星的相互作用，采用星上的磁力矩器和可用的一切手段而设计的一整套抢救这颗卫星的技术方法，并简述了经过75天的艰苦努力，使这颗濒临失败的卫星重新建立三轴稳定的对地定向姿态的历程。