The rigidity dependence of characteristic decay time and mean free path in SCR events

Combination of data on declined intensities of particles of different nature (e, p, and α) into a single dependence of characteristic decline time τ on particle rigidity in a wide range of R reveals the diversity of forms of τ(R) in different events: regular increase, decrease, and independence of R, as well as the presence in some events of maxima and minima. The problem of studying τ(R) has something in common with long standing problem of the rigidity dependence of mean free path λ(R). The considered set of forms of τ(R) allows one to conclude that at present there is no uniform dependence τ(R), as well as λ(R), and, therefore, no their common model interpretation in a wide range of rigidities exists.     

Determination of parameters of rotational motion of the <Emphasis Type="Italic">Monitor-E</Emphasis> spacecraft from the telemetry data on solar batteries’ current

The Monitor-E spacecraft executed uncontrolled flight due to emergency situation, no telemetry information on parameters of the spacecraft’s attitude motion being available. So, the problem arose to determine the spacecraft’s rotational motion from the accessible indirect information—the electric current provided by solar batteries. In this paper the integrated statistical technique is described, that allows one to solve this problem. The values of current, obtained over the time interval some tens of minutes long, have been processed simultaneously by the least squares method using the integration of the equations of spacecraft’s rotational motion. As a result of processing, the initial conditions of motion were estimated, and the spacecraft’s moments of inertia were updated, as well as the angles, specifying solar batteries position in the spacecraft-fixed coordinate system. The results of processing of 12 data sets are presented, which allowed us to reconstruct the actual rotational motion of the spacecraft.     

Stable spatial orbits around collinear libration points

A technique of generation of spatial periodic solutions to the restricted circular three-body problem from periodic orbits of the planar problem has been used for the families of orbits around collinear libration points L ₁ and L ₂. Developing the families obtained at the 1: 1 resonance, we have obtained stable solutions both in the Earth-Moon system and in the Sun-Earth system. Of course, the term “around the libration point” is rather conventional; the obtained orbits become more similar to the orbits around the smaller attracting body. The further development of the family of orbits “around” the libration point L ₂ in the Sun-Earth system made it possible to find the orbits satisfying the new, much more rigorous constraints on cooling the spacecraft of the Millimetron project.     

Study of the mode of angular velocity damping for a spacecraft at non-standard situation

Non-standard situation on a spacecraft (Earth’s satellite) is considered, when there are no measurements of the spacecraft’s angular velocity component relative to one of its body axes. Angular velocity measurements are used in controlling spacecraft’s attitude motion by means of flywheels. The arising problem is to study the operation of standard control algorithms in the absence of some necessary measurements. In this work this problem is solved for the algorithm ensuring the damping of spacecraft’s angular velocity. Such a damping is shown to be possible not for all initial conditions of motion. In the general case one of two possible final modes is realized, each described by stable steady-state solutions of the equations of motion. In one of them, the spacecraft’s angular velocity component relative to the axis, for which the measurements are absent, is nonzero. The estimates of the regions of attraction are obtained for these steady-state solutions by numerical calculations. A simple technique is suggested that allows one to eliminate the initial conditions of the angular velocity damping mode from the attraction region of an undesirable solution. Several realizations of this mode that have taken place are reconstructed. This reconstruction was carried out using approximations of telemetry values of the angular velocity components and the total angular momentum of flywheels, obtained at the non-standard situation, by solutions of the equations of spacecraft’s rotational motion.     

Kinematics of relative motion of two space bodies in close almost circular orbits

The paper is dedicated to a qualitative investigation of relative motion and close convergences of two space bodies located in close almost circular orbits. This problem is topical due to the asteroid hazard originating from the NEA group asteroids located in the orbits close to that of the Earth. P.E. El’yasberg [1] considered similar problems in the 1960s in relation to Earth’s artificial satellites in close almost circular orbits.     

Consequences of collisions of natural cosmic bodies with the Earth’s atmosphere and surface

Possible consequences of collisions of natural cosmic bodies with the Earth’s atmosphere and surface are described. The methodological basis of classification of consequences is the solution of meteor physics equations characterizing the trajectory of a body in the atmosphere, namely, the dependence of the body’s velocity and mass on the flight altitude. The solution depends on two dimensionless parameters characterizing the drag altitude and the role of mass loss by a meteoroid during its motion in the atmosphere. Depending on values of these parameters, the degree of effect on the planetary surface considerably changes. In particular, the conditions of cratering and meteorite fall on the planetary surface are obtained. The results are presented in a simple analytical form. They quite match to the real events considered in the paper. Recommendations are given on further investigations into the important problem of interaction of cosmic bodies with planetary atmospheres.     

Processing the data of measurements of angular velocity and microaccelerations onboard the <Emphasis Type="Italic">Foton-12</Emphasis> satellite

The results of reconstruction of uncontrolled rotational motion of the Foton-12 satellite using the measurement data of onboard sensors are presented. This problem has already been solved successfully several years ago. The satellite motion was reconstructed using the data of measuring the Earth’s magnetic field. The data of measuring the angular velocity and microaccelerations by the QSAM system were actually not used for this purpose, since these data include a clearly seen additional component whose origin was at that time unclear. This component prevented one from using these data directly for reconstruction of the angular motion. Later it became clear that the additional component was caused by the Earth’s magnetic field. Discovery of this fact allowed us to make necessary corrections when processing the QSAM system data and to use them for reconstruction of rotational motion of Foton-12. Below, a modified method of processing the QSAM system data is described together with the results of its application. The main result is obtained by comparing the motion reconstructed from measurements of angular velocity or acceleration with that found by way of processing the measurements of the Earth’s magnetic field. Their coincidence turned out to be rather accurate.     

Some issues of time-optimal control over a spacecraft programmed turn

The problem of optimal turn of a spacecraft from an arbitrary initial position to a final specified angular position in a minimum time is considered and solved. A case is investigated, when the constraint on spacecraft’s angular momentum during the turn is essential. Based on the quaternion method a solution to the posed problem has been found, and an optimal control program is constructed taking the constraints on controlling moment into account. The optimal control is found in the class of regular motions. A condition (calculation expression) is presented for determining the moment to begin braking with the use of measurements of current motion parameters, which considerably improves the accuracy of putting the spacecraft into a preset position. For a dynamically symmetrical spacecraft the solution to the problem of optimal control by the spacecraft spatial turn is presented in analytical form (expressions in elementary functions). An example of mathematical modeling of the spacecraft motion dynamics under optimal control over reorientation is given.     

Optimal control of reorientation of a spacecraft using free trajectory method

The problem of optimal control over spatial reorientation of a spacecraft is considered. The functional having a sense of propellant consumption is minimized. The analytical solution to the formulated problem is presented. It is shown that the optimal solution can be found in the class of two-impulse control at which the spacecraft’s turn is performed along a free motion trajectory. In order to improve the accuracy of spacecraft guidance into a specified angular position, methods of control are suggested that realize the method of free trajectories. The synthesized controls are invariant with respect to both external perturbations and parametric errors. The results of mathematical modeling are presented that demonstrate high efficiency of developed control algorithms. Propellant consumption for realizing a programmed turn is numerically estimated taking into account considerable gravitational and aerodynamic moments acting upon the spacecraft.     

Motion of three viscoelastic planets in the field of their mutual attraction forces

Translational-rotational motion of three planets modeled by viscoelastic balls in the gravitational field of mutual attraction is studied in this paper. The system of equations of motion for the mechanical system under consideration is deduced from the d’Alembert-Lagrange variational principle. Using the method of separation of motions, an approximate system of ordinary differential equations, describing the translational-rotational motion of the planets, is obtained with taking into account perturbations caused by elasticity and dissipation. The found steady-state motion of the system is an analog to triangular libration points in the classical three-body problem.     

Statistical analysis of turbulence in the foreshock region and in the Earth’s magnetosheath

Statistical properties of magnetic field and plasma flux fluctuations outside the Earth’s magnetosphere are studied on various time scales based on the INTERBALL-1 satellite data. The analysis of “rough” turbulence characteristics has shown that turbulence properties in various parts of the magnetosheath are distinct. The spectral density of the magnetic field undergoes a break at a frequency of ∼0.5 Hz. As a more “fine” characteristic of the fluctuations on various time scales, changes in the shape and parameters of the probability density function were studied. The analysis of the height of a maximum of the probability density function P(0) and of the kurtosis values have shown the presence of two asymptotic modes of P(0), which are characterized by different power laws. The critical scale, on which the properties of P(0) change, corresponds, presumably, to the scales of the Larmor radius of ions. Based on the results of studying structural functions of various orders, the conclusion is drawn that small-scale turbulence in the foreshock and magnetosheath is described by different phenomenological models.     

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.     

Acceleration and losses of energetic protons and electrons during magnetic storm on August 30–31, 2004

Variations of particle fluxes during a moderate magnetic storm on August 30–31, 2004 are analyzed in this paper using measurements on low-orbit polar satellites CORONAS-F and SERVIS-1. The Earth’s radiation belts were filled at this time by enhanced flux of energetic particles accelerated a month ago during magnetic storms on July 23–27. The analysis has shown that even during a moderate magnetic storm a set of several adiabatic and non-adiabatic processes is observed, which leads to acceleration or release of particles and acts selectively depending on the energy range and charge of particles.     

Development of auroral electrojets and low-latitude geomagnetic disturbances during strong magnetic storms on November 7–11, 2004

The influence of auroral electojets and solar wind parameters on variations in low-latitude geomagnetic disturbances and D _st during strong magnetic storms on November 7–8, 2004 with D _st ≈ −380 nT and on November 9–10, 2004 with D _st ≈ −300 nT is studied on the basis of global geomagnetic observations. It is found that the impulsive variations of the western electrojet intensity with a duration of Δt ≈ 1–2 h (probably, substorm disturbances) lead to positive low-latitude disturbances of ΔH at Φ′ ≈ 10°–30° and to disturbances of the same durations with an amplitude +ΔH ∼ 30–100 nT at latitudes of the polar cap (Φ′ ≈ 75°–80°). More durable (with Δt ≥ 10 h) convection electrojets whose centers are shifted to latitudes of ∼50°–55° in the process of storm development are the main cause of the increase in negative values of ΔH at low latitudes and D _st . It is shown that meridional dynamics of position of the center of electrojets and the equatorial boundary of the auroral oval is governed by variations (increase or decrease) in the intensity of negative values of the IMF B _z component. It is assumed that in these storms the intensification of the magnetospheric partially ring current closes the circuit to the ionosphere with the help of field-aligned currents at the equatorial boundary of the auroral oval is the main cause of the magnetic field depression at low latitudes.     

Periodic solutions in three-dimensional restricted three-body problem: 2. Loss of symmetry at the 1:1 resonance

Within the framework of the circular restricted three-body problem a family of inverse periodic orbits around the two attracting bodies (the Egorov’s family) and families generated by it at the 1:1, 2:1, and 3:1 resonances for three-dimensional orbits in the Sun-Earth and Earth-Moon systems are considered. Their relationship with families generated by orbits around the libration points L ₁, L ₂ and L ₃ is investigated. One of the families contains periodic solutions that seem promising as possible orbits for the space radio telescope of the Millimetron project.     

Activation of the tail open part during the magnetospheric storm

In each polar cap (PC) we mark out “old PC” observed during quiet time before the event under consideration, and “new PC” that emerges during the substorm framing the old one and expanding the PC total area. Old and new PCs are the areas for the magnetosphere old and new tail lobes, respectively. The new lobe variable magnetic flux Ψ₁ is usually assumed to be active, i.e. it provides the electromagnetic energy flux (Poynting flux) ɛ′ transport from solar wind (SW) into the magnetosphere. The old lobe magnetic flux Ψ₂ is supposed to be passive, i.e. it remains constant during the disturbance and does not participate in the transporting process which would mean the old PC electric field absolute screening from the convection electric field created by the magnetopause reconnection. In fact, screening is observed, but far from absolute. We suggest a model of screening and determine its quantitative characteristics in the selected superstorm. The coefficient of a screening is the β = Ψ₂/Ψ₀₂, where Ψ₀₂ = const is open magnetic flux through the old PC measured prior to the substorm, and Ψ₂ is variable magnetic flux through the same area measured during the substorm. We consider three various regimes of disturbance. In each, the coefficient β decreased during the loading phase and increased at the unloading phase, but the rates and amplitudes of variations exhibited a strong dependence on the regime. We interpreted decrease in β as a result of involving the old PC magnetic flux Ψ₂, which was considered to be constant earlier, in the Poynting flux ɛ′ transport process from solar wind into the magnetosphere. Transport process weakening at the subsequent unloading phase creates increase in β. Estimates showed that coefficient β during each regime and the computed Poynting flux ɛ′ varied manifolds. In general, unlike the existing substorm conception, the new scenario describes an unknown earlier of tail lobe activation process during a substorm growth phase that effectively increases the accumulated tail energy for the expansion and recovery phases.     

Evolution of motion of two viscoelastic planets in the field of forces of their mutual attraction

Translational-rotational motion of two viscoelastic planets in a gravitational force field is studied. The planets are modeled by homogeneous isotropic viscoelastic bodies. In their natural undeformed state each of the planets represents a sphere. We investigate a specific case when the planet’s centers of mass move in a fixed plane, the axis of rotation for each planet being directed along the normal to this plane. An equation describing the evolution of a slow angular variable (perihelion longitude) is derived. The observed displacement of the perihelion of Mercury is compared with the results obtained in the considered model problem about motion of two viscoelastic planets. Quite important is the fact that the planet of smaller mass (Mercury) moves not in a central Newtonian field of forces, but rather in the gravitational field of a rotating viscoelastic planet (Sun).     

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.