Rotational motion of <Emphasis Type="Italic">Foton M-4</Emphasis>

The actual controlled rotational motion of the Foton M-4 satellite is reconstructed for the mode of single-axis solar orientation. The reconstruction was carried out using data of onboard measurements of vectors of angular velocity and the strength of the Earth’s magnetic field. The reconstruction method is based on the reconstruction of the kinematic equations of the rotational motion of a solid body. According to the method, measurement data of both types collected at a certain time interval are processed together. Measurements of the angular velocity are interpolated by piecewise-linear functions, which are substituted in kinematic differential equations for a quaternion that defines the transition from the satellite instrument coordinate system to the inertial coordinate system. The obtained equations represent the kinematic model of the satellite rotational motion. A solution of these equations that approximates the actual motion is derived from the condition of the best (in the sense of the least squares method) match between the measurement data of the strength vector of the Earth’s magnetic field and its calculated values. The described method makes it possible to reconstruct the actual rotational satellite motion using one solution of kinematic equations over time intervals longer than 10 h. The found reconstructions have been used to calculate the residual microaccelerations.     

Uncontrolled motion of the <Emphasis Type="Italic">Foton M-2</Emphasis> satellite and quasistatic microaccelerations on its board

The results of determining the uncontrolled rotational motion of the Foton M-2 satellite (in orbit from May 31 to June 16, 2005) are presented. The determination was made using the data of onboard measurements of the Earth’s magnetic field strength. Segments 270 min long (three orbits) were selected from these data covering the first two thirds of the flight. On each such segment the data were processed jointly by the least squares method using integration of the equations of attitude motion of the satellite. In processing, the initial conditions of motion and parameters of the used mathematical model were estimated. The thus obtained results gave a complete overview of the satellite motion. This motion, having started with a small angular velocity, gradually accelerated, and in two days became close to the regular Euler precession of an axisymmetric solid body. On June 09, 2005 (the last day of measurements) the angular velocity of the satellite relative to its lengthwise axis was about 1.1 deg/s, while the projection of the angular velocity onto a plane perpendicular to this axis had an absolute value of about 0.11 deg/s. Deviations of the lengthwise axis from a normal to the orbit plane did not exceed 60°. Based on the results of determination of the rotational motion of the satellite, calculations of quasi-static microaccelerations on its board are performed.     

A simplified technique for determining the rotational motion of a satellite based on the onboard measurements of the angular velocity and magnetic field of the Earth

The mathematical model, which allowed us to reconstruct the rotational motion of the Bion M-1 and Foton M-4 satellites by processing the measurements of onboard magnetometers and the angular velocity sensor, is sufficiently detailed and accurate. If we slightly lower the requirements for accuracy and transfer to a rougher model, i.e., we will not update the biases in measurements of the angular velocity component, then the measurement processing technique can be significantly simplified. The volume of calculations in minimizing the functional of the least-square technique is reduced; the most complicated part of calculations is performed using the standard procedure of computational linear algebra. This simplified technique is described below, and the examples of its application for reconstructing the rotational motion of the Foton M-4 satellite are presented. A noticeable distinction in the reconstructions of motion, constructed by simplified and more exact techniques, is revealed in processing the measurements over time intervals longer than 4 hours.     

Uncontrolled rotational motion of the <Emphasis Type="Italic">Aist</Emphasis> small spacecraft prototype

The results of reconstructing the uncontrolled rotational motion of the Aist small spacecraft prototype during its flight in early 2014 have been presented. The reconstruction was carried out by processing data from onboard measurements of the Earth’s magnetic field. The processing procedure used portions of data covering intervals of time with durations ranging from a few dozen minutes to three hours. Data obtained in each such interval were processed jointly by the least-squares method by integrating the equations of the satellite motion relative to the center of mass. The initial conditions of the motion and the parameters of the used mathematical model during processing have been estimated. The results of processing for several data intervals have provided a fairly complete picture of the satellite motion. This was the weakly disturbed Euler–Poinsot motion.     

Experiments with the DAKON-M convection sensor

We have described an express technique for processing the results of experiments with a DAKON-M convection sensor on board the Service Module of the International Space Station (ISS) in 2011. The technique uses a certain rule to compare the sensor measurements with the calculated data on the quasistatic component of microacceleration at the point of installation. The sensor experiments have been conducted during shuttle docking and undocking, when low-frequency microaccelerations on the ISS were significant. The microaccelerations have been calculated using measurement data of the MAMS low-frequency accelerometer installed in the Lab module and the telemetry data on the ISS rotational motion. This has made it possible to convert the MAMS measurement data to the DAKON-M convection sensor installation point. A comparison of sensor readings with calculated microaccelerations has revealed fairly good agreement between them.     

Study of microaccelerations onboard the <Emphasis Type="Italic">International Space Station</Emphasis> with the DAKON-M convection sensor

The results of experiments with the DAKON-M convection sensor onboard the Russian orbital segment of the International Space Station are described. A comparison of the sensor measurements with the results of calculation of the quasistatic microacceleration component at the point of installation is made. For this comparison we have used three measurement intervals of the experiments in 2009, during which spacecraft were docked with the station, undocked from it, and actuation of jet engines of the attitude control system took place. When calculating microacceleration, we use the measurement data of the low-frequency MAMS accelerometer, installed on the American segment, and the telemetry data on the ISS rotational motion. This information allowed one to convert the MAMS measurements to the point of installation of the DAKON-M convection sensor. A comparison of sensor measurements with calculated microaccelerations showed sufficiently accurate coincidence between the calculated and measured data.     

Estimation of dynamic characteristics of the <Emphasis Type="Italic">International Space Station</Emphasis> from measurements of microaccelerations

We describe the results of determining the mass of the International Space Station using the data of MAMS accelerometer taken during correction of the station orbit on August 20, 2004. The correction was made by approach and attitude control engines (ACE) of the Progress transporting spacecraft. The engines were preliminary calibrated in an autonomous flight using the onboard device for measuring apparent velocity increment. The method of calibration is described and its results are presented. The error in station mass determination is about 1%. The same data of MAMS and similar data obtained during the orbit correction on August 26, 2004 were used for the analysis of high-frequency vibrations of the station mainframe caused by operation of the ACE of Progress. Natural frequencies of the ACE are determined. They lie in the frequency band 0.024–0.11 Hz. ACE operation is demonstrated to result in a substantial increase of microaccelerations onboard the station in the frequency range 0–1 Hz. The frequencies are indicated at which disturbances increase by more than an order of magnitude. The study described was carried out as a part of the Tensor technological experiment.     

Modes of uncontrolled rotational motion of the <Emphasis Type="Italic">Progress M-29M</Emphasis> spacecraft

We have reconstructed the uncontrolled rotational motion of the Progress M-29M transport cargo spacecraft in the single-axis solar orientation mode (the so-called sunward spin) and in the mode of the gravitational orientation of a rotating satellite. The modes were implemented on April 3–7, 2016 as a part of preparation for experiments with the DAKON convection sensor onboard the Progress spacecraft. The reconstruction was performed by integral statistical techniques using the measurements of the spacecraft’s angular velocity and electric current from its solar arrays. The measurement data obtained in a certain time interval have been jointly processed using the least-squares method by integrating the equations of the spacecraft’s motion relative to the center of mass. As a result of processing, the initial conditions of motion and parameters of the mathematical model have been estimated. The motion in the sunward spin mode is the rotation of the spacecraft with an angular velocity of 2.2 deg/s about the normal to the plane of solar arrays; the normal is oriented toward the Sun or forms a small angle with this direction. The duration of the mode is several orbit passes. The reconstruction has been performed over time intervals of up to 1 h. As a result, the actual rotational motion of the spacecraft relative to the Earth–Sun direction was obtained. In the gravitational orientation mode, the spacecraft was rotated about its longitudinal axis with an angular velocity of 0.1–0.2 deg/s; the longitudinal axis executed small oscillated relative to the local vertical. The reconstruction of motion relative to the orbital coordinate system was performed in time intervals of up to 7 h using only the angularvelocity measurements. The measurements of the electric current from solar arrays were used for verification.     

Observations of electromagnetic emissions inside the Earth’s plasmasphere from the <Emphasis Type="Italic">Interball-1</Emphasis> satellite

The spectrum analyzer AKR-X onboard the Interball-1 satellite at the beginning (August–October 1995) and at the end (August–October 2000) of satellite operation in perigees of its orbital motion recorded and analyzed electromagnetic emissions of the inner regions of the Earth’s plasmasphere in the frequency band 100–1500 kHz at distances of 1.1–1.8 R _E. The observations have shown that the electromagnetic modes (the Z and LO modes escaping the magnetosphere) which are formed at the altitudes 600–4000 km are associated with the subauroral nonthermal continuum and with the recently discovered kilometric continuum. There are noticeable differences in the spectral character of these emissions during the minimum (1996) and maximum (2000) solar activity, when, as a rule, the LO mode escaping the plasmaphere and the continua are not present.     

Electron flux variations at altitudes of 600–800 km in the second half of 2014. preliminary results of an experiment using RELEC equipment onboard the satellite <Emphasis Type="Italic">VERNOV</Emphasis>

The results of measurements of fluxes and spectra carried out using the RELEC (relativistic electrons) equipment onboard the VERNOV satellite in the second half of 2014 are presented. The VERNOV satellite was launched on July 8, 2014 in a sun-synchronous orbit with an altitude from 640 to 830 km and an inclination of 98.4°. Scientific information from the satellite was first received on July 20, 2014. The comparative analysis of electron fluxes using data from RELEC and using experimental data on the electron detection by satellites Elektro-L (positioned at a geostationary orbit) and Meteor-M no. 2 (positioned at a circular polar orbit at an altitude of about 800 km as the VERNOV satellite) will make it possible to study the spatial distribution pattern of energetic electrons in near-Earth space in more detail.     

Estimating the accuracy of the technique of reconstructing the rotational motion of a satellite based on the measurements of its angular velocity and the magnetic field of the Earth

The paper has studied the accuracy of the technique that allows the rotational motion of the Earth artificial satellites (AES) to be reconstructed based on the data of onboard measurements of angular velocity vectors and the strength of the Earth magnetic field (EMF). The technique is based on kinematic equations of the rotational motion of a rigid body. Both types of measurement data collected over some time interval have been processed jointly. The angular velocity measurements have been approximated using convenient formulas, which are substituted into the kinematic differential equations for the quaternion that specifies the transition from the body-fixed coordinate system of a satellite to the inertial coordinate system. Thus obtained equations represent a kinematic model of the rotational motion of a satellite. The solution of these equations, which approximate real motion, has been found by the least-square method from the condition of best fitting between the data of measurements of the EMF strength vector and its calculated values. The accuracy of the technique has been estimated by processing the data obtained from the board of the service module of the International Space Station (ISS). The reconstruction of station motion using the aforementioned technique has been compared with the telemetry data on the actual motion of the station. The technique has allowed us to reconstruct the station motion in the orbital orientation mode with a maximum error less than 0.6° and the turns with a maximal error of less than 1.2°.     

An analysis of low-frequency component in microacceleration measurements made onboard the <Emphasis Type="Italic">Foton M-2</Emphasis> satellite

The low-frequency component is investigated in the data of measurements performed onboard the Foton M-2 satellite with the three-component accelerometer TAS-3. Investigations consisted in comparison of this component with its calculated analog found from a reconstruction of the satellite’s attitude motion. The influence of the Earth’s magnetic field on the accelerometer readings is discovered by way of spectral analysis of the functions representing the results of determining the low-frequency microacceleration by two methods. After making correction for this influence, the results obtained by these two methods coincided within a root-mean-square error of less than 10^?6 m/s².     

Quasistatic Microaccelerations onboard the Foton Satellite during Its Flight at High-Altitude Orbits

The level of quasistatic microaccelerations onboard the Foton-M satellite is predicted for its flights in two orbits: the planned orbit with the altitudes in perigee h = 262 km and in apogee h = 304 km and the orbit with h = 262 km and h = 350 km. The prediction is based on mathematical simulation of the satellite motion with respect to its center of mass under the action of gravitational and aerodynamic moments. The model is represented by the system of equations of the satellite rotational motion. Parameters of this system are chosen from the condition of coincidence of the motion of preceding Foton satellites (h 220 km and h 400 km) calculated using this model with the results of determination of actual rotational motion of the Foton-11 and Foton-12 satellites. With the help of the model thus calibrated, a calculation is made of the rotational motion of the Foton-M satellite and of the quasistatic microaccelerations onboard it. As is shown by the results of simulation, the use of the first and the second orbits will result in reductions of microaccelerations by 30% and 60%, respectively.     

Fluxes of Quasi-trapped Electrons with Energies >0.08 MeV in the Near-Earth Space on Drift Shells <Emphasis Type="Italic">L</Emphasis> < 2

We study the characteristics of fluxes of electrons with energy >80 keV in the near-Earth space regions corresponding to the drift shells L = 1.7, 1.4, and 1.1 observed during the entire period of the GRIF experiment onboard the Spectr module of the Mir orbital station from October 1995 to June 1997. The obtained geographic maps of the distribution of electron fluxes at the height of the station flight (400 km) and, also, the estimates of the spectra indicate that the South-Atlantic Anomaly provides for a mechanism of stable replenishment for shells with L < 1.5. The mechanism of stable replenishment of shells with L < 1.5 may be due to the scattering, in the residual atmosphere, of electrons from the inner radiation belt precipitating into the region of the South-Atlantic Anomaly.     

Determination of attitude motion of the <Emphasis Type="Italic">Foton M-3</Emphasis> satellite according to the data of onboard measurements of the Earth’s magnetic field

The results of reconstruction of rotational motion of the Foton M-3 satellite during its uncontrolled flight in September 2007 are presented. The reconstruction was performed by processing the data of onboard measurements of the Earth’s magnetic field obtained by the DIMAC instruments. The measurements were carried out continuously throughout the flight, but the processing technique dealt with the data portions covering time intervals of a few orbital revolutions. The data obtained on each such interval were processed jointly by the least squares method with using integration of the equations of satellite motion relative to its center of mass. When processing, the initial conditions of motion and the used mathematical model’s parameters were estimated. The results of processing 16 data sets gave us complete information about the satellite motion. This motion, which began at a low angular velocity, had gradually accelerated and in five days became close to the regular Euler precession of an axisymmetric solid body. At the end of uncontrolled flight the angular velocity of the satellite relative to its lengthwise axis was 0.5 deg/s; the angular velocity projection onto the plane perpendicular to this axis had a magnitude of about 0.18 deg/s.     

Turbulent fluctuations of plasma and magnetic field parameters in the magnetosheath and the low-latitude boundary layer formation: Multisatellite observations on March 2, 1996

The results of simultaneous analysis of plasma and magnetic field characteristics measured on the INTERBALL/Tail Probe, WIND and Geotail satellites on March 2, 1996, are presented. During these observations the INTERBALL/Tail Probe crossed the low-latitude boundary layer, and the WIND and Geotail satellites measured the solar wind’s and magnetosheath’s parameters, respectively. The plasma and magnetic field characteristics in these regions have been compared. The data of the Corall, Electron, and MIF instruments on the INTERBALL/Tail Probe satellite are analyzed. Fluctuations of the magnetic field components and plasma velocity in the solar wind and magnetosheath, measured onboard the WIND and Geotail satellites, are compared. The causes resulting in appearance of plasma jet flows in the low-latitude boundary layer are analyzed. The amplitude of magnetic field fluctuations in the magnetosheath for a studied magnetosphere boundary crossing is shown to exceed the magnetic field value below the magnetopause near the cusp. The possibility of local violation of pressure balance on the magnetopause is discussed, as well as penetration of magnetosheath plasma into the magnetosphere, as a result of magnetic field and plasma flux fluctuations in the magnetosheath.     

Determination of quasi-static microaccelerations onboard a satellite using video images of moving objects

A space experiment aimed at determination of quasi-static microaccelerations onboard an artificial satellite of the Earth using video images of the objects executing free motion is considered. The experiment was carried out onboard the Foton M-3 satellite. Several pellets moved in a cubic box fixed on the satellite’s mainframe and having two transparent adjacent walls. Their motion was photographed by a digital video camera. The camera was installed facing one of the transparent walls; a mirror was placed at an angle to another transparent wall. Such an optical system allowed us to have in a single frame two images of the pellets from differing viewpoints. The motion of the pellets was photographed on time intervals lasting 96 s. Pauses between these intervals were also equal to 96 s. A special processing of a separate image allowed us to determine coordinates of the pellet centers in the camera’s coordinate system. The sequence of frames belonging to a continuous interval of photography was processed in the following way. The time dependence of each coordinate of every pellet was approximated by a second degree polynomial using the least squares method. The coefficient of squared time is equal to a half of the corresponding microacceleration component. As has been shown by processing made, the described method of determination of quasi-static microaccelerations turned out to be sufficiently sensitive and accurate.     

Optimization of planning the experiments to be carried out onboard orbital stations

The technique and algorithms for optimization of planning the program of experiments carried out onboard an orbiting spacecraft are described taking into account the execution of service operations. A general approach to optimization of planning the experiments is used, developed for investigations onboard the Salyut and Mir space stations, and on the International Space Station (ISS). The approach is based on formalization of the problem in the form of an integer linear programming problem. In this approach, the spacecraft orbit is considered to be known, and the optimization of the planning of experiments is reduced to composing the optimum sequence of zones for the performance of experiments. The list of experiments, service operations, and tasks to be solved during the planning interval are assumed to be specified.     

Analysis of Low-Frequency Microaccelerations onboard the Foton-11Satellite

The method and the results of investigating the low-frequency component of microaccelerations onboard the Foton-11satellite are presented. The investigation was based on the processing of data of the angular velocity measurements made by the German system QSAM, as well as the data of measurements of microaccelerations performed by the QSAM system and by the French accelerometer BETA. The processing was carried out in the following manner. A low-frequency (frequencies less than 0.01 Hz) component was selected from the data of measurements of each component of the angular velocity vector or of the microacceleration, and an approximation was constructed of the obtained vector function by a similar function that was calculated along the solutions to the differential equations of motion of the satellite with respect to its center of mass. The construction was carried out by the least squares method. The initial conditions of the satellite motion, its aerodynamic parameters, and constant biases in the measurement data were used as fitting parameters. The time intervals on which the approximation was constructed were from one to five hours long. The processing of the measurements performed with three different instruments produced sufficiently close results. It turned out to be that the rotational motion of the satellite during nearly the entire flight was close to the regular Eulerian precession of the axially symmetric rigid body. The angular velocity of the satellite with respect to its longitudinal axis was about 1 deg/s, while the projection of the angular velocity onto the plane perpendicular to this axis had an absolute value of about 0.2 deg/s. The magnitude of the quasistatic component of microaccelerations in the locations of the accelerometers QSAM and BETA did not exceed 5 × 10^–5–10^–4m/s²for the considered motion of the satellite.     

Study and comparison of the parameters of five hot flow anomalies at a bow shock front

Five hot flow anomalies (HFA) recorded by the Tail Probe of the INTERBALL satellite in 1996 are analyzed in present work. For the five chosen events the authors determined the characteristics of current sheets whose interaction with the bow shock front led to formation of an HFA, as well as the directions of external electric fields and the directions of motion of these HFAs over a shock front. The analysis of plasma convection in an HFA body is carried out; the average velocities of plasma motion in the HFA are determined in a coordinate system linked with the normal to a current layer and with the normal to the bow shock. According to the character of plasma convection in an HFA body, these five events may be divided into two types, which also differ in the direction of the motion over the front of the bow shock. In the first-type HFAs, the convection of plasma has a component directed from the intermediate region confirming its identification as a source of energy for the formation of an HFA. In the second-type HFAs, plasma motion from the intermediate region in leading and trailing parts is less expressed. This fact, as well as the great variation of peculiar velocities in the body of anomalies, allowed the assumption that second-type anomalies are nonstationary. Evidence is presented that the anomalies considered in the paper are bordered with shocks formed in solar wind passing a large-scale, decelerated body of heated plasma.