V. V. Sazonov

Uncontrolled Attitude Motion of the Foton-12 Satellite and Quasi-Steady Microaccelerations onboard It

The results of determination of the uncontrolled attitude motion of the Foton-12 satellite (placed in orbit on September 9, 1999, terminated its flight on September 24, 1999) are presented. The determination was carried out by the onboard measurement data of the Earths magnetic field strength vector. Intervals with a duration of several hours were selected from data covering almost the entire flight. On each such interval the data were processed simultaneously using the least squares method by integrating the satellites equations of motion with respect to the center of mass. The initial conditions of motion and the parameters of the mathematical model employed were estimated in processing. The results obtained provided for a complete representation of the satellites motion during the flight. This motion, beginning with a small angular velocity, gradually sped up. The growth of the component of the angular velocity with respect to the longitudinal axis of the satellite was particularly strong. During the first several days of the flight this component increased virtually after every passage through the orbits perigee. As the satellites angular velocity increased, its motion became more and more similar to the regular Euler precession of an axisymmetric rigid body. In the last several days of flight the satellites angular velocity with respect to its longitudinal axis was about 1 deg/s and the projection of the angular velocity onto the plane perpendicular to this axis had a magnitude of approximately 0.15 deg/s. The deviation of the longitudinal axis from the normal to the orbit plane did not exceed 60°. The knowledge of the attitude motion of the satellite allowed us to determine the quasi-steady microacceleration component onboard it at the locations of the technological and scientific equipment.

Determination of attitude motion of the Foton M-3 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.

Determination of characteristic frequencies of elastic oscillations of the International Space Station construction

The results of investigating free oscillations of the International Space Station construction appearing during spacecraft docking and undocking are described. The study is carried out using the measurement data of the low-frequency MAMS accelerometer. Several intervals of measurements performed in 2005 and 2006 were chosen to be studied. For chosen intervals, only the data intervals corresponding to the process of free attenuation of the oscillations construction elements were analyzed. Characteristic frequencies of elastic oscillations of the station construction and attenuation coefficients corresponding to them are found. The comparative analysis of the results obtained for various docking ports (nodes) is carried out. The described study is performed as a part of the technical experiment “The ISS Environment” carried out onboard the station in accordance with the Russian program of scientific and engineering experiments.

Periodic motions of a satellite-gyrostat relative to its center of mass under the action of gravitational torque

We investigated periodic motions of the axis of symmetry of a model satellite of the Earth, which are similar to the motions of the longitudinal axes of the Mir orbital station in 1999–2001 and the Foton-M3 satellite in 2007. The motions of these spacecraft represented weakly disturbed regular Euler precession with the angular momentum vector of motion relative to the center of mass close to the orbital plane. The direction of this vector during the motion was not practically changed. The model satellite represents an axisymmetric gyrostat with gyrostatic moment directed along the axis of symmetry. The satellite moves in a circular orbit and undergoes the action of the gravitational torque. The motion of the axis of symmetry of this satellite relative to the absolute space is described by fourth-order differential equations with periodic coefficients. The periodic solutions to this system with special symmetry properties are constructed using analytical and numerical methods.

Study of microaccelerations onboard the International Space Station 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 International Space Station 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.

Determining the rotational motion of the Bion M-1 satellite with the GRAVITON instrument

Actual controlled rotational motion of the Bion M-1 satellite is reconstructed for the modes of the orbital and single-axis solar orientation. The reconstruction was performed using data of onboard measurements of the vectors of angular velocity and the Earth’s magnetic field (EMF) strength. The reconstruction procedure is based on the kinematic equations of the rotational motion of a solid body. In the framework of this procedure, measurement data for two types collected at a certain time interval are processed jointly. Measurements of angular velocity are interpolated by piecewise–linear functions, which are substituted in the kinematic differential equations for quaternion giving the transition from the satellite instrument coordinate system to the inertial (the second geoequatorial) coordinate system. Thus the obtained equations represent the kinematic model of the satellite rotational motion. The solution to these equations approximating the actual motion is derived from the condition of the best (in the sense of the least-square method) matching measurement data of the EMF strength vector with the calculated values. The described procedure allows us to reconstruct the actual rotational satellite motion using one solution to kinematic equations over time intervals with durations of more than 5 h. Found reconstructions were used to calculate the residual microaccelerations.

An analysis of low-frequency component in microacceleration measurements made onboard the Foton M-2 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.

Uncontrolled attitude motion of the small satellite Aist

The results of the reconstruction of uncontrolled attitude motion of the satellite Aist during its flight in May 2013 are presented. The reconstruction was performed by the processing of data from onboard measurements of the Earth’s magnetic field. The processing technique was applied to data segments covering time intervals of about 100 min. The data obtained at each such interval were processed jointly using the least squares method by integrating the equations of the satellite motion relative to its center of mass. When processing, the initial conditions of motion and parameters of the used mathematical model were estimated. The results of processing several data intervals made it possible to obtain sufficiently complete information about the motion of the satellite.

Accuracy estimation for determining the orientation parameters of the coordinate system of the BOKZ-M astromeasuring device by the experimental data

The BOKZ-M star sensor (a unit for measuring star coordinates) is intended to determine the parameters of the orientation of the axes of its own coordinate system relative to the axes of the inertial system using the observations of the areas of the stellar sky. A large number of factors influence the accuracy of this determination, and the estimation of the contribution of every factor to the total error is not always possible. In general, it must be limited by an estimation of the total error according to the results of studying a longterm series of determinations of the orientation parameters obtained in the ground tests and in space flight. This paper presents accuracy estimations for the BOKZ-M device obtained during its flight operation on the Meteor-M satellite.