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.     

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 Earth's 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 satellite's 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 satellite's 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 orbit's perigee. As the satellite's 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 satellite's 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.     

The navigational experiments on microgravitational space platform “FOTON-M2”

This paper presents the review of results of the navigating experiments which have been carried out during flight of microgravitational space platform (MSP) Foton-M2 in May–June 2005. The brief characteristic of the created MIRAGE–M equipment consisting from magnitometric system and satellite radionavigation receiver is given. The measurements have allowed to restore unguided MSP movement and to estimate a level of microaccelerations (microgravitations) onboard during flight, and have provided precision time-position binding of the research experiments. The data from the equipments transmitted on the telemetering channel have allowed testing the information technologies of virtual support of experiments in space. Flight testing of the equipment has allowed make a conclusion on usefulness of accommodation onboard the small-sized auxiliary navigating system focused for work with users of research experiments. The experiments on MSP Foton-M2 are the development of experiments with MIRAGE equipment carried out in 1999 during flight time of MSP Foton-12 [N.D. Semkin, V.V. Ivanov, V.I. Abrushkin, V.L. Balakin, I.V. Belokonov, K.E. Voronov, The experiments with magnetic fields formed by technical equipment inside Foton-12 spacecraft: the results of the MIRAGE experiments, in: Proceedings of International Conference “Scientific and Technological Experiments on Russian Foton/Bion Recoverable Satellites: Results, Problems and Outlooks”, 25–30 June 2000, pp. 116–122; V.L. Balakin, I.V. Belokonov, V.V. Ivanov, “Determination of motion of spacecraft Foton-12 as a result of magnetic fields measurement in MIRAGE experiment”, pp. 231–238 (published in the same place)].Paper is executed within the framework of the grant of the Russian Fund of Fundamental Researches 06-08-00244.     

一种微米级粒子的静电发射加速装置

为了研究空间微小碎片碰撞对航天器的影响,国内外研制了各种类型的微小碎片加速器。文章简要介绍了一种很有前景的静电式微小碎片加速器及其关键部件的工作原理、结构特点及适用范围等。     

Simulation of cosmic man-made dust effects on space vehicle elements in rocket and laboratory experiments

Institute of Experimental Meteorology initiated investigations of anthropogenic contamination (AC) and its influence on the near-earth environment and orbiting vehicles. These investigations are based on rocket experiments on simulation of the effects of gas-dust fluxes at the rate of 7–8 km/s on vehicle optical elements under real space conditions. The fluxes are generated by rocket-borne explosive generators.     

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.     

Detector of Micrometeoroid and Artificial Space Debris Particles

The mathematical model of a space debris detector based on inflatable metal-dielectric-metal (MDM) film structure is presented. The efficiency of its implementation for detection of space debris particles at different altitudes is estimated, and the information obtained by the detector is investigated.     

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.     

Meteoroid and technogenic particle impact on spacecraft solar panels

This paper presents calculated models and the results of estimates of meteoroid and technogenic particle impact on spacecraft solar panels. It is shown that optical losses resulting from the formation of microcraters on the surface of protective glasses of semiconductor photoconverters (PC) are negligible (less than 0.01%). Significantly greater losses can occur as a result of shunting the PC p–n junction. In high and medium orbits, these losses are 0.1–0.2%/year for the glass thickness of 150 μm and the area of one PC of 30 cm². Decreasing the glass thickness up to 100 μm can lead to increasing power losses up to 0.6%/year.     

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.