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.     

Biaxial Mode of Rotation of a Satellite in the Orbit Plane

A mode of motion of a satellite with respect to its center of mass is studied, which is called the biaxial rotation in the orbit plane. In this mode of rotation, an elongated and nearly dynamically symmetric satellite rotates around the longitudinal axis, which, in turn, rotates around the normal to the plane of an orbit; the angular velocity of rotation around the longitudinal axis is several times larger than the orbital angular velocity, deviations of this axis from the orbit plane are small. Such a rotation is convenient in the case when it is required to secure a sufficiently uniform illumination of the satellite's surface by the Sun at a comparatively small angular velocity of the satellite. The investigation consists of the numerical integration of equations of the satellite's motion, which take into account gravitational and restoring aerodynamic moments, as well as the evolution of the orbit. At high orbits, the mode of the biaxial rotation is conserved for an appreciable length of time, and at low orbits it is destroyed due to the impact of the aerodynamic moment. The orbit altitudes and the method of constructing the initial conditions of motion that guarantee a sufficiently prolonged period of existence of this mode are specified.     

Uncontrollable Rotational Motion of the Mir Orbital Station

The results of determining the rotational motion of the Mir orbital station are presented for four long segments of its unmanned uncontrolled flight in 1999–2000. The determination was carried out using the data of onboard measurements of the Earth's magnetic field intensity. These data, taken for a time interval of several hours, were jointly processed by the least squares method with the help of integration of the equations of station motion relative to its center of mass. As a result of this processing, the initial conditions of motion and the parameters of the mathematical model used were evaluated. The technique of processing is verified using the telemetry data on angular velocity of the station and its attitude parameters. Two types of motion were applied on the investigated segments. One of them (three segments) presents a rotation around the axis of the minimum moment of inertia. This axis executes small oscillations with respect to a normal to the orbit plane. Such a motion was used for the first time on domestic manned orbital complexes. The second type of motion begins with a biaxial rotation which, in a few weeks, goes over into a motion very similar to the rotation around the normal to the orbit plane, but around the axis of the maximum moment of inertia.     

The Mode of Gravitational Orientation for the International Space Station

The results of the determination of the uncontrolled attitude motion of the International Space Station during its unmanned flight in 1999 are presented. The data of onboard measurements of three components of the angular velocity are used for this determination. These data covering an interval of slightly less than one orbit were jointly processed by the least squares method, by integrating the equations of motion of the station relative to its center of mass. As a result of this processing, the initial conditions of the motion and the parameters of the mathematical model used were estimated. The actual motion of the station has been determined for 20 such intervals during April–November. Throughout these intervals, the station rotated about the axis of the minimum moment of inertia, the latter executing small oscillations relative to the local vertical. Such a mode, known as the mode of gravitational orientation of a rotating satellite or the mode of generalized gravitational orientation, was planned before the flight. The measurements were made to verify it. The quasistatic component of the microaccelerations aboard the station is estimated for this mode.     

Low-Frequency Microaccelerations onboard the Foton-11 Satellite

We analyze the microacceleration measurements carried out onboard the Foton-11 satellite with the three-component accelerometer BETA. The microaccelerations were recorded virtually throughout the entire orbital flight of the Foton-11 satellite. The data obtained were analyzed in the following way. First they were used to determine the actual rotational motion of the satellite for several arbitrarily selected time intervals 4 h long. This problem was solved by constructing the approximation of the microacceleretation low-frequency component (previously determined from the data) by its calculated analog computed along the solutions to differential equations of rotational motion of the satellite. The approximation was made by the least squares method. As a result, those mathematical model parameters and the solutions to equations of motion were found that gave the best consistency of the microacceleretation low-frequency component and its calculated analog. Then the spectral analysis of the low-frequency component and its calculated analog was made. It was shown that, although basic harmonics of these functions coincided sufficiently well, some harmonics of the low-frequency component failed to be interpreted in terms of the satellite's rotational motion.     

Experimental investigation of the modes of operation of uncontrolled attitude motion of the Progress spacecraft

Results of in-flight tests of three modes of uncontrolled attitude motion of the Progress spacecraft are described. These proposed modes of experiments related to microgravity are as follows: (1) triaxial gravitational orientation, (2) gravitational orientation of the rotating satellite, and (3) spin-up in the plane of the orbit around the axis of the maximum moment of inertia. The tests were carried out from May 24 to June 1, 2004 onboard the spacecraft Progress M1-11. The actual motion of this spacecraft with respect to its center of mass, in the above-mentioned modes, was determined by telemetric information about an electric current tapped off from solar batteries. The values of the current obtained during a time interval of several hours were processed jointly using the least squares method by integration of the equations of the spacecraft’s attitude motion. The processing resulted in estimation of the initial conditions of motion and of the parameters of mathematical models used. For the obtained motions the quasi-static component of microaccelerations was computed at a point onboard, where installation of experimental equipment is possible.     

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.     

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.     

Variation of the Satellite Orbit Altitude by the Light Pressure Force

The possibility of the uncontrolled increase of the altitude of an almost circular satellite orbit by the force of the light pressure is investigated. The satellite is equipped with a damper and a system of mirrors (solar batteries can serve as such a system). The flight of the satellite takes place in the mode of a single-axis gravitational orientation, the axis of its minimum principal central moment of inertia makes a small angle with the local vertical and the motion of the satellite around this axis constitutes forced oscillations under the impact of the moment of force of the light pressure. The form of the oscillations and the initial orbit are chosen so that the transverse component of the force of the light pressure acting upon the satellite be positive and the semimajor axis of the orbit would continuously increase. As this takes place, the orbit remains almost circular. We investigate the evolution of the orbit over an extended time interval by the method which employs separate integration of the equations of the orbital and rotational motions of the satellite. The method includes outer and inner cycles. The outer cycle involves the numerical integration of the averaged equations of motion of the satellite center of mass. The inner cycle serves to calculate the right-hand sides of these equations. It amounts to constructing an asymptotically stable periodic motion of the satellite in the mode of a single-axis gravitational orientation for current values of the orbit elements and to averaging the equations of the orbital motion along it. It is demonstrated that the monotone increase of the semimajor axis takes place during the first 15 years of motion. In actuality, the semimajor axis oscillates with a period of about 60 years. The eccentricity and inclination of the orbit remain close to their initial values.     

Calculation of resultant vector and principal moment of light pressure forces acting upon the spacecraft with a solar sail

Two methods of calculating the resultant vector and principal moment of light pressure forces, having an effect on a spacecraft with a composite solar sail, are compared. The first method is based on analytical formulas obtained without regard to shading of some parts of the sail by others. The second method uses a detailed geometrical model of the sail, which allows one to take such shading into account. Some part of photons falling on a sail is supposed to be reflected from it in a mirror manner, while the others are completely absorbed. The range of variation of sail orientation parameters with respect to incident solar light streams, where the first method turns out to be accurate enough, is found.