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.     

Two-craft tether formation relative equilibria about circular orbits and libration points

The relative equilibria of a two spacecraft tether formation connected by line-of-sight elastic forces moving in the context of a restricted two-body system and a circularly restricted three-body system are investigated. For a two spacecraft formation moving in a central gravitational field, a common assumption is that the center of the circular orbit is located at the primary mass and the center of mass of the formation orbits around the primary in a great-circle orbit. The relative equilibrium is called great-circle if the center of mass of the formation moves on the plane with the center of the gravitational field residing on it; otherwise, it is called a nongreat-circle orbit. Previous research shows that nongreat-circle equilibria in low Earth orbits exhibit a deflection of about a degree from the great-circle equilibria when spacecraft with unequal masses are separated by 350 km. This paper studies these equilibria (radial, along-track and orbit-normal in circular Earth orbit and Earth–Moon Libration points) for a range of inter-craft distances and semi-major axes of the formation center of mass. In the context of a two-spacecraft Coulomb formation with separation distances on the order of dozens of meters, this paper shows that the equilibria deflections are negligible (less than 10^?6°) even for very heterogeneous mass distributions. Furthermore, the nongreat-circle equilibria conditions for a two spacecraft tether structure at the Lagrangian libration points are developed.     

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.     

Specific features of motion of geosynchronous satellites in the neighborhood of unstable stationary points

A study of peculiarities of the motion of equatorial circular geosynchronous satellites is performed in the neighborhoods of unstable stationary points with longitudes of 165° and 345°. The maps of initial conditions are constructed on the phase plane “longitude of subsatellite point-semi-major axis of orbit” corresponding to various types of regular motions and to quasi-random solutions. The dimensions of zones of the quasi-random solutions are within the limits from decimal fractions of a degree to a few degrees (in longitude) and from hundreds of meters up to several kilometers (along the semi-major axis).     

Stochastic motion of geosynchronous satellites

Long-period evolution of the orbital elements of geosynchronous objects moving in the neighborhood of separatrices of the region of libration resonance is studied. At the phase plane “the longitude of the subsatellite point-semi-major axis” the regions of migration of separatrices where the separatrices can move due to the influence of perturbations are isolated. The dimensions of these regions and the distances between them have the same order of magnitude, several kilometers along the semi-major axis. The regions of migration do not overlap at the initial value of the orbit inclination 0°. When inclination increases, gradual overlapping of these regions takes place. On average, the width of the zones of stochasticity increases when the area to mass ratio increases and decreases when inclination of the orbit increases. The zones of stochasticity corresponding to different separatrices are separated from each other. A catalog of the passive geosynchronous objects moving in the neighborhood of separatrices is compiled. The evolution of the objects of the catalog is studied.     

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.     

Evolution of the Orbit of an Earth Satellite with a Solar Sail

The efficiency of using the light pressure of solar radiation for increasing the semimajor axis of the orbit of an Earth Satellite carrying a solar sail is estimated. The orbit is nearly circular and has an altitude of about 900 km. The satellite is in the mode of single-axis solar orientation: it rotates at an angular velocity of 1 deg/s around the axis of symmetry, which traces the direction to the Sun. This mode is maintained by the solar sail, which serves in this case as a solar stabilizer. The following method of increasing the semimajor axis of the orbit (which is equivalent to increasing the total energy of the satellite's orbital motion) is considered. On those sections of the orbit, where the angle between the light pressure force acting upon the sail and the vector of geocentric velocity of the satellite does not exceed a specified limit, the sail is functioning as a solar stabilizer. On those sections of the orbit, where the above-indicated angle exceeds this limit, the sail is furled by way of turning the edges of the petals towards the Sun. Such a control increases the semimajor axis by more than 150 km for three months of flight. In this case, the accuracy of solar orientation decreases insignificantly.     

One method of gravitational attitude control of a rotating satellite

The mode of spinning up a low-orbit satellite in the plane of its orbit is studied. In this mode, the satellite rotates around its longitudinal axis (principal central axis of the minimum moment of inertia), which executes small oscillations with respect to the normal to the orbit plane; the angular velocity of the rotation around the longitudinal axis is several tenths of a degree per second. Gravitational and restoring aerodynamic moments were taken into account in the equations of satellite’s motion, as well as a dissipative moment from eddy currents induced in the shell of the satellite by the Earth’s magnetic field. A small parameter characterizing deviation of the satellite from a dynamically symmetric shape and nongravitational external moments are introduced into the equations. A two-dimensional integral surface of the equations of motion, describing quasistationary rotations of the satellite close to cylindrical precession of the corresponding symmetrical satellite in a gravitational field, has been studied by the method of small parameter and numerically. We propose to consider such quasistationary rotations as unperturbed motions of the satellite in the spin-up mode.     

Control of an orbiting flexible square platform in the presence of solar radiation

A mathematical model for the solar radiation forces and moments acting on a square plate (platform) in orbit is obtained by considering the plate mode shapes as combinations of free-free beam shape functions. The moment expressions for a plate of arbitrary reflectivity coefficient are obtained as a function of the solar incidence angle. It is seen that only the first three flexible modes of the plate generate a first order net moment about the center of mass, and that the solar radiation pressure does not influence the flexible modes of the plate for small amplitude vibrations. The solar radiation disturbance model is then included in the dynamic model of a square plate nominally oriented along the local vertical and having the major surface of the plate normal to the orbital plane. The roll angle of the plate is seen to increase steadily due to the solar radiation pressure whereas the pitch and yaw motions oscillate with an amplitude of approximately 0.2° for a 100 m square thin aluminum plate in synchronous orbit. To control the shape and orientation of the plate two point actuators are assumed—one whose force axis is normal to the plane of the plate, the second with a force axis in the plane of the plate. The control law and the feedback gain values are obtained based on linear quadratic Gaussian methods. Transient responses and control requirements are simulated for local vertical and horizontal orientations.     

Recovery of long-wavelength mean gravity anomalies for the dedicated gravitational satellite (gravsat) mission

This paper describes a computer simulation study that was undertaken to determine how well long-wavelength variations in the Earth's gravitational field can be recovered using data from the Dedicated$\text{Grav}$itational $\text{Sat}$ellite (GRAVSAT) mission. This mission is to consist of two low altitude (160 km) spacecraft in essentially the same orbit but separated in phase by 100–300 km. Geodetic data are measurements of the relative range rate to an accuracy of about 1 μm/s at 4 sec intervals. Specifically, a Bayesian covariance simulation was used to investigate simultaneous recovery of the spacecraft ephemerides and a global distribution of 20° × 20° mean gravity anomaly blocks. Sources of errors considered were tracking station positions, gravitational constant, Earth body tides, tropospheric modeling and measurement noise. It should be noted that this simulation does not include as an error source variations in the gravity field that have a character different from what was modeled. Consequently, this study demonstrates the potential of the low-low system as configured to recover the long-wavelength variations in the gravity field.Using only one days worth of data, the mean of the standard deviations of the 162 20° × 20° gravity anomaly blocks is about 1 μgal. For a 6 month mission (assuming a reduction proportional to the square root of the data intervals) this projects to < 0.1 μgal. Because of the potential of increased measurement precision at shorter separation distances, and the relative insensitivity of the recovery process to separation distance, it should be possible to recover both long and short wavelength variations with a modest distribution of separation distances tailored primarily to the short wavelength recovery. Effects of the uncertainty in the gravitational constant and Love's numbers are negligible. In a simulation not reported on, increasing the altitude of the orbit to 200 km from 150 km, degraded, as expected, the accuracy of the recovered parameters by only 7%.     

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.     

A specific case of stability of cylindrical precession of a satellite

In a central Newtonian gravitational field, the motion of a dynamically symmetrical satellite along an elliptical orbit of arbitrary eccentricity is considered. The particular motion of the satellite is known when its axis of symmetry is perpendicular to the orbit plane, and the satellite rotates about this axis with a constant angular velocity (cylindrical precession). A nonlinear analysis of stability of this motion has been performed under the assumption that the geometry of the satellite mass corresponds to a thin plate. At small values of orbit eccentricity e the analysis is analytical, while numerical analysis is used for arbitrary values of e.     

A study of evolution of spin-up mode of a satellite in the plane of its orbit

We investigate the mode of spinning up a low-orbit satellite in the plane of its orbit. In this mode the satellite rotates around its principal central axis of the minimum moment of inertia which executes small oscillations with respect to the normal to the orbit plane; the angular velocity of the rotation around this axis several times exceeds the mean orbital motion. Gravitational and restoring aerodynamic moments are taken into account in the satellite’s equations of motion. A small parameter characterizing deviation of the satellite from a dynamically symmetric shape is introduced into the equations. A two-dimensional integral surface of the equations of motion, describing quasi-steady-state rotations of the satellite close to cylindrical precession of the corresponding symmetrical satellite in a gravitational field, has been studied by the method of small parameter and numerically. Such quasi-steady-state rotations are suggested to be considered as unperturbed motions of the satellite in the spin-up mode. Investigation of the integral surface is reduced to numerical solution of a periodic boundary value problem of a certain auxiliary system of differential equations and to calculation of quasi-steady-state rotations by the two-cycle method. A possibility is demonstrated to construct quasi-steady rotations by way of minimization of a special quadratic functional.     

Results of measurements with the Planetary Fourier Spectrometer onboard Mars Express: Clouds and dust at the end of southern summer. A comparison with OMEGA images

We discuss the results of measurements made with the Planetary Fourier Spectrometer (PFS) onboard the Mars Express spacecraft. The data were obtained in the beginning of the mission and correspond to the end of summer in the southern hemisphere of Mars (L _s ～ 340°). Three orbits are considered, two of which passed through volcanoes Olympus and Ascraeus Mons (the height above the surface is about +20 km), while the third orbit intersects lowland Hellas (?7 km). The influence of the relief on the properties of the aerosol observed is demonstrated: clouds of water ice with a visual optical thickness of 0.1–0.5 were observed above volcanoes, while only dust was found during the observations (close in time) along the orbit passing through Hellas in low and middle latitudes. This dust is homogeneously mixed with gas and has a reduced optical thickness of 0.25±0.05 (at v = 1100 cm^?1). In addition to orographic clouds, ice clouds were observed in this season in the northern polar region. The clouds seen in the images obtained simultaneously by the mapping spectrometer OMEGA confirm the PFS results. Temperature inversion is discovered in the north polar hood below the level 1 mbar with a temperature maximum at about 0.6 mbar. This inversion is associated with descending movements in the Hadley cell.     

Single-Axis Solar Orientation of a Satellite of the Earth

The possibility of using the mode of single-axis solar orientation is considered for a satellite placed into a nearly circular orbit with an altitude of 900 km and bearing a solar sail. The satellite (together with the sail) has an axisymmetric structure, its symmetry axis being the principal central axis of the maximum moment of inertia. The center of the sail pressure lies on this axis and is displaced with respect to the satellite's center of mass. The symmetry axis of the satellite is set to the Sun so that its center of mass would be located between the Sun and the pressure center and would rotate around this axis with an angular velocity of a few degrees per second. The satellite's axis of symmetry makes a slow precession under the action of the gravitational moment and the moment of light pressure forces. Though the maximum magnitudes of these moments are comparable, the moment of the light pressure forces dominates and controls the precession in such a way that the symmetry axis orientation to the Sun remains unchanged.     

Longitude-dependent effects of fragmentation events in the geosynchronous orbit regime

The effects of on-orbit fragmentation events on localized debris congestion in each of the longitude slots of the geosynchronous orbit (GEO) regime are evaluated by simulating explosions and collisions of uncontrolled rocket bodies in multiple orbit configurations, including libration about one or both of the gravitational wells located at 75°E and 105°W. Fragmentation distributions are generated with the NASA Standard Breakup Model, which samples fragment area-to-mass ratio and delta-velocity as a function of effective diameter. Simulation results indicate that the long-term severity and consequence of a GEO fragmentation event is strongly dependent upon parent body longitude at the epoch of fragmentation, which can spawn bi-annual “fragment storms” in high-risk longitude slots, driven by lower-energy fragments that have been captured and have started librating around the nearby gravitational well.     

Evolution of Motion of a Binary Planet

A model of a binary planet, consisting of a material point of small mass and a deformable viscoelastic sphere, is suggested. The center of mass of the binary planet moves in the gravitational field of a central body in the plane, which contains planets forming the binary planet. A deformable spherical planet rotates around the axis orthogonal to the plane of planetary motion. Planet deformations are described by the linear theory of viscoelasticity. It is shown that with an appropriate approximation of the gravitational potential, there is a class of quasicircular orbits, when the eccentricities of an orbit of the center of mass of a binary planet and an orbit, describing mutual planet motion, are equal to zero. The further evolution of motion is investigated in this class of orbits with the use of the canonical Poincare–Andoyer variables. Corresponding averaged equations are found, and phase pictures are constructed; the stability of stationary solutions is investigated on the basis of equations in variations. For the Solar system planets with their satellites, forming binary planets, the application of the presented model allows us to conclude that satellites sooner or later will fall on the corresponding planets.     

电动绳系在低极轨卫星中的应用研究

低极轨卫星具有轨道周期短、对地观测分辨率高等优点,但由于所在轨道大气阻力大,其使用寿命受到较大限制。文章提出采用水平结构电动绳系抵消低极轨卫星大气阻力的方法,通过系绳电流与地球磁场相互作用产生洛仑兹力进行推进,进而在无燃料消耗的情况下实现对低极轨卫星轨道高度的维持。初步分析了该方法在低极轨不同尺寸卫星中的应用潜力,计算了160 、400 和800 km 典型高度低极轨卫星所经历的地球磁场、电离层和高层大气环境相关参数变化,比较了不同条件下电动绳系推力与大气阻力大小随轨道位置的变化。分析结果表明,该方法适用于400 km 轨道高度以上大卫星;在满足一定系绳长度和轨道高度的条件下,电动绳系可以有效延长低极轨卫星的轨道寿命。     

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.     

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.