Power law distribution in statistics of failures in operation of spacecraft onboard equipment

The possibility of using the statistics of recurrence time for extreme events is studied in this paper having in mind the problems of control and prediction of failures in spacecraft operation. The information about failures onboard satellites of various types presented by the US National Geophysical Data Center was analyzed. It was found that the probability density of recurrence intervals followed a power law of the Pareto type with an index equal to 2.3. The obtained result is consistent both with the theory of normal catastrophes and with the principle of self-organization of criticality for metastable active heterogeneous environment. A practical consequence of the obtained result consists in the fact that predictions of these extreme events should not rely on traditional models with the second-order Pearson statistics. To make predictions, the models are necessary that take into account the power law distribution of recurrence intervals for failures on satellites. The failures should be considered in these models as extreme events connected with manifestation of the space environment factors.     

Monitoring of the space system

We have performed monitoring of the space system that includes the Earth, the Moon, the Sun, and the GPS satellite group. We have discovered semi-diurnal and diurnal periodicities in the number of satellites detected as well as in the altitude, latitude and longitude by a GPS receiver. We have revealed tidal deformations related to changes in the Earth?s orientation with respect to the Moon and the Sun.     

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.     

Protons with energy of E P ≥ MeV under the earth’s radiation belts

Variations in fluxes of quasi-trapped energetic protons were studied on the basis of the data of the CORONAS-I satellite. These variations are characterized by an increase in the proton fluxes with E _P ≥ 1 MeV both in the vicinity of the geomagnetic equator and in the high-latitude region of the magnetosphere. The analysis of structural features of the proton distributions in the regions at L ～ 1–1.1; 3 < L < 4; and L > 4, was performed and made it possible to detect reliably the type of the proton flux increase in this region. The mechanisms of particle scattering leading to the precipitation of energetic protons under conditions of various types of geomagnetic disturbances are considered.     

Existence of nonimpact motions along a wire rope fixed to an extended spacecraft

The possibility of nonimpact tension of a cable after its weakening when a small load moves along the cable whose ends are fixed on a massive dumbbell-like spacecraft which is moving in a steady-state manner along a circular orbit is considered. The conditions of existence and classification of the trajectories of nonimpact motion, including periodic ones, are presented.     

Construction of theories of motion, ephemerides, and databases for natural satellites of planets

A knowledge base for natural satellites of planets is created. On the basis of observations, new numerical models of motion are constructed for all 96 outer satellites of Jupiter, Saturn, Uranus, and Neptune. A special database is compiled from all available observational data for natural satellites of planets, as well as a bibliographical database and information system of physical and orbital parameters of planets and satellites. The tools for calculations of ephemerides of all natural satellites (except for the Moon) of planets are developed. They represent the final result of studies and actually incorporate the entire knowledge about dynamics of the satellites of planets. Also developed are special ephemerides in order to observe singular phenomena in the apparent motion of the satellites of planets. A computer environment and the Internet allowed us to concentrate all above-listed options in a single toolkit easily available to any user in the world.     

Spatial structure of Pc5 waves in the outer magnetosphere according to observations onboard the THEMIS satellites

We have analyzed oscillations in the Pc5 range recorded in the outer region of the evening magnetosphere onboard 5 THEMIS satellites when all vehicles were moving with a small distance along one and the same orbit. Gradients of the spatial structure of oscillations and fluxes of energetic protons are determined. The observed phase shifts of the oscillation field between the satellites are presumably caused by their sunward (westward) propagation with azimuthal wave numbers m ～ 30–60. According the data of particle detectors, non-equilibrium character of the distribution of protons is found: their non-monotonous distribution in energy and sharp spatial heterogeneity. The calculated parameters of plasma and oscillations are not consistent with the assumption on drift-mirror instability as a source of the oscillations. A complete theory of these waves should include effects of the finite Larmor radius and simultaneous existence of two types of nonequilibrium plasma.     

Application of laser diode beacons for determination of coordinates of space and ground objects

We consider the principles of constructing measurement schemes with optical autonomous laser diode beacons for space and ground objects. The structure, functional scheme, and cyclogram of operation of such beacons are described. Possible scenarios of application of the beacons for providing high-precision localization of space and ground devices are analyzed.     

Navigation support for the RadioAstron mission

A developed method of determination of orbital parameters allows one to estimate, along with orbit elements, some additional parameters that characterize solar radiation pressure and perturbing accelerations due to unloadings of reactiion wheels. A parameterized model of perturbing action of solar radiation pressure on the spacecraft motion is described (this model takes into account the shape, reflecting properties of surfaces, and spacecraft attitude). Some orbit determination results are presented obtained by the joint processing of radio measurements of slant range and Doppler, laser range measurements used to calibrate the radio measurements, optical observations of right ascension and declination, and telemetry data on spacecraft thrusters’ firings during an unloading of reaction wheels.