Microdisturbances on the International Space Station during dynamic operations

The results of analysis of microdisturbances on the International Space Station (ISS) at performing various dynamic operations are presented. Docking of transfer manned and cargo vehicles Progress and Soyuz to various docking modules of the ISS, docking of the Space Shuttle Discovery, the ISS orbit correction and, also, disturbances at “EVA” (Extra Vehicular Activity) operations during astronauts working on the external ISS surface are considered. The results of measuring microaccelerations by sensors of both Russian and American segments are analyzed.     

Definition and analysis of properties of optimal three-impulse point-to-orbit transfers under time constraint

This paper deals with energetically optimal multi-impulse transfers of a spacecraft in the central Newtonian gravitational field near a planet. The transfer from a point on initial orbit to the final orbit with the given angular momentum and energy constants is considered. The transfer time is bounded above.With the distance from spacecraft to planet limited and the time free, such parameters of given orbits are chosen that the 3-impulse apsidal transfer T_r is optimal with an intermediate impulse at the maximum distance. On the basis of necessary optimality conditions an algorithm is developed to numerically determine the desired optimal transfer trajectory T_t under time constraint, the apsidal trajectory T_r being taken as initial approach. From the geometry and energy viewpoints, both trajectories T_t and T_r are close to each other. The trajectory T_t is also 3-impulsive, all impulses on it are nonapsidal. The distance from the planet is larger and the sum of impulses is less for this trajectory than for the initial trajectory T_r with the same transfer time.The simplified solution of the problem is constructed producing good approximation to the exact numerical optimization results. The solution asymptotics is found when the transfer time tends to infinity.     

Venus Express: Scientific goals, instrumentation, and scenario of the mission

The first European mission to Venus (Venus Express) is described. It is based on a repeated use of the Mars Express design with minor modifications dictated in the main by more severe thermal environment at Venus. The main scientific task of the mission is global exploration of the Venusian atmosphere, circumplanetary plasma, and the planet surface from an orbiting spacecraft. The Venus Express payload includes seven instruments, five of which are inherited from the missions Mars Express and Rosetta. Two instruments were specially designed for Venus Express. The advantages of Venus Express in comparison with previous missions are in using advanced instrumentation and methods of remote sounding, as well as a spacecraft with a broad spectrum of capabilities of orbital observations.     

A diffusion model of radial distributions of plasma density from measurements on the Cassini spacecraft in the inner magnetosphere of Saturn

Equatorial radial distributions of plasma density in the 3 < L < 9 region of Saturn’s magnetosphere, obtained from measurements on the Cassini spacecraft, are considered on the basis of diffusion theory. The concentration of particles in the magnetic tubes is found to grow with L. The external source is located at L ? 9. The particles diffuse to Saturn. In the 5 < L < 9 interval the distribution is close to equilibrium. A relation between the diffusion coefficient and the densities of internal sources and losses is obtained in this interval. Prevalence of losses over sources is very probable. Estimates of the diffusion flux and its derivative are given. If the diffusion coefficient is expressed as D _LL = D _o L ³ and the contencentration of particles depends on L according to a power law, the diffusion rate is constant.     

Aristotelian syllogisms

Aristotelian assertive syllogistic logic (without modalities) is embedded in the author’s Lingua Cosmica. The well-known basic structures of assertions and conversions between them in this logic are represented in LINCOS. Since these representations correspond with set-theoretic operations, the latter are embedded in LINCOS as well. Based on this valid argumentation in Aristotle’s sense is obtained for four important so-called perfect figures. Their constructive (intuitionistic) verifications are of a surprisingly elegant simplicity.     

The mass loss of spacecraft polyimide films under the action of atomic oxygen and vacuum ultraviolet radiation

The threshold values of the annual fluence of atomic oxygen (F _AO ≈ 10²⁰ cm^?2), as well as the ratios of the energy-flux density of vacuum ultraviolet radiation of the solar spectrum to the flux density of atomic oxygen (Φ _ν /Φ _AO ≈ 8 × 10^?15 mJ) were determined, which are characterized the influence of the synergistic effect on the mass loss of Kapton-H, PM-A, and PM-1E polyimide films, which are spacecraft materials.     

SETI terminology: Do we interpret SETI terms correctly?

Many important SETI terms are either ambiguously defined or interpreted by different experts differently. Based on the author's experience with astronautical terminology (IAA multilingual space dictionary) a summary of the usual problems connected with an uniform definition of fundamental terms is attempted. In the second part several examples are quoted from the SETI literature—including the terms ETI, SETI and METI themselves, the definition of a habitable zone, of alien life, of an extraterrestrial artifact, of the Drake equation, of the Fermi-paradox, etc. In the third part of the paper a new task for the SETI social sciences community is raised, namely to collect “Lasting Universal Terms”; i.e. terms the meaning of which did not change since millennia, are independent on geographic position and also on the terrestrial environment and biology. Such terms might be preferably used in interstellar communication. All these questions are related to the manner how we might think about ETI and SETI in new ways. The paper tries to summarize the problems connected with exact SETI terminology and its potential implications for the future.     

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.     

Stability of resonance rotation of a satellite with respect to its center of mass in the orbit plane

The stability of resonance oscillations and rotations of a satellite in the plane of its orbit in the case when the difference of the moments of inertia with respect to the principal axes lying in the orbit plane is small is determined at a given rotation number m by the sign of function Φ_m(e), introduced by F.L. Chernous’ko in 1963. In this paper, convenient analytical representations of functions Φ_m(e) are described in the form of integrals and series of Bessel functions regular at e → 1^?. Values of Φ_m(1) are calculated in explicit form. A theorem about the double asymptotic form of functions Φ_m(e) at m → ∞ and e → 1^? is proved by the saddlepoint method.     

Radial profile of pressure in a storm ring current as a function of D st

Using satellite data obtained near the equatorial plane during 12 magnetic storms with amplitudes from ?61 down to ?422 nT, the dependences of maximum in L-profile of pressure (L _m) of the ring current (RC) on the current value of D _st are constructed, and their analytical approximations are derived. It is established that function L _m(D _st ) is steeper on the phase of recovery than during the storm’s main phase. The form of the outer edge of experimental radial profiles of RC pressure is studied, and it is demonstrated to correspond to exponential growth of the total energy of RC particles on a given L shell with decreasing L. It is shown that during the storms’ main phase the ratio of plasma and magnetic field pressures at the RC maximum does not practically depend on the storm strength and L _m value. This fact reflects resistance of the Earth’s magnetic field to RC expansion, and testifies that during storms the possibilities of injection to small L are limited for RC particles. During the storms’ recovery phase this ratio quickly increases with increasing L _m, which reflects an increased fraction of plasma in the total pressure balance. It is demonstrated that function L _m(D _st ) is derived for the main phase of storms from the equations of drift motion of RC ions in electrical and magnetic fields, reflecting the dipole character of magnetic field and scale invariance of the pattern of particle convection near the RC maximum. For the recovery phase it is obtained from the Dessler-Parker-Sckopke relationship. The obtained regularities allow one to judge about the radial profile of RC pressure from ground-based magnetic measurements (data on the D _st variation).     

Gravitation effect on a flux of sporadic micrometeoroids in the vicinity of near-Earth orbits

The new approach to gravitation effect determination in calculating the flux of sporadic micrometeoroids in the near-Earth space is proposed. The technique is based on integration of the equations of motion of sporadic micrometeoroids with accounting for bending their trajectories when particles are approaching the Earth. The technique and results of calculation of the gravitational focusing factor k_g for various conditions are presented. The feature of the proposed technique for calculating coefficient k_g consists in the fact that this coefficient does not explicitly depend on the values of particles velocity at the last point. The results of investigation of coefficient k_g have shown that, for the given initial velocity of micrometeoroids, the values of this coefficient depend on deflection of its direction from the direction to the Earth center. It is shown that for low-altitude orbits the flux density can increase up to 60%. The distribution of probabilities of various directions of particles flying to spacecraft structural elements is found to be non-uniform.     

Luni-solar perturbations in the extended phase space representation of the Vinti problem

Perturbation theory is applied to the Vinti problem—motion about an oblate spheroid—to include the gravitational effects of the sun and moon. The problem is formulated using the extended phase space method which introduces a new independent variable similar to the true anomaly. The disturbing Hamiltonian H₁ for third bodies is of order J₂² (second order) and the final goal is a theory including second order short and long period terms and third order secular terms. The current paper however carries the development only to the second order in the secular terms and the first order in the periodic terms. Problems of including the higher orders are discussed. Therefore, in the development of H₁ all terms of order 10^?9 or larger are retained. The lunar emphemeris retains terms to e′² in the lunar eccentricity. The perturbation analysis is carried out by means of Lie series and is developed through the first order only which is consistent with the final accuracy desired. The generating function W₁ is obtained and separated into the long period, short period and secular terms. From W₁ the coordinates are defined from the Lie series by means of a transformation equation. These coordinates are non-singular for small eccentricity and inclination. Because of the complexity of the equations all algebraic computations were accomplished by means of a computerized Poisson series manipulator developed at the Naval Research Laboratory.     

Organization of the on-ground data processing for remote sensing purposes using finite rings and fields concept

In most of the modern on-ground data processing systems for remote sensing the digital signal conversions, on the analogy of the analog signal, are defined over a field of complex numbers, C, as the digital signal values (as well as those of the analog one) may be regarded as a subset of the field. Such an approach requires substantial computing and hardware expenses. For a signal defined in the finite range N (N = 0, 1, …, n − 1) most of the algorithms require the number of operations proportional to log N, N, N² and even to greater powers of N. That is why the building up of the data processing system mathematical model with a minute number of computations, as well as the computations organization, is a problem of great importance. It is not always necessary to build up a model using transformations over the field C. These transformations may be also defined over some other (abstract) fields, e.g. over the finite field GF(p) or finite residue ring moduli M, Z_M. This approach gives numerous advantages. They are discussed in the presented paper along with limitations of the approach. A series of the data processing system models are described. The design concepts for the on-ground images processing equipment are also discussed.     

Estimation of the soil composition by IR observation of the Earth by satellites

A number of missions are in progress for Earth resources satellites to perform soil diagnosis by observing the bare soil thermal response to the heat input from the surrounding atmosphere. Heat capacity missions (and similar missions) are accomplished by measuring the soil temperature at the times of the satellite passes over the soil site.The models which are usually adopted assume that, for atmospheric conditions periodically changing during the day, the surface temperature time dependence is a function of the soil thermal inertia alone (for a dry soil).The present author has shown elsewhere that a more appropriate, two dimensional finite element modelling of the thermal behaviour of the soil, exhibits a dependence of the surface temperature time evolution on both the thermal conductivity (k) and on the volume heat capacity (?c) (for no evaporation at the interface). At least two independent temperature measurements are necessary in order to get information about k and ?c. It is shown that, within the range of values of k and ?c of the usual soils, temperature measurements taken at two successive satellite passes may yield the necessary information on the soil thermophysical properties. Charts can be constructed which will provide information on k and ?c when two soil temperatures are measured at proper times.     

Artificial satellites orbits in 2:1 resonance: GPS constellation

In this work, the resonance problem in the artificial satellites motion is studied. The development of the geopotential includes the zonal harmonics J₂₀ and J₄₀ and the tesseral harmonics J₂₂ and J₄₂. Through an averaging procedure and successive Mathieu transformations, the order of dynamical system is reduced and the final system is solved by numerical integration. In the simplified dynamical model, three critical angles are studied. The half-width of the separatrix is calculated through a linearized model which describes the behavior of the dynamical system in a neighborhood of each critical angle. Through the resonance overlap criterion the possible regular and irregular motions are investigated by the time behavior of the semi-major axis, argument of perigee and eccentricity. The largest Lyapunov exponent is used as tool to verify the chaotic motion.     

A small parameter method in problems of maneuvering space vehicles with aerodynamic efficiency

The motion of a satellite with aerodynamic efficiency along a low near-circular orbit is considered in the paper. The controls of bank angle γ and lift coefficient C_y are used as control functions. The introduction of a small parameter ($\text{? = (}\text{?}{}_0\text{· S · g}{}_0\text{2G}\text{)}$) makes it possible to integrate an adjoint system of equations and to obtain an approximate solution to the complete problem in the class of piecewise-constant control functions. Maximum values for the coordinates of heading angle η and lateral derivation from the plane of a reference orbit ?, which are connected with orbit plane angle by the relation cos i = cos ? · cos h, are used as criteria of maneuvering capability for a satellite with aerodynamic efficiency. Optimal programs for bank angle and incidence variation are derived and the influence of lift-to-drag ratio on the vehicle maneuvering capabilities has been estimated.It is shown that the process of the optimal motion is a special kind of gravitational skipping similar to the Keplerian motion but with continuous descent.     

Long-term variations of asymmetry of the solar magnetic field and geometry of the interplanetary magnetic field

A comparative analysis of variations of the mean solar magnetic field and the interplanetary magnetic field over all history of their measurements is performed. Asymmetry of the solar magnetic field and its manifestation in the heliosphere is investigated. Long-term variations of the solar magnetic field and the heliosphere, which manifest themselves in alternation of dominating magnetic polarities of different sign, are discovered. On the basis of the analysis of cumulative sums of the IMF components, long-term variations of the IMF geometry and of the solar wind spiral angle are found. The cumulative sum of the IMF B _z component perpendicular to the ecliptic plane also shows long-term variations. Time intervals are revealed, in which negative values of the IMF B _z component dominate, and an increased geomagnetic activity is observed.     

Artificial satellites orbits in 2:1 resonance: GPS constellation

In this work, the resonance problem in the artificial satellites motion is studied. The development of the geopotential includes the zonal harmonics J₂₀ and J₄₀ and the tesseral harmonics J₂₂ and J₄₂. Through an averaging procedure and successive Mathieu transformations, the order of dynamical system is reduced and the final system is solved by numerical integration. In the simplified dynamical model, three critical angles are studied. The half-width of the separatrix is calculated through a linearized model which describes the behavior of the dynamical system in a neighborhood of each critical angle. Through the resonance overlap criterion the possible regular and irregular motions are investigated by the time behavior of the semi-major axis, argument of perigee and eccentricity. The largest Lyapunov exponent is used as tool to verify the chaotic motion.     

Equilibrium attitude and stability of a spacecraft on a stationary orbit around an asteroid

The stationary orbits around an asteroid, if exist, can be used for communication and navigation purposes just as around the Earth. The equilibrium attitude and stability of a rigid spacecraft on a stationary orbit around a uniformly-rotating asteroid are studied. The linearized equations of attitude motion are obtained under the small motion assumption. Then, the equilibrium attitude is determined in both cases of a general and a symmetrical spacecraft. Due to the higher-order inertia integrals of the spacecraft, the equilibrium attitude is slightly away from zero Euler angles. Then necessary conditions of stability of this conservative system are analyzed based on the linearized equations of motion. The effects of different parameters, including the harmonic coefficients C₂₀ and C₂₂ of the asteroid and higher-order inertia integrals of the spacecraft, on the stability are assessed and compared. Due to the significantly non-spherical shape and rapid rotation of the asteroid, the effects of the harmonic coefficients C₂₀ and C₂₂ are very significant, while effects of the third- and fourth-order inertia integrals of the spacecraft can be neglected. Considering a spacecraft on a stationary orbit around an example asteroid, we show that the classical stability domain predicted by the Beletskii–DeBra–Delp method on a circular orbit in a central gravity field is modified due to the non-spherical mass distribution of the asteroid. Our results are confirmed by a numerical simulation.