Identification of sources of Pc1 geomagnetic pulsations on the basis of proton aurora observations

The relationship between proton aurora and geomagnetic pulsations Pc1, which are an indicator of development of ion-cyclotron instability in the equatorial magnetosphere, are studied on the basis of the observations of proton aurora from the IMAGE satellite, observations of particle fluxes onboard the low-orbiting NOAA satellites, and geomagnetic pulsation observations at the Lovozero observatory. A conclusion is drawn that the subauroral spots in the proton emission projected into the magnetosphere near the plasmapause are two-dimensional images at the ionospheric “screen” of the region of intense scattering of energetic protons into the loss cone at the development of an ion-cyclotron instability.     

Trajectories for missions of low-thrust spacecraft aimed at delivery of soil samples from main belt asteroids and Phobos

Trajectories of spacecraft with electro-jet low-thrust engines are studied for missions planning to deliver samples of matter from small bodies of the Solar System: asteroids Vesta and Fortuna, and Martian moon Phobos. Flight trajectories are analyzed for the mission to Phobos, the limits of optimization of payload spacecraft mass delivered to it are determined, and an estimate is given to losses in the payload mass when a low-thrust engine with constant outflow velocity is used. The model of an engine with ideally regulated low thrust is demonstrated to be convenient for calculations and analysis of flight trajectories of a low-thrust spacecraft.     

The family of potentials admitting integration of the perturbed two-body problem in regular coordinates

An infinite system of potentials is presented that admits separation of regular variables in the perturbed two-body problem. The regular coordinates are constructed using a specially selected L-matrix. An explicit solution to the problem in the elliptical case is constructed. In the general case the solution is reduced to inversion of hyper-elliptic integrals. The cases of motion with and without constraints are considered. The results of numerical experiments are presented.     

Semianalytic estimations of boundaries of a corridor of spacecraft entry into the planetary atmosphere at considerable values of permissible maximum overload

Trajectories of spacecraft entry into the planetary atmosphere with a velocity essentially exceeding the first cosmic velocity are considered. An estimation of the minimum permissible value of the altitude of conditional pericenter (perigee in the case of the Earth), at which extreme permissible value of maximum overload is reached, is of the main interest. Semianalytic formulas including the cases of considerable values of the maximum overload are suggested.     

Calculation of quasisynchronous orbits of a spacecraft around Phobos for solving the problem of landing on its surface

The problem of selecting quasi-synchronous orbits of a spacecraft around Phobos is considered. These quasi-synchronous orbits are far (with respect to the Hill’s sphere) quasi-satellite orbits with retrograde rotation in the restricted three body problem. The orbit should pass through a given point at a specified time instant. It should also possess a property of minimum distance from the Phobos surface at every passage above the region of planned landing. The equations of dynamics are represented in the form describing the orbit as a combination of motions in two drifting ellipses, inner and outer ellipses. The center of the outer ellipse is located on the inner ellipse. A formula is derived that relates averaged values of half-axes of the inner and outer ellipses. It is used for construction of the first approximation of numerically designed orbit, which makes it possible to simplify and speed up the computing process. The tables of initial conditions obtained as a result of calculations are presented.     

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).     

Ultraviolet studies of the interplanetary and local interstellar medium

A review of the last results of UV observations in the interplanetary space of neutral hydrogen and neutral helium in resonance lines HI λ1215.7 Å and HeI λ584 Å is presented. The history of discovery of the interstellar wind effect is expounded in the review, and interaction of the solar wind with the interstellar medium is briefly described. Models of the inner-heliospheric distribution of emissivity in the lines HI λ1215.7 Å and HeI λ584 Å are discussed, and possibilities of getting the solar wind parameters from UV observations in the L _α line are considered. Currently accepted parameters of the local interstellar medium are presented. The parameters obtained are compared with those derived from non-optical measurements.     

Ballistics, navigation, and motion control for a spacecraft during its landing on the surface of Phobos

Basic concepts and algorithms laid as foundations of the scheme of landing on the Martian moon Phobos (developed for the Phobos-Grunt project) are presented. The conditions ensuring the landing are discussed. Algorithms of onboard navigation and control are described. The equations of spacecraft motion with respect to Phobos are considered, as well as their use for correction of the spacecraft motion. The algorithm of estimation of the spacecraft’s state vector using measurements with a laser altimeter and Doppler meter of velocity and distance is presented. A system for modeling the landing with a firmware complex including a prototype of the onboard computer is described.     

A method of calculation of vertical cutoff rigidity in the geomagnetic field

On the basis of generalization of the results of extensive trajectory calculations for trial charged particles moving in the geomagnetic field the method of calculation of effective vertical cutoff rigidity, taking into account the values of K _p -index and local time, is developed. The IGRF and Tsyganenko-89 models are used for the geomagnetic field. A comparison of the results of model simulations with the experimental data on penetration of charged particles into near-Earth space is made, and penetration functions for typical spacecraft orbits are calculated.     

Optimum conditions of observation of tubular-loop structures of the interplanetary magnetic field and estimation of their lifetime

Basic conditions of observation of IMF tubular-loop structures are considered on the basis of experimental data of studying the fluxes of solar cosmic ray protons in the interplanetary medium. Lifetime of these structures, when their sources disappear on the Sun, is estimated.     

Estimation of dynamic characteristics of the <Emphasis Type="Italic">International Space Station</Emphasis> from measurements of microaccelerations

We describe the results of determining the mass of the International Space Station using the data of MAMS accelerometer taken during correction of the station orbit on August 20, 2004. The correction was made by approach and attitude control engines (ACE) of the Progress transporting spacecraft. The engines were preliminary calibrated in an autonomous flight using the onboard device for measuring apparent velocity increment. The method of calibration is described and its results are presented. The error in station mass determination is about 1%. The same data of MAMS and similar data obtained during the orbit correction on August 26, 2004 were used for the analysis of high-frequency vibrations of the station mainframe caused by operation of the ACE of Progress. Natural frequencies of the ACE are determined. They lie in the frequency band 0.024–0.11 Hz. ACE operation is demonstrated to result in a substantial increase of microaccelerations onboard the station in the frequency range 0–1 Hz. The frequencies are indicated at which disturbances increase by more than an order of magnitude. The study described was carried out as a part of the Tensor technological experiment.     

Experimental and theoretical investigation of encounter of a group of particles with protecting elements of spacecraft

We present the results of comprehensive experimental and theoretical investigations of encounter with a barrier of a group of bodies thrown with a high-velocity. Throwing of a group of particles (from two to twelve bodies) was realized on a ballistic route using powder and light-gas units of different calibers in the range of velocities 500–3500 m/s. The process of particle throwing was controlled by acting aerodynamic forces. In experiments on collisions with barriers of a finite thickness (which imitates the protective shield of spacecraft) the number of particles in a homogeneous stream was varied from 2 to 7 at changing the flux density (distances between particles). Experimental data are obtained on variations of the area and mass of back-surface splinters. Numerical calculations simulated a knock of 2 to 4 particles against a barrier in the cases of normal impact and at an angle. The calculations were performed in three-dimensional formulation and applying criteria of complete destruction of material. The appearance of additional destruction centers in the barrier due to mutual influence of particles is revealed. Simple criteria are obtained for estimating the degree of interference of particles and the character of barrier destruction.     

Design of satellite constellations with continuous coverage on elliptic orbits of <Emphasis Type="Italic">Molniya</Emphasis> type

New methods of choosing the structures of satellite constellations (SC) on elliptical orbits of the Molniya type are presented. The methods, using critical inclination and putting the orbit apogee in the Earth’s hemisphere with an area of continuous coverage, are based on geometrical analysis of two-dimensional representation of the coverage conditions and SC motion in the space of inertial longitude of the orbit ascending node and time. The coverage conditions are represented in the form of a certain region. Dynamics of all satellites in this space is represented by uniform motion along a straight line approximately parallel to the ordinate axis, while the satellite system forms a grid. The problem of choosing a minimal (as far as the number of satellites is concerned) SC configuration can be formulated as a search for the most sparse grid. The contemporary advanced methods of computational geometry serve as an algorithmic basis for the problem solution. Design of SC for continuous coverage of latitude belts with the use of kinematically regular systems is considered. A method of analyzing single-track systems for continuous coverage of arbitrary geographic regions is described, which makes a region at any time instant observable by at least one satellite of the system. As an example, SC on elliptical orbits are considered with periods of ～4, 12, and 24 hours.     

Sporadic structures and small-scale irregularity in the nighttime polar ionosphere in the period of high solar activity according to the data of radio occultation measurements on satellite-to-satellite paths

Results of the analysis of 327 sessions of radio occultation on satellite-to-satellite paths are presented. The data are taken in the nighttime polar ionosphere in the regions with latitudes of 67°–88°, and in the period of high solar activity from October 26, 2003 to November 9, 2003. Typical ionospheric changes in the amplitude and phase of decimeter radio waves on paths GPS satellites-CHAMP satellite are presented. It is demonstrated that these data make it possible to determine characteristics of the sporadic E _s structures in the lower ionosphere at heights of 75–120 km. Histograms of distribution of the lower and upper boundaries, thickness, and intensity of the E _s structures are presented. Dispersion and spectra of amplitude fluctuations of decimeter radio waves caused by small-scale irregularity of the ionospheric plasma are analyzed. The relation of the polar E _s structures and intensity of small-scale plasma irregularity to various manifestations of solar activity is discussed. The efficiency of monitoring the ionospheric disturbances caused by shock waves of the solar wind by the radio occultation method on satellite-to-satellite paths is demonstrated.     

Optimization of interplanetary trajectories for spacecraft with ideally regulated engines using the continuation method

The problem of optimization of interplanetary trajectories is considered for spacecraft with a small-thrust ideally regulated engine. When the maximum principle is used, determination of the optimal trajectory is reduced to solution of a two-point boundary value problem for a system of ordinary differential equations. In order to solve this boundary value problem, the method of continuation in parameter is used, and with the help of it the formal reduction of the boundary value problem to a Cauchy problem is performed. Different variants of the continuation method are considered, including the method of continuation in the gravitational parameter which allows one to find extreme trajectories with a preset angular distance. The issues of numerical realization of the continuation method are discussed, and numerical examples of its use for solving the problems of optimization of interplanetary trajectories are presented.     

Characteristics of high energy cosmic ray diurnal anisotropy on day-to-day basis

Diurnal variation of cosmic ray intensity for the period of 1989 to 2000 at Kiel, Haleakakla, Rome, Hermanus, Calgary, and Goose Bay neutron monitors has been studied. Frequency histograms are generated for each year by using the daily values of amplitudes and phases. In the present analysis we have derived the yearly mean amplitude and phase of the diurnal variation of cosmic ray intensity. It has been concluded from the analysis that the diurnal amplitude is mostly concentrated in between the amplitude values of 0.1% and 0.4%, whereas the phase of diurnal anisotropy is concentrated in the belt of 100 to 225 degrees. As such, the various characteristics of long-term diurnal variation of cosmic ray intensity for the maxima of solar activity cycle 22 to the next maxima of solar activity cycle 23 have been studied. The minimum amplitudes are apparent for the minimum solar activity periods starting from 1995 and up to 1997 at Kiel, Haleakakla, Rome, Hermanus, Calgary and Goose Bay stations. The diurnal amplitude has been found to have almost recovered to its values observed during 1989 to 1990. It is also seen that the diurnal amplitudes are much larger by a factor of two at high/middle latitude stations as compared to that for low latitude stations, where the amplitudes are even ～01% or less during 1996. The phase is significantly earlier during 1996 and 1997 with some significant change starting in 1995. As such, competitive is a continuous decreasing trend in the diurnal phase with smaller change at high/middle latitude and significantly much larger change at low latitudes.     

Study of singular surfaces of systems of unsupported gyrodynes by the parameter continuation method

A system of two-degree-of-freedom force gyroscopes (gyrodynes) is considered to be used for spacecraft attitude control. Possible values of its total angular momentum form some finite region P in the frame of reference rigidly connected with the spacecraft. Near the boundary of this region and singular surfaces located inside it the control of the angular momentum is complicated or impossible. The program angular momentum of the gyrodynes, realizing the law of variation of the spacecraft orientation, should lie inside P and outside some singular surfaces, and due to this fact the boundary and internal singular surfaces should be studied. This work is dedicated to the numerical construction of region P and its internal singular surfaces by the method of parameter continuation. Using the results by E.N. Tokar’ we formalize sufficient conditions which in some cases allow one to determine the type of the singular surface. As an example, a system of six gyrodynes is considered, for which the regions of variations of the intrinsic angular momentum and singular surfaces are constructed. The possibilities of the system are demonstrated for the case when one gyrodyne fails.     

Optimization of passive orbit with the use of gravity maneuver

A high-precision method of calculating gravitational interactions is applied in order to determine optimal trajectories. A number of problems, necessary for determination of optimal parameters at a launch of a spacecraft and during its flyby near celestial bodies, are considered. The spacecraft trajectory was determined by numerical integration of the equations of passive motion of the spacecraft and of the equations of motion for planets, the Sun, and the Moon. The optimal trajectory of the spacecraft approaching the Sun is determined by fitting its initial conditions.     

Planar inertial motion of an elastic cluster of three bodies

A problem of planar inertial motion of three bodies connected in the form of a triangle by an elastic imponderable filament is considered, as well as a particular case of the problem of motion of a closed chain of n bodies. This configuration can be a basis for extended planar constructions in deep space.The bodies are considered as material points. The paper elaborates a subject of [1]     

Vertical distribution of the power of short- and long-period oscillations in a sunspot and in surrounding magnetic elements

We present the results of processing three 256-min series of observations of quasi-periodic oscillations of the field of line-of-sight velocities in three sunspots. The Doppler shifts were determined simultaneously for six spectral lines formed at different heights in the solar atmosphere. In addition to the well-known high-frequency (periods of 3–5 min) oscillations, a band of low-frequency oscillations with periods of 60–80 min is revealed in the spectra of the sunspot umbra and magnetic elements located in immediate proximity of the sunspot. Unlike the short-period modes, the power of the long-period mode of line-of-sight velocity oscillations in the sunspot decreases sharply with height: these oscillations are distinctly seen in the line formed at a height of 200 km and almost are not seen in the line with the formation height of 500 km. This is indicative of different physical nature of the short-period and long-period oscillations of a sunspot. If the former are caused by slow magnetosonic waves within the field tube of the spot, the latter are representative of global vertical-radial oscillations of a magnetic element (spot, pore) as a whole near the position of a stable equilibrium.