Family <Emphasis Type="Italic">h</Emphasis> of periodic solutions of the restricted problem for big μ

The results of the computation of the family h of symmetric periodic solutions of the circular planar restricted three-body problem for μ = 0.3, 0.4, and 0.5 are presented. This family begins with retrograde circular orbits around a massive body. Associated with each value of μ are the table of critical orbits, the orbit pictures, the graphs of characteristics of the family in four coordinate systems, and the graphs of the period and traces (planar and vertical). Regularities on the family and its evolution as μ increased were observed.     

Closed families of periodic solutions of a restricted three-body problem

The planar restricted three-body problem has an infinite number of families of symmetric periodic solutions (SPSs). The natural SPS families include certain families which are self-closed with respect to small variations in a parameter. These families remain closed for any admissible variations in the mass parameter μ. However, there are closed SRS families of another type, which exist only in bounded intervals of μ and are formed via self-bifurcations of some SPS families. This type of SPS families is poorly understude. This work describes the initial stage (4 bifurcations) of a bifurcation cascade of the natural family i and points out other closed SPS families known to date.     

Determination of the orbits of inner Jupiter satellites

Some problems in determining the orbits of inner satellites associated with the complex behavior of the target function, which is strongly ravine and which possesses multiple minima in the case of the satellite orbit is determined based on fragmentary observations distributed over a rather long time interval, are studied. These peculiarities of the inverse problems are considered by the example of the dynamics of the inner Jupiter satellites: Amalthea, Thebe, Adrastea, and Metis. Numerical models of the satellite motions whose parameters were determined based on ground-based observations available at the moment to date have been constructed. A composite approach has been proposed for the effective search for minima of the target function. The approach allows one to obtain the respective evaluations of the orbital parameters only for several tens of iterations even in the case of very rough initial approximations. If two groups of observations are available (Adrastea), a formal minimization of the target function is shown to give a solution set, which is the best solution from the point of view of representation of the orbital motion, which is impossible to choose. Other estimates are given characterizing the specific nature of the inverse problems.     

The orbit of asteroid (99942) Apophis as determined from optical and radar observations

The results of improving the orbit accuracy for the asteroid Apophis and the circumstances of its approach to Earth in 2029 are described. Gravitational perturbations from all of the major planets and Pluto, Ceres, Pallas, and Vesta are taken into account in the equations of motion of the asteroid. Relativistic perturbations from the Sun and perturbations due to the oblateness of the Sun and Earth and due to the light pressure are also included in the model. Perturbations from the Earth and Moon are considered separately. The coordinates of the perturbing bodies are calculated using DE405. The phase correction and the gravitational deflection of light are taken into account. The numerical integration of the equations of motion and equations in variations is performed by the 15th-order Everhart method. The error of the numerical integration over the 2005–2029 interval, estimated using forward and backward computations, is not more than 3 × 10^?11 AU. Improved coordinates and velocities at epoch JD2454200.5 (April 10, 2007) were obtained applying the weighted leastsquares fit. For the period from March 15, 2004, to August 16, 2006, 989 optical and 7 radar observations were used. The resulting system represents the optical observations with an error of 0.37 (66 conditional equations were rejected). The residuals of the radar observations are an order, or more, smaller than their errors. The system of Apophis’ elements and the estimates of their precision obtained in this study are in perfect agreement with the results published by other authors. The minimum Apophis-Earth distance is about 38 200 km on April 13, 2029. This estimate agrees to within 20 km with those calculated based on other published systems of elements. The effect of some model components on the minimum distance is estimated.     

Hierarchy of periodic solutions families of spatial Hill’s problem

Many modern space projects require the knowledge of orbits with certain properties. Most of these projects assume the motion of a space vehicle in the neighborhood of a celestial body, which in turn moves in the field of the Sun or another massive celestial body. A good approximation of this situation is Hill’s problem. This paper is devoted to the investigation of the families of spatial periodic solutions to the three-dimensional Hill’s problem. This problem is nonintegrable; therefore, periodic solutions are studied numerically. The Poincare theory of periodic solutions of the second kind is applied; either planar or vertical impact orbits are used as generating solutions.     

Research on selenodesy and dynamics of the Moon in Kazan

In this review, we consider all aspects of the development of heliometric and positional observations of the Moon and the investigation of its figure, rotation (physical libration), and gravitational field as well as other similar questions at the Engelhard Astronomical Observatory (EAO) and the Kazan Municipal Astronomical Observatory (KMAO) at Kazan University.     

Optimization of the interplanetary energetic proton flux database and its application in modeling radiation conditions

The dissimilarity of the results of solar and galactic proton flux measurements made on different spacecraft is pointed out. It is caused, in addition to instrument errors, by differences in the temporal and spatial conditions of the measurements. We suggest using statistical analysis of proton fluences calculated for different long time intervals, from half a year to 10 years, for the optimization of the interplanetary proton database. An example of such analysis is presented and a probabilistic model of total proton fluences at the Earth’s orbit outside the magnetosphere, constructed using the analysis, is described. A formalized method for separating proton fluxes in solar proton events from protons of galactic cosmic rays is suggested. A conclusion is made that sources of cosmic ray protons with energies of less than 4 MeV should be examined in more detail.     

The negative polarization parameters of the light scattered by the lunar surface: Mapping

The images of the southwestern part of the lunar disk showing the distributions of the negative polarization parameters of the light scattered by the lunar surface are presented. The distributions of the negative polarization minimum P _min, the inversion angle α_inv, and the polarization slope at the inversion point h significantly differ from the albedo image. This testifies to the fact that polarimetry yields independent information on the structure and optical properties of the lunar regolith.     

Gamma-ray emission from solar flares of January 2005 observed by the AVS-F apparatus onboard the CORONAS-F satellite

Six solar flares were detected by the AVS-F apparatus onboard the CORONAS-F satellite in January 2005. We discuss the temporal profiles and energy spectra of the solar flares of January 20, 17, and 15, 2005 (class X7.1, X3.8, and X2.6, respectively) on the AVS-F data. The active region NOAA 10720 was the source of these flares. The spectra of the flares of January 17 and 20, 2005 contain nuclear lines, a positron line, and a line due to neutron capture line, while only the positron and neutron capture lines can be identified in the spectrum of the flare of January 15, 2005. The spectral features corresponding to these lines were observed during the whole duration of the flares. Analysis of the temporal profile of the flare of January 20, 2005 with a 1-ms temporal resolution in the energy range 0.1–20 MeV reveals the presence of a thin structure (at the 99% confidence level) with typical timescales of 7 to 35 ms.     

Monitoring of interplanetary and ionospheric scintillation of an ensemble of radio sources

The results of a series of 24-hour observations of radio-source interplanetary and ionospheric scintillation performed on April 4–10, 2006, at the Pushchino Radio Astronomy Observatory are presented. The observations were carried out with the Large Phased Array radio telescope of the Lebedev Institute of Physics, Russian Academy of Sciences, at a frequency of 110 MHz. The scintillating fluxes of all radio sources that fall within a field of sky between declinations +28° and +31° were automatically recorded applying eight beams of the reception pattern operating simultaneously. All of the sources with flux densities of 0.2 Jy or higher were detected. The structure functions of the flux fluctuations were measured for time shifts 1 and 10 s, which characterize the interplanetary (1 s) and ionospheric (10 s) scintillation, respectively. The mean scintillation index m _IPP (on a characteristic time scale of 1 s) of an ensemble of radio sources located within a sky band 4° wide in declination and 1 h wide in right ascension was measured as the parameter that characterizes the interplanetary plasma. Diurnal variations of the interplanetary scintillation index were determined. The maximum m _IPP value at daytime equals 0.3, and the minimum value at nighttime equals 0.10. Weak interday variations of the mean daytime and nighttime scintillation indices were detected. The ionospheric scintillation indices m _Ion are small compared to m _IPP at daytime, but m _Ion ? m _IPP at nighttime. On the whole, both the interplanetary plasma and ionosphere were quiet during the observations.     

Radiation conditions of a mission to Jupiter and Europa

Radiation conditions in Jupiter’s environment and the plasma environment in interplanetary space during a Jupiter-Europa mission are estimated. The numerical modeling results can be used when planning the mission.     

Evolution characteristics of Jupiter’s outer satellites orbits

A systematic study is made of the long-period evolution of all distant satellite orbits in the system of Jupiter. We determine the extreme eccentricities and inclinations, as well as the circulation periods of the pericenter arguments and of the longitudes of the nodes. Moreover, we perform a comparative analysis of the research methods employed—analytical, numerical, and numerical—analytical methods.     

Resonance orbits of near-Earth asteroids

Asteroid 99942 Apophis is one of the most hazardous NEAs (near-Earth asteroids) today. Some specific features of its travel are the possibility of repeated Earth approaches, loss of forecast precision due to trajectory dispersions, and nondeterministic motion. These specific features do not only characterize Apophis. Special methods are needed to find possible collision trajectories among these travels. These trajectories are located in the vicinity of resonance collision orbits.The present paper discusses methods of detecting hazardous trajectories in the event of nondeterministic motion and characterizing these trajectories as applied to asteroid Apophis, precision losses in the event of trajectory dispersions, conditions of determinacy losses, and hazardous trajectories in the vicinity of resonance orbits.     

Variations in solar shortwave radiation in the solar activity cycle as measured by the <Emphasis Type="Italic">CORONAS</Emphasis> satellites

The CORONAS-I and CORONAS-F data on variations in the ionizing shortwave ultraviolet (UV) solar radiation (EUV radiation) at wavelengths of less than 130 nm and near the H Lyman-alpha line are presented. The CORONAS-I data refer to the period close to solar minimum (the index F _10.7 = 80?100), and the CORONAS-F measurements were held close to solar maximum (F_10.7 = 140?280). The UV data are compared to those from the UARS and SOHO satellites and to the results obtained from the ionospheric measurements of ionosphere critical frequencies.     

Comparison of three solar activity indices based on sunspot observations

The following sunspot formation indices are analyzed: the relative sunspot number R _z, the normalized sunspot group number R _g, and the total sunspot area A. Six empirical formulas are derived to describe the relations among these indices after 1908. The earlier data exhibit systematic deviations from these formulas, which can be attributed to systematic errors of the indices. The Greenwich data on the sunspot total area A and the sunspot group number in 1874–1880 are found to be doubtful. Erroneous data at the beginning of the Greenwich series must spoil the values of the index R _g in the XVII–XIX centuries. The Hoyt-Schatten series of R _g may be less reliable than the well-known Wolf number series R _z.     

Numerical simulation of high-velocity impact ejecta following falls of comets and asteroids onto the Moon

High-velocity comet and asteroid impacts onto the Moon are considered and the material masses ejected after such impacts at velocities above the second-cosmic velocity for the Moon (2.4 km/s) are calculated. Although the results depend on a projectile type and the velocity and angle of an impact, it has been demonstrated that, on average, the lunar mass decreases with time. The Moon has lost about 5 × 10¹⁸ kg, that is, about one-hundredth of a percent of its mass, over the last 3.8–3.9 billion years. The ejection of lunar meteorites and lunar dust, rich in ³He, is considered as well. The results of the study are compared to the results of earlier computations and data on lunar meteorites.     

The Pribram,Lost City,Innisfree, and Neuschwanstein falls: An analysis of the atmospheric trajectories

To date, several meteorites have been found for which their flight in the atmosphere was recorded by special fireball camera networks. Because of this, a thorough analysis of the instrumentally registered falls is of current importance. For such fireballs, not only the high-quality photo images of the motion in the atmosphere exist, but also the density and the shape of the meteor body fragments reached the Earth’s surface are known for sure. In the present study, for the Innisfree, Lost City, and Pribram fireballs, new models of the entry to the atmosphere have been built. The values of the ballistic coefficient and the mass-loss parameter providing the best approximation for the observations of the luminous trajectory segment with the analytical solution of the meteor physics equations have been obtained. From recent results of the numerical experiments on the supersonic airflow of bodies of various shapes, the preatmospheric masses of the fireballs, as well as the dynamic estimates of the mass at the other trajectory points, were obtained. In particular, the terminal mass of the fireballs in the lower segment of the analyzed trajectories is in good agreement with the total mass of the meteorite material recovered in all of the cases considered. Moreover, to calculate the acceleration of the meteor bodies, a new analytical formula has been suggested, which allows the obtained theoretical time dependencies of the velocity and altitude to be compared with the observational data.     

Photometric function variations observed on the near side of the Moon: Mapping

During two lunations, telescopic imaging of the near side of the Moon was performed at the Maidanak mountain observatory (Uzbekistan) with the use of digital cameras based on CMOS detectors. In different ranges of phase angles, the slope of the phase function of the lunar surface was mapped at a wavelength of 0.52 μm with the method of phase ratios. It has been shown that when the phase angle is gradually decreasing, the correlation between the phase-function slope and the albedo first disappears, and then even changes its sign at small phase angles.     

Determining the age of meteor streams with the retrospective evolution method

We show that the retrospective evolution method yields excessively large inaccuracies in determining the age of meteorid streams. The cause is in its sensitivity to the errors in the initial conditions. The study was fulfilled with the Geminid, Quadrantid, Orionid, Perseid, and Leonid meteor showers as an example.     

Venusian novae (Astra): Classification and associations to different geological environments

On the Venusian surface, there can be found a rather large population of structures with prominent radial features. The term “nova” or “astrum/astra” are used to describe this special group of volcanotectonic structures with a stellate fracture pattern radiating around a central summit or fracture. In this paper, we studied the distribution and characteristics of 74 novae to determine if there are suitable ways to categorize them and to find out how this categorization could explain the differences in nova characteristics. The nova locations establish that these structures are not distributed sporadically, but they display both latitudinal and longitudinal concentrations. In addition, it is evident that the geological environments represent the major differences between individual novae. Most of them, in general, are connected to some larger volcanotectonic unit. The differences in geological surroundings can be used as the basis for characterizing novae by dividing them into different categories: (a) novae located either within or close to a rather large deformation zone, (b) novae located on plains, (c) novae located close to tessera terrain, and (d) novae situated within volcanic areas either close to volcanoes or within an area with a high density of coronae. The analysis of this characterization establishes that geological environments are the main cause for divergent nova characteristics, i.e., differences in morphology, volcanism, and topography, which, on the other hand, are possible ways to classify novae. In particular, the morphological classification (Type I, novae with features radiating from the same point; Type II, radial structures radiating from a fissure or other linear structure; Type III, lava flows or fields covering radiant point area; Type IV, semiradial structures which do not radiate from a well-defined radiant point, fissure, or area) shows some correlations between geological environments and the type of nova, indicating that the morphological appearance and the location—and, thereby, the geologic environment—of the novae are correlated to some extent.