A brief outline of the development of ideas and a review of some achievements in modern celestial mechanics are presented. The emphasis is on the fact that the classical definition of this science given by Laplace does not fully reflect the content of modern celestial mechanics, and the term dynamic astronomy is more capacious. Dynamic astronomy studies almost everything that moves and rotates in space: from dust particles to comets and asteroids, from artificial satellites, planets, and their satellites to stars and galaxies. This complex science includes problems of both classical and relativistic celestial mechanics; it includes the theory of equilibrium figures and various numerical and computer simulation methods. Qualitative methods are of great importance, the culmination of which was the creation of the KAM theory. The development of celestial mechanics went through the practice of various applications, and the range of problems in it is exceptionally wide. A striking stimulus for the development of dynamical astronomy was the discovery of exoplanets around other stars. The article traces a chain of ideas from Keplerian orbits to osculating Lagrangian ellipses, from two-body problems to many-body problems, and from Gaussian rings to models built on the basis of precessing analogues of these rings.

At the LPA LPI radio telescope, a search was conducted for pulse signals in a specific area with declinations + 52^circ < delta < + 55^circ . The processing involved ten months of observations recorded in six frequency channels, each with a channel width of 415 kHz and a total bandwidth of 2.5 MHz. The analysis of the data revealed 22 000 events, exhibiting a pronounced dispersion delay of signals over the frequency channels, which are indicative of pulsar pulses. These pulses were found to belong to four known pulsars and two new rotating radio transients (RRAT). Additional pulse search was carried out in 32-channel data with a channel width of 78 kHz. This led to the discovery of 8 pulses for the transient J0249+52 and 7 pulses for the transient J0744+55. No periodic emission of transients was detected. The analysis of the observations indicates a high probability that the identified RRATs are pulsars with nullings, where the fraction of nullings is greater than 99.9%.

In this paper, we have studied the effect of oblateness of the Earth on the resonant curve in synchronous satellite under the gravitational effect of the Sun, the Moon and the Earth. By following the procedure of Frick and Garber (1962), we obtained the equations of motion of the synchronous satellite in the form of a second order linear differential equation by using the perturbation technique. From the solution, we observed that oscillatory amplitude becomes infinitely large when the ratio of two frequencies $$\dot {\alpha }$$ (angular velocity of the bary-center system around the Sun) and $${{\dot {\theta }}_{{\text{E}}}}$$ (spin rate of Earth) are commensurable. With the help of different graphs, we have shown the effect of $$\alpha $$ and $${{J}_{2}}$$ (coefficient of Earth's oblateness) on the resonant curves. It is observed that oscillatory amplitude increases when $$\alpha $$ (orbital angle of the bary-center system around the Sun) increases and the value of $${{J}_{2}}$$ is very close to zero. We also analyzed the phase portrait and phase space by using the method of Poincare section when the system is free from all the forces. Finally, we have obtained the expression for the energy integral, motion of mean longitude near the synchronous satellite.

We study the light-time effect in the eclipsing binary system FL Lyr using data of the Kepler and TESS space missions. We demonstrate that the system contains a candidate exo-Jupiter FL Lyr b, its probable orbital period being about 22 years.

A new 3D parallel numerical code in spherical coordinates has been developed to study the stellar wind flow around hot Jupiter. The peculiarity of the spherical coordinate system in the vicinity of the poles is overcome by using a ternary spherical grid, which is a composite grid consisting of three separate sectors. The numerical model of multicomponent magnetohydrodynamics, developed earlier for Cartesian coordinates, has been transferred to the new model. The results of a numerical calculation of the structure of an extended envelope of a quasi-open type for the case of a super-Alfvenian flow around a hot Jupiter are presented. We showed that the spatial resolution of the grid is sufficient for a self-consistent calculation of the structure of the atmosphere of a hot Jupiter. This allows further use of the new model for 3D aeronomic calculations.

On the Large Phased Array (LPA) of Lebedev Physics Institute (LPI), a search for pulsars outside the Galaxy plane was carried out in a 300 sq. deg area. The search with a sensitivity 5-10 times better than that of previously conducted surveys was at a frequency of 111 MHz. The search was carried out in the summed power spectra. With an accumulation equivalent to 100 hours of continuous observations for each point of the area, 5 known pulsars were detected with a signal-to-noise ratio (S/N) from 20 to 1300 in the first harmonic of the spectrum. Average profiles were obtained for the detected pulsars. Estimates of the peak and integral flux densities of the found pulsars are given for individual sessions and for the power spectra summarized over 5.5 years, obtained using the developed method based on measurements of the height of harmonics in the power spectrum. No new pulsars have been detected in the area. Apparently, when searching for pulsars in the area, we have approached the lower limit of the luminosity of the second pulsars. The completeness of the survey is at the level of 0.5 mJy.

A technique is described for achieving high accuracy (relative error up to ≈0.001%) for measuring the absolute wavelengths of the spectral lines of multiply charged ions with an average (Z = 17–25) by the nuclear charge, the spectra of which can be used for plasma diagnostics in laboratory astrophysics experiments. It is based on irradiation with subnanosecond laser pulses with an intensity of 1015–1016 W/cm2 targets with a multicomponent chemical composition, including atoms with both medium and low Z. The presence of the latter ensures the presence in the emission spectrum of the resulting laser plasma of lines of hydrogen-like ions used as references. An atomic-kinetic code was created, and the intensities of possible reference and investigated spectral lines were calculated. The principles of selecting the target material, the features of the implementation of the technique on the example of a focusing spectrometer with spatial resolution based on spherically curved mica and α-quartz crystals are considered, and specific parameters of spectrometer circuits and types of targets for precision measurement of the wavelengths of spectral lines of helium- and lithium-like ions with nuclear charges are given. Z = 13–25. The results obtained in this work will be used in the planning of fundamental X-ray spectral studies at the ELF laser facility being developed at MEPhI.

An active medium for fiber lasers is proposed, the core of which contains an epoxy oligomer structurally activated by organic dye molecules and a hardener. The hardener is a finely dispersed glass with a surface chemically activated by reactive groups with the following ratio of ingredients, in mass parts: organic dye 0.0075–0.1, epoxy oligomer 8.0–31.5, finely dispersed glass 68.4925–91.9. The technical result consists in providing the possibility of adjusting the refractive index of the active optical fiber core and, as a consequence, tuning the laser radiation wavelength to 589.6 nm to form sodium “laser guide stars.”

The features of estimating the energies of the magnetic field and relativistic electrons of synchrotron radio sources, the X-ray emission of which is produced by the invers Compton scattering of synchrotron photons (the synchrotron self-Compton process), are considered. Estimates of these physical parameters depend on the angular dimensions of the radiation sources. The effect of angular dimensions on the estimates of physical parameters is illustrated by an estimate of the magnetic induction of the hot spot A of the radio galaxy Cygnus A. We showed why it is impossible to use apparent angular dimensions of non-uniform radio sources for estimating their physical parameters. To obtain correct estimates of the energies of the field and particles, we need to use the angular size from the spherical model of the source under study, the spectrum of which coincides with the radio spectrum of the object under study. Taking such an angular size of the source, we obtain the same estimates of the physical parameters of this object, both from radio and X-ray observations.

In this paper, we theoretically study the linear polarization of radiation that arises in the lines of atomic helium in the solar chromosphere and in solar protuberances. In the visible region of the solar spectrum, several intense lines of the He I atom are observed, in which polarization can occur when the solar plasma is impacted by accelerated proton and electron flows. We present the results of calculations for two lines of the atom, namely the D3 5876 Å line, which is widely observed in the experiment, as well as the He I 5015 Å line, for which the degree of linear polarization turned out to be the highest among the lines studied by us in the helium spectrum (more than 30%). Our calculations point to good opportunities for experimental detection of polarization in both of these lines, both in the course of ground-based observations, for example, during solar eclipses, and during space experiments.