The paper presents the principle of operation, the main components and the results of the work of the software created in the Sternberg Astronomical Institute of Moscow State University. The PC is designed for processing of large volumes of space geodetic data. The developed software was used to process inter-satellite measurements of a space-based constellation intended to measure the parameters of the Earth’s gravitational field (EGF). The experimental option of the software enables working with both simulated data and real data of GRACE and GRACE Follow-on missions. This experimental version was used to recover the EGF parameters on real GRACE and GRACE-FO mission data. Solutions were developed for every month within the measurement time intervals from 2010 to 2021, as well as for extended time intervals of 4.3 and 7.6 years. A comparison of the obtained solutions with the results of the EGF recovery obtained by other researchers is presented.

Nonstandard techniques to deliver a payload from the Moon to Earth are explored. Two approaches are compared, which are based on using a space elevator and an acceleration device, the Artsimovich railgun. The energy needed to launch a payload to a low lunar orbit and the L_1 libration point in the Earth–Moon system is estimated. We conclude that the railgun is economically advantageous compared to the space elevator and standard jet technologies.

A near-Earth gravity experiment is considered in which a pair of satellites exchange laser signals. As a concrete example, numerical estimates were made using the satellite configuration in the GRACE-FO mission. An expression for the signal phase is obtained, which provides an accuracy of 1 picometer (pm) when calculating the distance between satellites. The influence of all significant gravitational effects on the signal propagation, such as the gravimagnetic field of the Earth and the tidal fields of the Sun and Moon, is considered. Special attention is paid to the study of the contributions of the Earth's potential harmonics. Phase perturbations of the first and second orders are considered, and it is shown that the effect of the second-order corrections lies beyond the accuracy of 1 pm. This makes it possible to express the signal phase in a fairly compact form.

— The theory of relativistic reductions for future challenges of space gravimetry with target accuracy of up to 1 picometer is developed in this paper.

The advancement of space technology opens new perspectives in developing high-resolution models of the Earth’s gravitational field. The use of a precision laser interferometric system requires taking relativistic effects in the inter-satellite ranging within the satellite constellation into account. The main quantity measured by the laser system is the phase incursion of the laser beam when passing a double one-way range between the satellites. A solution for the relativistic phase is obtained that considers not only the usual Shapiro term but also the contribution of the quadrupole term to distributions of the Earth’s mass, the Earth’s spin, and tidal gravitational fields caused by the gravitational potentials of the outer bodies of the Solar System. Relativistic reduction terms are estimated at the accuracy level of ∼1 nm, which fully satisfies the accuracy of precision measurements in the two-spacecraft formation. It will be necessary to take the relativistic effects of the next order of smallness into account in the next-generation gravitational twin missions.

This review considers the problem of autonomously determining the position of a spacecraft in space based on the analysis of pulses emitted by X-ray pulsars. The characteristics of the prospective equipment and lists of pulsar candidates for reference sources are given. The navigation algorithm and resulting accuracy characteristics are substantiated.

The conference “Modern Astrometry 2017,” which took place on Octobr 23–25, 2017 at the Sternberg Astronomical Institute of Lomonosov Moscow State University, was dedicated to the memory of the eminent astrometrist, teacher, and outstanding scientist and Doctor of Physical–Mathematical Siences Konstantin Vladslavovich Kuimov, who worked at the Sternberg Astronomical Institute during 1962–2017. This article is based on a presentation made at this conference.

It has recently become clear that the potential role of astrometry in cosmological studies has been underestimated. Some areas of cosmology that should be investigated using astrometrical methods are discussed. This paper is based on a presentation made at the conference “Modern Astrometry 2017,” dedicated to the memory of K.V. Kuimov (Sternberg Astronomical Institute, Moscow State University, October 23–25, 2017).

Astronomical catalogs created as a result of the “Carte du Ciel” project are considered, including the work of K.V. Kuimov in this area, its methodological importance, and perspectives in the GAIA era. This paper is based on a presentation made at the conference “Modern Astrometry 2017,” dedicated to the memory of K.V. Kuimov (Sternberg Astronomical Institute, Moscow State University, October 23–25, 2017).

A new version of the HDEC (Henry Draper Extension Charts) catalog is presented. The catalog includes 88,548 entries, more than 3500 of which (components of binary systems) were earlier corrupted by an algorithmic error (1579 multiple systems were revealed). Spectral classification of these objects has been corrected manually using the CDS data. We also corrected some mistakes of the catalog detected by the measurement model and cross matching with other CDS catalogs, and, in some cases, by the authors of the catalog and through collaboration of the HDEC users.

In this paper, the apparent motions of quasars, which are the reference sources of the international celestial reference system (ICRS), are analyzed. Kinematic parameters from four catalogs compiled by different research groups are used. Apparent motions are expanded on a special set of vector functions on the sphere that are an irreducible representation of the rotation group O(3). The degree of the noninertiality of the barycentric reference system caused by the rotation of the solar system around the galactic center is estimated according to expansion coefficients. The direction and magnitude of the acceleration vector are calculated and compared with the alternative estimates. This method is discussed as a way to test Newton’s law on a large scale.

Binary stars are considered as possible sources of monochromatic gravitational waves. The amplitude of corrections to the metric generated by such sources is discussed. Three systems that have amplitudes for stresses of the metric exceeding 10 −20 are identified (V1182 Aql, V3903 Sgr, and DH Cep).

We consider the detection of cosmic strings using observations of the anisotropy of the Cosmic Microwave Background. Several methods for detecting cosmic strings are analyzed, using a threshold filter and expansion in orthogonal Haar functions. Computer simulation provides estimates of the noise present in experiments aimed at detection of cosmic strings. Attempts to detect cosmic strings were carried out using the full-sky ILC map obtained as a result of the WMAP space mission. A list of cosmic string candidates has been compiled using the Haar function method.