Millimetron is a space observatory for millimeter and sub-millimeter observations planned for launch around 2030. The 10-meter diameter space unfolded telescope will be cooled down to 10 K and operated in the vicinity of Lagrange point L2. Mission lifetime is 10 years and it includes astronomical observations in two modes: as a space-ground interferometer and as a single-dish telescope. This paper presents the results of the Millimetron space observatory orbit design that takes into account technical and scientific requirements and constraints. It covers the computation of suitable operational orbits, the selection of an orbit, and the transfer from Earth. Furthermore, scientific objectives are demonstrated through VLBI visibility simulation and image reconstruction. Unlike previous works that used analytical methods, this work employs numerical integration for orbital design. Based on the orbital design methods developed in this work, the exact dates for departure, halo formation, and trajectory correction were determined. Additionally, the short baseline projections and its specific dates for VLBI mode were found. The feasibility of scientific objectives were demonstrated through VLBI visibility simulation and image reconstruction.

The Millimetron Space Observatory will be equipped with the cryogenically cooled instrument for a Space-Earth Very Large Baseline Interferometry (S-E VLBI). It will be a multi-channel heterodyne receiver with 7mm, 3mm, 1.3mm and 0.8mm channels. The VLBI instrument will have a multi-frequency capability, provided by signal splitting in the input optics and by back-end functionalities. The optical design is shown in this report.

The paper examines the possibilities of using the multifrequency synthesis method to improve the quality of images obtained by the space-ground very long baseline radio interferometer mode of the Millimetron observatory. Simulation of imaging observations for the close vicinity of the supermassive black hole M87 was carried out. The advantages of multifrequency synthesis compared to single-frequency observations are shown. The requirements and limitations of its applicability to space-ground interferometry with the Millimetron observatory are formulated.

Searching for a suitable very long baseline (VLBI) interferometer geometry is a key task in planning observations, especially imaging sessions. VLBI image quality is characterized by (u,v)-coverage. With one or more radio telescopes located in space, such a task becomes more complex. This paper presents a method of recovering the optimal orbital parameters for space radio telescopes having a given desired (u,v)-coverage. In turn, this task can be called the inverse of the task of searching for the optimal geometry and orbital configurations of space-ground and pure space VLBI interferometers.

Spacecraft positioning plays a crucial role in scientific space mission design, as well as in the further scheduling of scientific observations for such a mission. We examine the application of global navigation satellite systems (GNSS) to solve the orbit determination problem in a pure space very long baseline interferometer (VLBI) project. A network of GPS, GLONASS, Galileo and BeiDou navigation satellites may be a more efficient solution to determining the position and velocity of space radio telescopes and space interferometer baselines. For such a project, it is necessary to take into account the special conditions of GNSS observations, as well as the high accuracy of determining not only position but also velocity. In this paper, we estimate visibility of navigation satellite systems for Low and Medium orbits of a pure space-VLBI system and simulate GNSS code and phase measurements. Orbit determination was performed on smoothed code measurements. Phase measurements simulated with a step of 1 s and combined in Doppler measurements yield average position and velocity errors of 1.01 m and 8.8 mm/s in Medium Earth orbit. The results showed that GNSS observations are sufficient to solve the problems of orbit determination of a space-VLBI interferometer both in Low-Earth and Medium Earth orbits.

В работе рассмотрены научные и технические перспективы и возможные направления развития субтерагерцовой астрономии в Российской Федерации. Предложена концепция создания субтерагерцовых инструментов в виде универсальной компактной антенной решетки для размещения на территории России. На базе концепции такой антенной решетки возможна реализация нескольких космических проектов субтерагерцового диапазона нового поколения – космического интерферометра и телескопа, расположенного на поверхности Луны. Наземные антенные решетки смогут выступить в качестве поддержки режима интерферометра со сверхдлинной базой обсерватории «Миллиметрон».

The paper examines the possibilities of using multi-frequency synthesis methods for very long baseline (VLBI) space radio interferometers to improve the (u,v) coverage and the quality of the resulting synthesized images. To evaluate the contribution of multi-frequency synthesis methods, simulations of VLBI observations were performed using the example of the space VLBI concept that is based on a combination of circular near-Earth orbits.

This paper addresses the scientific and technical prospects and potential directions for the development of subterahertz astronomy in the Russian Federation. The concept of creating subterahertz instruments in the form of a universal compact antenna array for placement on the territory of the Russian Federation is proposed. It is possible to implement several space projects in the subterahertz range using such an antenna array, including a space interferometer and a telescope on the surface of the Moon. Ground-based compact antenna arrays will be able to act as a support for the very long baseline interferometer mode of the Millimetron observatory.

This paper examines options for orbit configurations for a space interferometer. In contrast to previously presented concepts for space very long baseline interferometry, we propose a combination of regular and retrograde near-Earth circular orbits in order to achieve a faster filling of $(u,v)$ coverage. With the rapid relative motion of the telescopes, it will be possible to quickly obtain high quality images of supermassive black holes. As a result of such an approach, it will be possible for the first time to conduct high quality studies of the supermassive black hole close surroundings in dynamics.

In this paper, we describe the first multi-frequency synthesis observations of blazar 0059+581 made with the Radioastron space-ground interferometer in conjunction with the Korean VLBI Network (KVN), Medicina and Torun ground telescopes. We conducted these observations to assess the spaceground interferometer multi-frequency mode capability for the first time.

As part of the creation of the Millimetron Space Observatory, the task was set to develop a reliable tool for ballistic and navigational support of the Spektr-M spacecraft. This article describes software developed to determine and refine the orbital parameters of spacecraft, including the Millimetron Observatory. This paper briefly describes the project of the Spektr-M observatory, algorithms for determining the orbit, and presents the results of the software. In addition, the number of ground-based tracking stations was estimated for optimal measurements of the orbit of the Spektr-M spacecraft to ensure the required orbital accuracy and to reduce the time the space observatory is out of sight. The implemented algorithms were tested on model and real observation data.

Imaging of the shadow around supermassive black hole (SMBH) horizon with a very long baseline interferometry (VLBI) is recognized recently as a powerful tool for experimental testing of Einstein’s General relativity. The Event Horizon Telescope (EHT) has demonstrated that an Earth-extended VLBI with the maximum long base (D = 10, 700 km) can provide a sufficient angular resolution θ ∼ 20 μas at λ = 1.3 mm (ν = 230 GHz) for imaging the shadow around SMBH located in the galaxy M87. However, the accuracy of critically important characteristics, such as the asymmetry of the crescent-shaped bright structure around the shadow and the sharpness of a transition zone between the shadow floor and the bright crescent silhouette, both of order Δθ ∼ 4 μas, is still to be improved. In our previous paper we have shown that Space-Earth VLBI observation within a joint Millimetron and EHT configuration at the near-Earth high elliptical orbit (HEO) can considerably improve the image quality. Even more solid grounds for firm experimental validation of General relativity can be obtained with a higher resolution available within the joint Millimetron and EHT program at the Lagrangian point L2 in the Sun-Earth system with an expected resolution of Δθ ∼ 0.1 μas. In this paper we argue that in spite of limitations of L2 orbit an adequate sparse (u, v) coverage can be achieved and the imaging of the shadows around Sgr A∗ and M87∗ can be performed with a reasonable quality.

In this contribution a primary feasibility study of different orbital configurations for Millimetron space observatory is presented. Priority factors and limitations were considered by which it is possible to assess the capabilities of a particular orbit. It included technical and scientific capabilities of each orbit regarding the fuel costs, satellite observability, the quality of very long baseline interferometric (VLBI) imaging observations and source visibilities.

High resolution imaging of supermassive black holes shadows is a direct way to verify the theory of general relativity at extreme gravity conditions. Very Long Baseline Interferometry (VLBI) observations at millimeter/sub-millimeter wavelengths can provide such angular resolution for supermassive black holes, located in Sgr A* and M87. Recent VLBI observations of M87 with the Event Horizon Telescope (EHT) has shown such capabilities. The maximum obtainable spatial resolution of EHT is limited by Earth diameter and atmospheric phase variations. In order to improve the image resolution longer baselines are required. Radioastron space mission has successfully demonstrated the capabilities of Space-Earth VLBI with baselines much larger than Earth diameter. Millimetron is a next space mission of the Russian Space Agency that will operate at millimeter wavelengths. Nominal orbit of the observatory will be located around Lagrangian L2 point of the Sun-Earth system. In order to optimize the VLBI mode, we consider a possible second stage of the mission that could use near-Earth high elliptical orbit (HEO). In this contribution a set of near-Earth orbits is used for the synthetic space-ground VLBI observations of Sgr A* and M87 in joint Millimetron and EHT configuration. General-relativistic magnetohydrodynamic models (GRMHD) for black hole environment of Sgr A* and M87 are used for static and dynamic imaging simulations at 230 GHz. A comparison preformed between ground and space-ground baselines demonstrates that joint observations with Millimetron and EHT significantly improve the image resolution and allow the EHT+Millimetron to obtain snapshot images of Sgr A* probing dynamics at fast timescales.

Very long baseline interferometry (VLBI) is a unique technique allowing observations of the most compact astronomical objects with high angular resolution. In this study, we demonstrate the capabilities of the Millimetron VLBI mode regarding the tasks of two-dimensional imaging of black hole shadows and observing compact structures around them. Attention is paid not only to the sensitivity and frequency configuration of the space–ground interferometer, but also to its geometry, namely possible orbital configurations of the Millimetron observatory and their observational capabilities.

Within the Radioastron interferometer scientific program, observational data of the H2O maser at a frequency of 22.2280 GHz in the NGC 2071 nebula were processed. A space radio telescope (SRT — 10 m) and three radio telescopes of the ground network: RT — 32 m (Medicina, Italy), RT — 32 m (Torun, Poland) and RT —64 m (Kalyazin, RF) took part in the observations. A map of the maser spot distribution has been obtained, where there are 13 spatial components with VLSR in the range 4.7 — 20.5 km/s. Correlation is observed on ground-space baselines for the component on VLSR = 14.3 km/s. Based on the visibility function dependence analysis from the baseline projection values, there was proposed a twocomponent model of this component spatial structure with the dimensions of the extended and compact constituent of 4 and 0.06 msec, i.e. 1.56 and 0.023 au, respectively.

The observational data of an H2О maser at a frequency of 22.2280 GHz in the dark reflection nebula NGC 2071 in the direction of the infrared object IRS 1 at the target coordinates RA(2000) = $${{05}^{{\text{h}}}}{{47}^{{\text{m}}}}04_{.}^{{\text{s}}}758$$ , DEC(2000) = $$00{}^\circ 21' 42_{.}^{'' }700$$ have been processed as part of the scientific program of the ground-space interferometer RadioAstron. The duration of the session on January 11, 2014 was 70 min. The space radio telescope (SRT-10) and three radio telescopes of the ground-based network took part in the observations: RT-32 (Medicina, Italy), RT-32 (Toruń, Poland), and RT-64 (Kalyazin, Russia). The following parameters were implemented: angular resolution 70 μs at the ground-space baseline with maximum baseline projections 3.1 ED ( $$ \sim {\kern 1pt} 40{\kern 1pt} {\kern 1pt} 000$$ km); synthesized beam of the ground-based part of the interferometer $$0.006'' \times 0.0006'' $$ (PA = –23°); spectral resolution 7.81 kHz (i.e., 0.11 km/s). A map of the distribution of maser spots with 13 spatial components was obtained. The map has a size $$ \sim {\kern 1pt} 100 \times 100$$ mas (milliarcseconds), which corresponds to $$ \sim 40 \times 40$$ AU at a distance of 390 pc to the nebula. The range of the line-of-sight velocities of the components is 4.7–20.5 km/s with a width of spectral features 0.2–0.6 km/s; the density of the correlated flux at the line maximum varies from $$ \sim {\kern 1pt} 4$$ to $$ \sim {\kern 1pt} 29$$ Jy. There was recorded one spatial component (with a radial velocity of 14.3 km/s) for which there was a correlation at the ground-space baselines SRT–Tr and SRT–Mc at an ultrahigh angular resolution with a reliability level above 6σ. Based on the analysis of the dependence of the visibility function on the baseline projections, a two-component model is proposed for the spatial structure of this component with the angular dimensions of the extended and compact constituents 4 mas and 0.06 mas, i.e., 1.56 AU (with an uncertainty of 10%) and 0.023 AU (with an uncertainty of 50%), respectively.