The Russian Academy of Sciences and Federal Space Agency, together with the participation of many international organizations, worked toward the launch of the RadioAstron orbiting space observatory with its onboard 10-m reflector radio telescope from the Baikonur cosmodrome on July 18, 2011. Together with some of the largest ground-based radio telescopes and a set of stations for tracking, collecting, and reducing the data obtained, this space radio telescope forms a multi-antenna groundspace radio interferometer with extremely long baselines, making it possible for the first time to study various objects in the Universe with angular resolutions a million times better than is possible with the human eye. The project is targeted at systematic studies of compact radio-emitting sources and their dynamics. Objects to be studied include supermassive black holes, accretion disks, and relativistic jets in active galactic nuclei, stellar-mass black holes, neutron stars and hypothetical quark stars, regions of formation of stars and planetary systems in our and other galaxies, interplanetary and interstellar plasma, and the gravitational field of the Earth. The results of ground-based and inflight tests of the space radio telescope carried out in both autonomous and ground-space interferometric regimes are reported. The derived characteristics are in agreement with the main requirements of the project. The astrophysical science program has begun.

This paper describes outstanding issues in astrophysics and cosmology that can be solved by astronomical observations in a broad spectral range from far infrared to millimeter wavelengths. The discussed problems related to the formation of stars and planets, galaxies and the interstellar medium, studies of black holes and the development of the cosmological model can be addressed by the planned space observatory Millimetron (the "Spectr-M" project) equipped with a cooled 10-m mirror. Millimetron can operate both as a single-dish telescope and as a part of a space-ground interferometer with very long baseline.

High-resolution imaging of supermassive black hole shadows is a direct way to verify the theory of general relativity under extreme gravity conditions. Very Long Baseline Interferometry (VLBI) observations at millimetre/submillimetre wavelengths can provide such angular resolution for the supermassive black holes located in Sgr A* and M87. Recent VLBI observations of M87 with the Event Horizon Telescope (EHT) have shown such capabilities. The maximum obtainable spatial resolution of the EHT is limited by the Earth's diameter and atmospheric phase variations. In order to improve the image resolution, longer baselines are required. The Radioastron space mission successfully demonstrated the capabilities of space–Earth VLBI with baselines much longer than the Earth's diameter. Millimetron is the next space mission of the Russian Space Agency and will operate at millimetre wavelengths. The nominal orbit of the observatory will be located around the 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 a near-Earth high elliptical orbit (HEO). In this paper, a set of near-Earth orbits is used for synthetic space–Earth VLBI observations of Sgr A* and M87 in a joint Millimetron and EHT configuration. General relativistic magnetohydrodynamic models for the supermassive black hole environments of Sgr A* and M87 are used for static and dynamic imaging simulations at 230 GHz. A comparison preformed between ground and space–Earth 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 the dynamics at fast time-scales.