MSTU named after NE Bauman Faculty of Special Mechanical Engineering - Department M1 "Spacecrafts and launch vehicles", M2 "Aerospace systems".
I studied there, we recruited. You need excellent health, 99% did not pass the medical examination.
Knowing space is a very exciting and ambitious goal! And this is what astronomers (in theory) and cosmonates (in practice) do :))
Not very many Russian universities teach in programs related to astronomy and cosmautics, those that conduct such programs: MAI, MIPT , RUDN, KFU, SPbPU Peter the Great, Lomonosov Moscow State University, SPbSU, Ural Federal University named after M.V. B.N. Yeltsin and others.
Look here for a detailed description of programs related to astronomy, and here are programs after which you can become an astronaut. For admission to all programs, you need to take the Unified State Exam in Russian, physics and mathematics of the profile.