The Study deals with a problem of the spacecraft (SC) flights between the Earth and Geostatio-nary Equatorial Orbit (GEO), especially with a problem of the SC re-entry from the GEO to the Earth. In addition to “direct” return trajectories with initial decreasing velocity of spacecraft and flight to Earth, there are proposed, received and studied some “detour” ones using initial increasing velocity, flight to Moon, a lunar gravity assist and following flight to the Earth. It is shown that from the energy point of view the “detour” flight with the lunar gravity assist is better considerably than the “direct” one. The sets of the trajectories for the GSO-Earth flight are constructed. Osculating perigee radius of the final orbit at the entrance to Earth’s atmosphere is varied here from zero to about the Earth radius. These trajectories can be used for the spacecraft destruction at Earth’s atmosphere and for its soft landing on the Earth surface. The trajectories are presented with the flyby of the Moon near both ascending and descending nodes of the lunar orbit relatively Earth’s equator plane. There are analyzed the peculiarities which are caused by the fact that the geographic longitude of the spacecraft on GSO is fixed. An analysis of permissible deviations in initial data because of the rocket-launcher errors is given for the re-entry trajectory with a normal nominal entrance to the Earth atmosphere. It is shown that the permissible errors are large enough, and these trajectories can be implemented without the orbital correction.

Theoretical and applied problems of mechanics