This work is devoted to the problem of neutron field formation near elliptical orbits of space objects equipped with nuclear power plants. The high-energy part of the fission spectrum is not affected by the gravitational field. Radiation safety is ensured by the triad fair for a point source: activity-distance-time. The connection between space object orbit parameters and neutron flux density occurs for the thermal (near-thermal) part of the spectrum. The possibility of formation of a stable neutron trace in the volume of a «torus» around the orbit of a space object is considered. The paper presents theoretical and numerical evidence of the validity of the hypothesis put forward. The introduction considers the separation effect of Galileo's relativity principle in the case of rectilinear uniform motion of a point isotropic neutron source on a plane. The occurrence of angular asymmetry of the neutron distribution in a stationary coordinate system when their relative velocity is close to the transport velocity of the source is illustrated. Under these conditions, a significant velocity dispersion of initially monochromatic neutrons is also recorded. This expected fundamental kinematic effect determines the characteristic distribution of neutrons in the gravitational field when the source moves along the Kepler orbit. The solution of the problem is carried out in the velocity space. It is argued that if the distribution of neutrons in the velocity space is such that their velocities are collinear to the orbital velocity of the source, this indicates the existence of a neutron flux near the orbit. The problem is analysed on the example of one revolution of a hypothetical space station by simulation modelling. For this purpose, thermal neutron packets with isotropic angular distribution were generated at eight points of an elliptical orbit. The neutron and source velocity fluxes at the selected points of the orbit were compared in a coordinate system related to the earth. The obtained data made it possible to calculate the densities of neutron velocity fluxes to the front and rear hemispheres relative to the source orbital motion as a function of the polar angle, while the value of the determinant of the correlation matrix – an indicator of collinearity of neutron velocity vectors in the flux - was fixed. The results of the studies confirm the hypothesis put forward about the possibility of formation of a «trace» in the orbit of a thermal neutron source, which determines the need to take it into account as a significant component of radiation risk.