We investigate four modes of the spacecraft Progress uncontrolled attitude motion, which are offered for carrying out experiments in microgravity science. They are 1) triaxial gravitational orientation, 2) gravitational orientation of a rotating satellites, 3) spacecraft rotation in the orbital plane around the axis of the maximal moments of inertia, 4) biaxial spacecraft rotation in the orbital plane. Three conditions are tested for these modes: stability (invariability of the main characteristics of the motion in long time intervals, weak dependence on errors in setting of initial conditions), the low level of residual accelerations on board the spacecraft, acceptable mean electric current from the solar arrays. The tests are carried out by mathematical modelling of the spacecraft attitude motion under the action of the gravitational and aerodynamic torques. We describe the situations in which some mode has advantages over others. For example, triaxial gravitational orientation provides the minimal acceleration level in short (less two days) time intervals. It provides acceptable mean current from the solar arrays only in the case when the sun is sufficiently far from the orbital plane.

Theoretical and applied problems of mechanics