**Abstract**

Mathematical models of the controlled motion of a spacecraft with a solar sail and the possibilities are considered, taking into account the translational motion in the gravitational field, the forces of light pressure, and rotational motion relative to the center of mass. The structure of possible problems of photogravitational celestial mechanics is proposed. To control movement, it is possible to change the size, shape, surface properties, and orientation of the elements of the sail system in relation to the flow of sunlight. The equations of motion can be presented on the basis of the problem of motion in a photogravitational field, taking into account the action of other disturbing forces. When studying the orbits of motion in the vicinity of the Earth, one should use a more general model of the photogravitational field of the restricted three-body problem. In this case, the gravitational action of the Sun and the Earth is supplemented by the field of forces of light pressure, which makes it possible to simulate real problems of dynamics.

**Keywords:** light pressure, photogravitational field, space flight, solar sail, spacecraft
