*Astrodynamics in Photogravitational Field of the Sun: Space Flights with a Solar Sail DOI: http://dx.doi.org/10.5772/intechopen.102005*

Opening the sail in orbit will cause the light pressure to partially compensate for the sun's gravity. If the gravitational field of attraction is supplemented by the field of forces of light repulsion, then for problems of celestial mechanics one can speak of a mathematical model of the photogravitational field [3–5]. The acceleration imparted to the spacecraft by the flow of solar rays depends on the ratio of the sail area to the mass of the entire structure. With such modeling, it is sufficient to restrict oneself to taking into account two main forces: the gravitational interaction of bodies *Fg* and the light pressure *Fp* on the body from the flow of solar radiation. But for problems of motion in the vicinity of the Earth, it is necessary to take into account the features of the Geopotential and other forces (atmospheric resistance, the influence of other bodies, etc.).

The use of a solar sail will provide the spacecraft with a low-thrust engine, which has an almost unlimited supply of fuel. However, it has a disadvantage: Unlike jet engines, we cannot use its thrust in an arbitrary direction with the same efficiency. The resulting force is determined by the position of the spacecraft in space, as well as by the orientation of all elements of the solar sail relative to the attracting centers and centers of radiation. It is necessary to specifically orient the sail to obtain the desired change in orbital parameters.

Problems of motion control with a solar sail lead to the study of mathematical models of dynamics in photogravitational fields of orbital motion and problems of control over the rotation of the entire spacecraft complex relative to the center of mass [2–21].

The influence of the main forces determines not only the orbital and rotational motion, but can also be used to implement control during interplanetary flights and maneuvering in the sphere of action of the next planet, or to stabilize the spacecraft orientation during its orbital motion. This will make it possible to form the direction and thrust of such a solar-powered engine with an unlimited margin (solar sails with a good mirror surface for reflecting the light flux), which depends on the distance to the source, and the area and shape of the surface of the spacecraft sail elements [3, 9].
