This article is devoted to moment interactions of rigid bodies. It consists of four parts:

- Statement of the problem.
- The potential energy of gravitational interaction between two remote bodies. Gravitational moment.
- The motion of a body with rotational symmetry fixed in its centre of mass under effect of gravitational moment caused by mass point.
- The orthotropical continuum of rotating particles.

It seems to be necessary to take into consideration rotational degrees of freedom of particles forming real bodies. In terms of theory of moment elasticity media is continuum of small rigid bodies. But it describes well infinitesimal turnes only while taking spins of particles into account seems to be quite important.

To create a model of continuum of rotating particles it is necessary to have ideas about the structure of moment interaction between particles. The law of gravity is the fundamental law of nature. So we can try to use it as a base for modelling of moment interaction.

In part 2 we consider two remote gravitationally interacting bodies of general shape. The formula of potential energy of their interaction is obtained in terms of series. The explicit formulas of some terms of potential energy and gravitational moment are derived. The first term in moment series is zero for rigid bodies, the second and the third terms depend on the turn of the body under effect of moment and the mass of the second one. The third term is equal to zero for body with rotational symmetry. The forth term in the series depends on relative turn of bodies.

The case of a rigid body under effect of gravitational moment caused by mass point is the first approximation for the problem of two interacting rigid bodies. Part 3 is devoted to the problem of a body with rotational symmetry in Newton field of forces. This problem is discussed in literature. The new result is investigation of the regular precession and its stability.

It would be interesting to study the influence of the forth term in moment series depending on relative turn of particles. Let us consider an infinite cubical lattice in points of which similar bodies with rotational symmetry are fixed. In such a system the forth term in moment series (depending on a relative turn) becomes the general one. The motion of this system is investigated in part 4. The bodies rotation on their axes coinciding with one of lattice axes is possible. The equation of motion of the particle is linearized relatively to the described stationary rotation. Then this equation is continualized. Thus we obtain equations of dynamics of the linear continuum of rotating particles. But we can see that this media does not exist: this motion is unstable although the rotation makes it stable relatively to larger domain of perturbations. Hence it can be concluded that for existing of such media the base interaction must be of another nature.

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