2. Gravitational field

Any field may be presented by a totality of two components: potential and vortex (solenoidal). As to the latter, nothing is clear about it in relation to gravitational field. In any case neither the gyroscopes well screened from the effect of magnetic field nor the rotating cosmic bodies are likely to orientate the rotation axes parallel to each other, what could be inevitable if sufficient vortex component of gravitational field was present.

So we will describe gravitational field as a potential field the only source of which is a body mass m , so for it

, (12à)
or
, (12b)
where  - volumatic density of mass in given point, D0 - density vector of gained mass, analogous to the vector of shift flow in electrodynamics, S - square of the arbitrary closed around m of the integration surface

Let us pay attention to the fact that, different from electrodynamics where the equations similar to (12 a) and (12b) stay invariable in all regimens, and dynamics is reflected in solenoidal component of electromagnetic field, due to the absence of any gravitational field rotation the dynamics is expressed in the weakening of potential field.

Truly, as

D0 = dmg /dS, (13)
where mg- mass, gained by field on the surface dS, normal to vector D0, à dS = dl x dl, where dl - length of an area dS side, then according to (6à) at the motion of the field source with velocity v along one of the area dS sides in the average there will be a seeming increase of the area up to  and a corresponding reduction (13) up to
. (13à)

So instead of (12 a) and (12b) in general case we have

(14à)
or
. (14b)
However the latter expression (14b) is true only if all mass m moves with velocity v. If separate parts of a body move with different velocities vk, as in the case of a body rotation, then
(14c)

where V - cubic capacity of a body inside closed surface S.

In particular, as the radial component of gravitational field of a rotating hoop is (13a), then, deducting it from the same component of the gravitational field of a stationary hoop, we get the so-called-God-knows-what- field D- of mass rotation

(14d)

where- angle velocity of hoop rotation, R - its radius. In case of spherical field symmetry from (14b) there results  or , which corresponds to Newton's rule of a moving body.

For two bodies with masses m1 è m2, moving with velocities v1 è v2, we also have

, and (14à) in transformed to

, (15)
which for v1 = v2 = v gives
. (15à)
-hus if the experimenter judges the value of the moving mass by density D gained by its mass field, then for him the body mass as if reduces , times which of course is due to the special features of the gravitational method of measuring D, but not to the real reduction of the mass of the moving body. As to D, at mutual motion with equal velocities v of the interacting bodies
D** = D0 (1 - v2/ñ2). (16)
Now getting back to statics let us remember the principle of statics and kinematics equivalence in gravitation. According to this principle the U potential of gravitational field in size and on the whole is equivalent in number to kinetic energy of a trial body in calculation by its mass unit, and the body would acquire this energy if it was flying freely from the infinity till the given point, coming up to velocity v, so that |U| = v2/2.

In other words, the potential of gravitational field is expressed as a square of some false velocity with which the two interacting bodies move, and according to this D is subject to (16) with v2 being replaced for U, i.e. even in statics we have the following instead of (12a) 
or

, (17)
where D = D0 (1 - U/c2).
Let us pay attention to the fact that (17) differs by form from (15a), for field potential U unlike v has a gradient. Besides, as it results from (17), due to the mass and energy equivalency, not only mass but the energy of a field itself can be the source of a field. Truly, having written (17) again in the form divD =(1 - U/c2) - (DgradU/c2)/(1 - U/c2), it is easy to see that the second item from the right is a volumatic density of mass which was initiated by field energy, the density of which is -DgradU/(1 - U/c2).
This corresponds to (10), i.e. false kinetic energy, though (17) describes the field statics.
Thus, even if = 0, divergence of gravitational field is not always zero, for in this occasion divD = - DgradU/(1 - U/c2) # 0. This is non-linearity of gravitational field if compared with a linear electromagnetic field.