The interaction of rotating bodies is carried out by means of tidal waves, which are gravitational waves and the existence of which has recently been proved by science (February 11, 2016). The medium in which the interaction is carried out is a physical vacuum (density of 400-500 photons per cm^3; T = 2,725 K; F = 160 Ghz.)
In modern science, four types of interaction are considered: strong, weak, gravitational and electromagnetic. In this case, the gravitational interaction is considered in the form in which it was formulated by I. Newton; that is, in the static state of non-rotating bodies.
In the absence of rotation of the two bodies [FIG.1] relative to each other, their interaction is determined by mutual attraction with a force in accordance with the Law of Universal Gravitation, while there are tidal accelerations that are not taken into account by the law of Universal attraction. Tidal accelerations occur due to the difference in the accelerations of points of bodies at different distances from the source of gravity.
δw zi = a zi — a si (for the zenith point) 
δw ni = a ni — a ci (for the nadir point)
where: a ci is the acceleration of the center of the body;
and zi , and ni are the accelerations of points of the body that are at different distances from the center .
| δw zi | > | δw ni | — therefore, bodies have an additional attraction (during attraction or entrainment), in A. Einstein’s GR, it is known as an additional curvature of space by a massive body. It is quite clear that space is bent by both massive bodies. Under repulsion, the inequality changes | δw zi | < / δw ni | .
Assume that the body (1) is located under the force of gravity of the body (2). A tidal wave on the illuminated side dominates the tidal wave on the shady side, the center of mass is shifted toward the source of gravity.
Suppose now that body (1) repels body (2). This becomes possible if an external force acts on the body (1) and the body (1) repels the body (2 )with its gravitational field. The tidal wave on the shadow side of the body (2) prevails over the tidal wave on the illuminated side, the center of inertia is shifted away from the source of the repulsive force.
Goals, objectives, materials and methods.
Such non-rotating bodies do not exist in nature. All bodies rotate and interact with each other by gravitational waves, which are a manifestation of gravitational induction. The purpose of this article is to develop common features for the interaction of rotating bodies in order to create a general law of gravitational induction.
For clarity, we consider the interaction of two bodies (1) and (2) [FIG. 2], like the Earth having a hydrosphere.
A rotating body creates a tidal wave in the surrounding bodies and in itself induces tidal waves from the surrounding bodies. A tidal wave creates a force whose magnitude depends on the speed of rotation of the body, and the direction depends on the ratio of the velocities of the interacting bodies. The body (1) is in the gravitational field of the body (2). Tidal waves occur on the body on the illuminated side (3) and on the shadow side (5). Body (1) having a lower speed of rotation and the predominance of the forces involved, a tidal wave on the illuminated side is superior to the magnitude of the tidal wave on the shady side, but for the body (2) which has the greater speed and the dominance of repulsive forces, tidal wave on the shady side of (6) exceeds a tidal wave on the illuminated side (4). This occurs due to the displacement of the center of inertia O1 and O2 in O1 and O11 position 2, which determines the direction of movement of solids when rotated in the direction of the body with greater speed.
When the rotation of the body (1) with the lower speed (for greater clarity, the body (1) is shown without rotation) what is the velocity of the body (2) there is a phenomenon of twisting, reflected in the increase of the velocity of the body (1) due to the fact that tidal wave induced on it by the body (2), drags the body (1). Friction force — Fтр1 increases the speed of rotation of the body (1) using projection -Fc and the projection of the friction force Fпв1 — the power of the tidal wave attracting body (1) body (2). This force is applied, regardless of the force of mutual attraction.
When the rotation of the body (2) at a speed greater than the speed of the body (1) the phenomenon of inhibition, reflected in the reduction of the velocity of the body (2) due to the fact that tidal wave induced on it by the body (1) brakes body (2) and pushes the body (2) body (1) force Fпв2 . This force is applied, regardless of the force of mutual attraction.
The interaction of bodies occurs with a physical vacuum, so there is really no interaction of two bodies. In real life, there is an interaction of an infinite number of bodies through a physical vacuum. We can only conditionally consider the interaction of two bodies, abstracting from an infinite number of other bodies. As the angular momentum of the body (1) increases, the angular momentum of the body (2) decreases, which is associated with it by interaction through gravitational waves. When the speed of the body (2) is higher than the speed of the body (1), the speed of the body (2) decreases, and the speed of the body (1) increases, while the body (1) is attracted to the body (2), and the body (2) is repelled from the body (1). As a result, the bodies form a spiral motion, well known in astronomy and now observed on the example of the binary system PSRJ 1141-6545. The law of conservation of momentum is not violated, but there is only a redistribution of the angular momentum between the bodies (1) and (2) during their interaction.
The centers of inertia of the bodies are located at points (O11) and (O21), being constantly displaced relative to their geometric centers (O1) and (O2 ) due to the inequality of tidal waves on the midday and midnight sides, and as a result of rotation they are shifted to points ( O1 11) and (O211 1). If a body is attracted by another body, the center of inertia shifts towards the midday line [body (1) If the body is repelled from the other body, the center of mass is shifted towards the midnight line /body (2), and although tidal wave on the midnight side in this case will be greater the friction force on the midnight side is less than the midday due to the fact that the flow of tidal waves on the midnight side sent in accordance with the direction of rotation of the body, and to the South, are directed oppositely. The common center of inertia moves from a point (O1m) to a point (O11m), that is, it rests relative to the position of the bodies. When considering the interaction and relative displacement of two bodies, the interaction of both bodies with a physical vacuum and the movement of their center of mass in a physical vacuum and relative to other bodies, which represents an absolute displacement, remain outside the frame.
In accordance with the law of universal gravitation [1 p. 63], all bodies are mutually attracted by a force that is calculated by the formula
F = G*M1*M2/R^2 
G is the gravitational constant;
M1,M2 -masses of celestial bodies;
R is the distance between the bodies
According to the author, the interaction of bodies is carried out by gravitational waves. The nature of gravity comes from the interaction of infinitesimal particles of matter, when the only way of interaction is a collision, in which gravitational waves appear, both the transmission of the collision along the chain, and vortices appear due to the need to change the direction of motion of a particle of matter due to the inability to move in the direction of another particle. The simplest vortex is already a rotating body, the freedom of rotation of which is limited by other vortices. The tidal wave reflects the interference pattern of the influence of physical bodies on the parameters of the gravitational waves of other bodies, which is a new gravitational wave.
The acceleration for a body (2) located in the gravitational field of the body (1) can be calculated if both parts of the expression  are divided by M2, knowing that F2=a2*M2 ; F2 = G*M1*M2/R^2
a2 = G*M1/R^2 
By its physical nature, tidal acceleration is a derivative of acceleration over distance. Take the derivative of the expression  by distance (for clarity, only the first derivative is taken) [2 c. 106]we get:
w2 =d(a2)/d R= -2G1*M1*d(R) /R^3 
The gravitational constant (G) changes its value and dimension to G1 (m3 / kg. sec.) and its value changes for each pair of interacting bodies and even for each of the bodies. A more differentiated account of the gravitational constant allows us to take into account the influence of other bodies of different composition for each of the considered bodies. It is proposed to call it the gravitational constant at the first derivative.
The resulting acceleration expresses an additional acceleration, described by A. Einstein as an additional curvature of space that occurs near massive bodies, and can be calculated at different values (ΔR), where (ΔR) is the change in the distance between the bodies. Additional (w1d ; w2d ) acceleration is experienced by both interacting bodies.
w1d =-2G1*M2*/ R^3; w2d = -2G1*M1* ΔR/R^3 ;
Similar accelerations can occur when one of the bodies is forced to move in the direction of another body (repulsion or entrainment).
Tidal accelerations depend inversely on the cube of the distance (not on the square), and the interaction of rotating bodies is carried out by the surface masses of the bodies, so the change in the distance between the bodies can be represented as a change in the distance between two rotating masses of tidal waves, whose masses are proportional to the masses of the bodies and with radii of rotation equal to the radii of these bodies. Tidal waves are stationary, but not stationary. The velocities of tidal waves on the surfaces of bodies are proportional to the rotational velocities of the interacting bodies. The equivalent substitution allows us to formulate the formula for the change in the distance (δR) between these bodies as a function of the speed of rotation of the bodies, which will be the difference in the projections of the vectors of the radii of rotation of the bodies on the axis connecting them.
δ(R) = [R1* cos (ω1* t+ φ1) — R2cos(ω2* t+ φ2) ] 
ω1, ω2 are the angular velocities of rotation;
φ1, φ2 is the initial rotation angles;
R1 and R2 are the radii of the heavenly bodies;
The expression  is a complex function due to the presence of a term of the form [ cos (ω* t+ φ)], which, when differentiated, takes the form [d(cos(ω*t+φ)/dt = — ω*sin ( ω*t + φ)] ;
For ease of understanding, only the first time derivative is taken, but in practice, derivatives of other orders can also be taken and trigonometric series made from them.
d(R)/dt= — R1*ω1* sin (ω1* t+ φ1) + R2*ω2*sin(ω2* t+ φ2) 
The derivative of the angular velocity of rotation is taken similarly to the time derivative:
d(R)/dω = -t* R1* sin (ω1* t+ φ1) + t* R2*sin(ω2* t+ φ2) 
The formula , taking into account the formulas ,, will take the form:
w1 = 2G1*M2*t*[ R2*ω2*sin(ω2* t+ φ2) — R1*ω1* sin (ω1* t+ φ1)] * [R1* sin (ω1* t+ φ1) — R2*sin(ω2* t+ φ2)]/R^3
w2 = 2G1*M1*t*[ R1*ω1* sin (ω1* t+ φ1) — R2*ω2*sin(ω2* t+ φ2)] * [R1* sin (ω1* t+ φ1) — R2*sin(ω2* t+ φ2)]/R^3 
where: G1 (m^2/kg. sec.^2) is the gravitational constant for the first derivative of the acceleration. This constant is characteristic only for a particular pair of bodies and depends on a lot of arguments, which can be discussed in detail in a separate article. If the derivative is taken only in time, the dimension G1 (m^3/kg. sec.)
also changes, the total acceleration (aΣ2) experienced by the rotating body (2) when interacting with the rotating body (1) will be:
aΣ2 = a + w1d + w2d + w2
The total acceleration (aΣ1) experienced by the rotating body (1) when interacting with the rotating body (2) will be:
aΣ1 = a + w1d + w2d + w1
The analysis of the formula  shows that the n-order derivative has the form:
w1(n) = (n+1)*Gn*M2*t*[ R1*ω1 n * sin (ω1* t+ φ1) — R2*ω2 n *sin(ω2* t+ φ2)] * [R1* sin (ω1* t+ φ1) — R2*sin(ω2* t+ φ2)]/R 2+ n
w2(n) =(n+1)*Gn*M1*t*[ R1*ω1 n * sin (ω1* t+ φ1) — R2*ω2 n *sin(ω2* t+ φ2)] * [R1* sin (ω1* t+ φ1) — R2*sin(ω2* t+ φ2)]/R 2+ n 
As the order of the derivative increases and the distance between the interacting bodies (R,) decreases, the value of w (n) tends to infinity, as the numerator increases and the denominator decreases infinitely. This explains the rigidity of the intra-nuclear interactions.
The analysis of the formula  shows. when bi-directional rotation of the body, the interaction is similar to the strong nuclear interaction, mutual unwinding of the body and reducing the distance or mutual inhibition bodies with increasing distance. Mutual unwinding means that a body whose speed is greater has a load in the form of a body whose speed is less and the speed difference is a hysteresis, which will change the sign if the other body starts to increase the speed. Similarly, with mutual braking. The author suggests that mutual unwinding with decreasing distance can be observed when matter enters a «black hole,» when matter stores the energy of rotation. The energy source in this case is alpha particles decaying to plasma at the event horizon of the black hole’s past. Mutual deceleration with increasing distance can be observed at the exit of plasma matter from the «black hole», when there is either radiation radiation of superdense elements synthesized from this plasma in the form of jets from the event horizon of the future of the black hole, or explosive expansion of the plasma, as in the Big Bang. The energy carrier after the Big Bang is the photons of microwave radiation.
With unidirectional rotation, an interaction similar to the weak nuclear interaction occurs with the formation of orbits, the average position of which is determined by the law of universal attraction of I. Newton, and the deviation from the average orbit is determined by the action of tidal forces. When the bodies approach, the repulsive forces increase due to an increase in the rotation speed of the body (2), and when moving away, the attractive forces increase due to a decrease in the rotation speed of the body (2).
The strong and weak interactions can pass from one to the other if one of the bodies makes a semi-somersault of Dzhanibekov, the causes of which can be both the action of external forces and a decrease in the kinetic moment of one of the bodies. If the body has enough energy, then it finishes the somersault, and if not, then there is a transition to another type of interaction.
Tidal accelerations, and hence the tidal wave forces, vary inversely with the cube (if only the first derivative is taken) of the distance, which distinguishes their action against the action of the gravitational attraction forces, which depend on the inverse proportion of the square of the distance. This served to understand the action of tidal forces as an additional curvature of space near massive objects by the General Theory of Relativity. A. Einstein did not understand that the displacement of the orbit of Mercury occurs not only because of the massiveness of the Sun, but also because of its rotation. The problem solved for Mercury was not suitable for the Earth, because the speed of rotation of the Earth is much higher than the speed of rotation of Mercury. Academician A.D. Sakharov suggested that the second body should also affect its acceleration, but he did not understand that it affects its rotation.
The tidal acceleration has a factor of the form (t*ω), which, on the scale of the Universe, can be considered as the number of revolutions of photons of the relic microwave radiation since its appearance. The main conclusion from this can be drawn that the Universe is not infinite and when reaching (t*ω)< 1, the Universe will begin to collapse.
The gravitational constant (G) may change, as it was calculated for other purposes. This is taken into account by introducing (G1), (G2)…(Gn) for different orders of derivatives.
In accordance with this law, the spirals of galaxies and the universe are formed. In the figure [Fig.3] shows the formation of a spiral by two cosmic bodies with different angular velocities of rotation. The body And extends to the body In a force of attraction Fпр and gravity tidal wave Fпв, the body is attracted to the body And the force of mutual attraction Fпр, but is repelled by the power of the tidal wave Fпв (this force is sometimes mistakenly take for antigravity). An important feature of the joint motion of two bodies is that a body with a lower rotation speed will always catch up with a body with a higher rotation speed and at the same time they both move relative to the physical vacuum and other bodies.
Both in the nature of its action and in its main manifestations, gravitational induction is similar to electromagnetic induction and is subject to the action of its own laws. One of the defining laws may be the law «Interaction of rotating bodies». This law allows us to take a new look at many issues that were previously impossible to solve (solving the three-body problem, creating gravitational thrusters, gravitational locators, gravitational lags, media separators, understanding the nature of «black holes», ball lightning and radiation emissions, etc.).)
The law (hypothesis): Interaction of rotating bodies:
In the interaction of two rotating bodies having a common plane of rotation, in a body whose gravitational field rotates at a lower speed, tidal waves are induced by another body, the result of which is an increase in the speed of rotation of the body and its attraction to another body, and in a body whose gravitational field rotates at a higher speed, tidal waves are induced by another body, the result of which is a decrease in the speed of rotation of the body and its repulsion from the other body.
- Quarks and tidal waves (hypothesis).
- The gravitational nature of electricity and magnetism (hypothesis).
- Reasoning about the structure of a black hole (hypothesis)
- Interaction of the physical vacuum with baryonic matter and radiation emissions (hypothesis)
- The effect of a tidal wave on the Earth’s climate (Hypothesis).
1. E. I. Butikov, A. S. Kondratiev Physics. Book 1. Mechanics. — M.: Nauka, 1994. — 138 p.;
2. Piskunov N. S. Differential and integral calculus for higher education institutions. vol. 1; 13th edition; Nauka; 1985.