Everyone knows that the proper time of a material object flying relative to a resting frame of reference differs from the time of the resting frame of reference and is calculated by the formula.

Where t0 is the time of the reference frame, V is the velocity of relative motion, C is the velocity of light.
Suppose that two spherical bodies of diameters D1 and D2,
where D1 = D2 = D and masses m1 and m2, where m1 = m2 fly towards each other with velocity V1 and V2, where V1 = V2, as well as proper time t1 and t2, where t1 = t2 and fly relative to each other at distance R with relative velocity VREL Figure 1.

If we consider this example from the reference frame of body 1, body 2 is flying relative to body 1 with velocity V21.

From the General Theory of Relativity we know that the expression for the time t21 of body 2 flying relative to the frame of reference of body 1 will look like this.

Just as if we take body 2 as the reference frame, the expressions for time and velocity are identical.


Where

Then the time of body 2 t21 (2) flying with velocity V21 relative to the frame of reference of body 1 with time t1, is less than time t1 by the value ∆t.

Just as for body 1 with time t12 (3) flying with velocity V12 relative to the frame of reference of body 2 with time t2, is less than time t2 by the value ∆t.

Based on my assumption, expressed in the article “Relativity of the principle of relativity” that the increment of time ∆t extends to the distance R from the center of mass of the body moving relative to the center of mass of the reference frame with the regularity ∆t/R2.
We obtain that the change of the time course ∆tR in points of space at a distance R from a material body of mass m2 and velocity V2 moving relative to a stationary frame of reference, is equal to ∆tR = ∆ t/R2 where

That is, in the general case.

The time course of an object moving relative to the reference frame slows down. Correspondingly, when moving away from such a body, time accelerates its course towards t0. Thus, the time course at a distance R from such an object tR = t0 – ∆tR


We obtain that the time course at a distance R from the center of body 2 flying relative to body 1 taken as a reference frame is tR2 and the time course at a distance R from the center of body 1 will also be tR1 where tR1 = tR2 = tR
Hence the distance L traveled by points a and b of bodies 1 and 2 flying relative to each other Fig. 2 with velocity V1 = V2 = V will be equal to L = V tR.

From the condition of equality of velocities, masses and sizes of bodies we obtain that,
La1 = La2
Lb1 = Lb2
La1 < Lb1
La2 < Lb2
Fig. 2

Where Ra1 = Ra2 = Ra, Rb1 = Rb2 = Rb, Ra = R – 1/2D, Rb = R + 1/2D, Rb = Ra + D,
Ra = Rb – D.


From which it follows that the bodies will describe some arc around each other, Fig. 3.

Let’s try to calculate the radius of the described arc.
The angles ϕ for the arc described by point a and point b of the body will be equal to ϕa = ϕb and from the formula for arc length L = πR ϕ/180 , where ϕ is the angle of the described sector per unit time, R is the radius of the arc.
From the formula for arc length, ϕ is equal to.

Where Ra = Rb – D
From here we can find out the radius described by a body relative to another body.

Or
Rb = Ra + D

The question arises at what velocity of relative motion
VREL = V12 = V21 bodies 1 and 2 will rotate around each other while flying uniformly straight and without experiencing any centrifugal forces.
Let us solve this problem by fitting values of V, R and D, so that the result of calculation of the radius described by the body Ra and Rb is equal to the substituted value.

The results of the calculations are recorded in the table.
| R | 1·10-3 m. | 1m. | 1.8 m. | |
| D/R | ||||
| 1/2 | D= 0.5·10-3 m. V=0.0011365·108m/s. | D=0.5 m. V=1.227·108m/s. | D=0.9 m. V=2.7971·108m/s. | |
| 1/5 | D=0.2·10-3 m. V=0.001211·108m/s. | D=0.2 m. V=1.32295·108m/s. | ||
| 1/10 | D=0.1·10-3 m. V=0.001221·108m/s. | D=0.1 m. V=1.3358·108m/s. | ||
| 1/100 | D=0.01·10-3 m. V=0.001225·108m/s. | D=0.01 m. V=1.3415·108m/s. | ||
| 1/1000 | D=0.001·10-3 m. V=0.0012247·108m/s. | D=0.001 m. V=1.34187·108m/s. |
It is clear from the obtained results that the formation of such groups of bodies rotating in time warped space with R value more than 1.8 meters is impossible. The interaction of bodies with parameters R greater than 1.8 meters will only change their flight trajectory towards each other.
There is no doubt that such a structure of curved space can involve in its rotational motion and electromagnetic waves.
The possibility of the existence of such structures can explain the existence of such objects as ball lightning, light lensing, changes in the trajectory of celestial bodies and even the forces holding particles in atoms.
28.06.2025
Свідоцтво: 108775 зареєстровано 20.10.2021



