V.4 No 1

53

On orbital stability of oscillators

To illustrate it, in Fig. 12 we show the diagram of dynamic scalar potential excited by a celestial body in its surrounding space.

Fig. 12. Distribution of dynamic scalar potential excited by the celestial body in its environment. The size of studied region is 2000 light years, period of orbiting T = 900 years

This diagram was plotted with the help of method of transforming grid, presented in [8]. We took the calculation formulas for plotting from the above shown calculation (12)- (18). To plot the distribution of potential, we determined  r_N  in (18) by way of parameters selection for each node of grid, and then by the standard formula (12) determined the potential of all points of studied region for each moment of time.

Here we would like to note that the amplitude of wave is not so large comparing to Coulomb's potential. So to reveal the field, we plotted the diagram not directly for scalar potential but for log R_N , where, as it follows from the construction in Fig. 2 , R_N   denotes the distance between the centre of body's orbit and studied point. Otherwise we would observe the dynamic field on a high cone of stationary Coulomb's field masking the sought effect. Thus, with the given conditions, the amplitude of cone was near the centre about four conventional units, whilst the swing of dynamic field was so small as 0,06 conventional units. This feature says also that, considering the dynamic field excited by moving charge, we should not neglect the stationary Coulomb's field which remains and can be in average determined through the distance from the orbit centre to the studied point.

We should also mark, with such method to reveal the dynamic field, a parasitic peak appears in the centre of diagram, it is well seen in Fig. 12. The cause is that we multiplied the values of potential into R_N . But as we were interesting just in the outer region, the presence of this peak does not notedly affect the field visualisation. Simply we have to remember of this feature of method. In studying the internal region of the orbit, as it is small, we have no necessity to multiply the field potential into R_N . Then the peak, naturally, does not arise and does not distort the pattern of studied field.

We would like also to point that we intentionally did not refer the parameters at which we studied the field in Fig. 12 to some particular celestial body, since our aim was to visualise the field structure as it is. As we see, the field has the same shape that the field of proton, though its size is much larger. Neither the mass of the object nor the size of its orbit affect the structure of this spiral, they affect only the amplitude and lead of spiral. In particular, the less diameter of object's orbit and its inertia the larger period of orbiting and lead of spiral. Proceeding from this, by parameters of spiral we can judge of orbital velocity of celestial body, its charge and disbalance inside the body. From this feature also follows that for more clear visualisation of the pattern of dynamic field, we harmlessly can, in sensible limits, increase the radius of orbit of the field source. With it only the amplitude of wave increases, but the field structure does not change.