V.4 No 1

49

On orbital stability of oscillators

When the delay took place, Fig. 9 will considerably change. In this case the proton orbits together with the delaying electron, as it is shown in Fig. 10.

Fig. 10. Proton's interaction with orbital electron when noting the delay of interaction

As we can see from the construction, the electron interacts with the field of delaying proton, and proton correspondingly - with the delay field of electron; with it the difference of phase between the locations of proton and electron is already not equal to a half-period, as in the above calculation. Jointly with the delay of proton's motion in the field of electron, the common phase delay of proton's location as to the electron can be estimated as follows:

(34)

Given

(35)

we yield

(36)

Thus, we see that electron's maximal departure from the axis going through the mass centre of the system depends on electron's orbital velocity and does not exceed 2 radian. This means, phase difference between the field of proton and location of electron in the orbit will be well less than a half-period. Electron will move in permanently tangentially accelerating field of proton, and all losses for radiation will automatically compensate. With it, as we see from (36), electron basically cannot revolve in phase with proton - this means, it basically cannot appear at the minimum of potential energy of spiral field. And this situation will just force the electron to stabilise in its motion in orbit, doing not violating the conservative system of atom, and to choose the position corresponding to the balance between the energy loss for radiation and the energy gained as the result of acceleration. It is important that this stabilisation is determined by the field of proton's charge, not by the balance of centrifugal and centripetal forces, as it was thought before. This gives the answer of electron's stability in the orbit in time, as the stabilising forces arising simultaneously with the dynamic field of proton are determined by stable in time charge of proton. With it the indicated forces form in the spiral arm the line of stable balanced motion of electron - and this is an important feature of dynamic fields which was never noted by Niels Bohr and his followers. While the disregard of this feature has led immediately to postulating the electron's orbit stable.

As we see, the carried out analysis, when took into account the dynamics of atomic system, has revealed many important nuances, essentially changing and refining the model of interactions in atom. This, in its turn, will undoubtedly raise great mathematical difficulties, because of implicit functions appearing in the modelling equations. At the same time, despite arisen problems, just in this path there lay the solution of nature of Planck's quantum postulate, refined structure of interaction within atom, and even revelation of conditions of formation of neutron's system. Possibly, when dynamic system of nuclei is refined, we would be able to get over the barrier and to synthesise new stable chemical elements, to make clear the cause and conditions, why known elements are stable or unstable dependently on conditions under which the substance is. We cannot exclude that chemical elements unstable on the Earth can be quite stable in the stars and much more massive planets than the Earth.