SELF

48

S.B. Karavashkin and O.N. Karavashkina

Actually, if we disregard the delay of interaction, proton and electron in case of conservative system would orbit around some centre of masses, as it is shown in Fig. 9.

Fig. 9. Motion of proton and electron when calculated in disregard of the delay of interaction

With it the modelling system of equations for proton would be the following:

(24)

(q₁, m_p, r_p and r₁ are measured in CGS electrostatic system). Without having solved this system, we cannot estimate the parameters of motion of system elements, because, "as it concerns the motion of each charge, without having solved the system (24) we cannot find the law of such motion" [9, p. 90].

If the system was conservative and proton and electron move along stationary circular orbits, we can assume

(25)

Given this, we can rewrite (24) in the complex form

(26)

where _p and _e are the angles corresponding to the momentary location of proton and electron in their orbits, and r_pe is the momentary distance between the proton and electron.

Given

(27)

we can approximately take

(28)

With it (26) is easily twice integrable over the time, and we yield

(29)

and

(30)

Similarly, the equation for electron in the complex form would be as follows:

(31)

With the above approximations its solution would be such:

(32)

Joining (29) and (32), we yield

(33)

i.e., quite expectable result, which says that the relation of radii of orbits of proton and orbital electron is inversely as the ratio of their masses.