Все науки. №12, 2024. Международный научный журнал - страница 3

With respect to the obtained function of the first angle in the spherical coordinate system, which also depends on the independent constant and the introduced constant, there are also boundary conditions derived from the available empirical data (18). The application of each of them creates 3 forms of the function with the specified values of the angle variable and the value of the function as a whole, while the third form causes the variable to be replaced in the first and further transition from a system with 3 equations to 2 equations, and then, after deducing the function for the independent constant into a single equation. The expression formed in this way, after elementary algebraic transformations, leads to the value of the introduced third coefficient (40), its substitution into the formula of the independent constant (41), which can be substituted into the form of a function (42).

As a result, a uniform form with constants for the first function is obtained, on the basis of which it is possible to continue the given ratio with transformation into the form of an ordinary differential equation of the second degree relative to the second angle. The solution is carried out after the conversion of the function, where all 3 specified constants are enclosed, which are used during the conversion. During the double integration on the left side, due to the fact that the first angle is used as a variable in the square of the sine, double integration relative to the second angle cannot be performed in principle, which is why the first and second independent coefficients appear.

Thus, a relation is created with respect to which natural logarithm is performed, which, after appropriate algebraic operations, leads to a single form of the function with respect to the second angle (43).

Based on the experimental data in (15—17) [1—5; 13—17; 19], boundary conditions can be used [17—19] and, consequently, 3 equations for the second angle, each of which is solvable after converting the third equation and reducing to 2 equations. After applying the substitution method, a single equation is output for the system of equations, after which the value for the first coefficient is calculated, as well as the square of the sine of the first angle relative to the specified boundary conditions, which can then be used in the substitution method, creating a single form of the equation (44).

As a result of the calculations, the function has already been determined in time, the first and second corners, taking into account that the value of the function in radius is equal to one, the general appearance of the function looks according to (45).

The resulting function can describe the energy value taking into account the empirical coefficient, so that a graph of the function (45) can be presented. It is important to note that the function depends on 3 variables – the first and second angles, as well as time, which can be represented as an animation, as well as by a single time.

Results

In this case, the graph is plotted relative to each angle and shape relative to a given time of 4.5 billion. years after the formation of the Sun, which is also used in a given function (Fig. 1—2).

Fig. 1. The first perspective of the constructed three-dimensional graph at the time of 4.5 billion years after the formation of the Sun