Все науки. №12, 2024. Международный научный журнал - страница 6

From the first ratio in (34), a second-order differential equation with respect to radius is formed, which can be solved after revealing the ratio and using the integral of the second degree with respect to the radius variable in the second degree. When integrating in both directions, in the right case, a known ratio is obtained, in the left case, the function itself is used as a variable, which allows us to arrive at the resulting equation between the value of the function and the variable of the radius of this function.

Transformations with respect to double logarithm, followed by further exponentiation after transformations and repeated logarithm in kind, allow us to arrive at a function relation that becomes complete after being reduced in an algebraic transformation (35)

Taking into account the obtained type of function, as well as the known ratio, it can be noted that in (34) an additional second coefficient was introduced, which took part in (35) and the resulting formula of the radius function. The value of this coefficient can be calculated based on the appropriate type of function, taking into account the fact that the radius is a constant equal to a single astronomical unit, calculations become the simplest and most definite (36).

Thus, the function from (35), taking into account the value of the coefficient (36), takes the form (37) with a single value of the function at a given radius in (38).

Since the type and value of the radius function has been determined, the ratio in (35—36) can be used later to operate with the function of the first angle from a given spherical coordinate system. After converting the ratio, a third additional coefficient is introduced, from which, consequently, a new ordinary differential equation of the second degree is created using trigonometric functions. Subsequently, after the transformation, the operation of integration, exponentiation, logarithmization and transformations with logarithms, which were carried out within the framework of calculations in (35), are applied to the function of the first angle using the general form of this function (39).

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).