Все науки. №12, 2024. Международный научный журнал - страница 4

At the moment, a dynamic problem has been formed with respect to the Laplace equation (1), with respect to the function (2), with known initial conditions (3—4), proceeding from the phenomenon of thermonuclear fusion.

To determine the boundary conditions, it is sufficient to adopt a spherical coordinate system, despite the fact that the coordinate at zero angles at a radius of 1 astronomical unit is the position of the planet Earth on New Year’s Day – the transition from the night of December 31 to January 1. The Sun is also accepted as an absolutely smooth body, spreading uniform radiation over the entire surface, due to which an error for the presence of black spots is initially stipulated, which can be eliminated later. Thus, based on the above, it is necessary to state the fact that, based on the conditions taken, the Earth is located at 0 degrees in the latitude angle of the Sun, also taking into account the deviation of 23.497 degrees of the Earth’s axis, while the maximum deviation to the poles of the planet in the form of the specified angle can be calculated.

Fig. 1. Spherical coordinate system

The conditions set lead to the fact that between the center of the Sun, the Earth and one of the poles of the Earth there are 3 imaginary straight lines forming at the time of the vernal equinox a right triangle with legs of 1 astronomical unit (1,496*108 km) and 1 radius of the Earth (for the polar case 6,356.8 km and for the equatorial 6,378.1 km), from where it is possible to calculate the angle according to the Pythagorean theorem (5).

Fig. 2. The modeling schemes

Also, from the same ratio, but in a transformed form, it is possible to obtain the angle of deviation at the time of June 21 and December 21 according to the cosine theorem (6—9).

Similar calculations are used to determine the boundary conditions with respect to the angle of longitude (10—13).

Based on certain data, it is possible to state the change of function (2) to (14) and the problem of the following boundary conditions (15—18), given that the boundary conditions and the dynamic phenomenon are known, the Fourier method of variable separation can be adopted as a solution for it.

Now that the initial and boundary conditions, as well as the corresponding equation, have been determined at the specified moment, it is necessary to pay attention to the effect of the Laplace equation in static form, and it, as a partial equation from the Helmholtz equation, can be interpreted as follows. Namely, for the reason that in this case the phenomenon of energy transfer is observed, and in this case the Laplace equation is used to display in a global sense a model of an emitter or an energy-emitting «charge» in the face of the Sun. Thus, on a more local scale, the harmonic function taken will satisfy, based on these conditions, the homogeneous equation of thermal conductivity or energy conductivity (19), including based on the transformation model for the connection of the Helmholtz equation and the wave equation.