Abstract

JATTIN-BALCAZAR, Jairo J. et al. CHARACTERIZATION OF THE DEGREE OF COMPLEXITY OF THE SOLAR SYSTEM THROUGH ZIPF/MANDELBROT'S LAW. Momento [online]. 2022, n.64, pp.28-38.  Epub Apr 26, 2022. ISSN 0121-4470.  https://doi.org/10.15446/mo.n64.97365.

The Zipf/Mandelbrot law has allowed to characterize phenomena with a hyperbolic organization in biomedical sciences and natural languages, among others; however, its application could be extended to study planetary characteristics. Therefore, the objective of this research is to apply the Zipf/Mandelbrot law to characterize the degree of complexity of the orbital period, the planetary mean orbital velocity, and the mean distance to the sun of the planets of the solar system. For this purpose, the values of the orbital period, the mean orbital velocity, and the mean distance of the planets of the solar system to the sun were taken to evaluate their hyperbolic distribution. Subsequently, the Zipf/Mandelbrot law was applied to calculate the fractal dimension of both variables. The values of orbital period, orbital velocity and planetary mean distance were found to be hierarchically distributed, which allowed the fractal dimension values to be calculated. These values were 0.28, 0.88 and 0.42, with R2 coefficients of 0.92, 0.87 and 0.92, respectively. The above suggests that the application of the Zipf/Mandelbrot law reveals the existence of undescribed mathematical orders in the celestial kinematics by finding a greater degree of complexity of the mean orbital velocity with respect to the mean planetary distance to the sun and the orbital period, implying that the analysis parameters of planetary systems could be complemented with this approach.

Keywords : orbital velocity; solar system; fractal.

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