The analysis of Venus’ physical surface using methods of fractal geometry

Abstract

In this paper, the work on investigating fractal structures on Venus was performed on the basis of observations taken by the “Magellan” spacecraft (NASA). The uncertainties in some data produced by “Magellan” were filled by the information that had been collected before – in “Venera 15”, “Venera 16”, and “Pioneer” missions. During the implementation of the work a digital map of Venus’ surface was built, and its spatial model was created. It is worth noting that the choice of basic level surface on Venus is defined by a certain value of potential or a point on its surface through which the geoid passes. The model of Venus’ physical surface was created use the harmonic expansion into spherical functions of altimetry data the “Magellan” mission. In the present paper, for determining and analyzing fractal dimensions the Minkowski mathematical algorithm, which is a simplified option of Hausdorff-Besicovitch dimension and provides high reliability and accuracy, was used. As a result, fractal correlations of Venus’ geoid anomalies in both longitude and latitude as well as the mean value of fractal dimensions were calculated. The following values of mean fractal dimension for Venus surface are obtained: in latitude – Dβ = 1.003; in longitude – Dλ = 0.98. Based on these values, we may conclude that the topographic model of Venus’ physical surface is close to spherical figure. The comparison between the obtained Venus fractal parameters with the ones of the Earth shows the good agreement.