Mathematics – Logic
Scientific paper
Dec 1995
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995sosyr..29..421s&link_type=abstract
Solar System Research, Vol. 29, No. 6, p. 421 - 432
Mathematics
Logic
1
Planetary Surfaces: Photometry, Planetary Surfaces: Methods Of Observation
Scientific paper
The scale self-similarity of the surfaces of atmosphereless celestial bodies is demonstrated to be liable to control their photometric properties, particularly, the brightness distribution across the visible disk. Mathematical objects called fractoids are introduced for the sake of modeling the effect of the self-similarity. Fractoids are self-similar structures with an infinity of scales, but, as distinct from fractals, they keep the equality of topological and fractal dimensions. A general method for determining photometric functions of fractoids is proposed, taking advantage of the scale invariance of the classic photometry problems. Examples of application of the method are offered. In particular, a fractoid with a generating structure of the random relief type furnishes, at certain values of the parameter, Akimov's scattering law, which was derived previously from other considerations. The case of a degenerate fractoid, formed by the superposition of single-scaled generating structures, is also discussed.
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