Introduction on background medium theory about celestial body motion orbit and foundation of fractionaldimension calculus about selffractal measure calculation
YAN Kun(Xi'an Modern Nonlinear Science Applying Institute,Xi'an 710061,China)
In this paper,by discussing the basic hypotheses about the continuous orbit and discrete orbit in two research directions of the background medium theory for celestial body motion,the concrete equation forms and their summary of the theoretic frame of celestial body motion are introduced.Future more,by discussing the general form of Binet's equation of celestial body motion orbit and it's solution of the advance of the perihelion of planets,the relations and differences between the continuous orbit theory and Newton's gravitation theory and Einstein's general relativity are given.And by discussing the fractionaldimension expanded equation for the celestial body motion orbits,the concrete equations and the prophesy data of discrete orbit or stable orbits of celestial bodies which included the planets in the Solar system,satellites in the Uranian system,satellites in the Earth system and satellites obtaining the Moon obtaining from discrete orbit theory are given too.Especially,as the preliminary exploration and inference to the gravitation curve of celestial bodies in broadly range,the concept for the ideal black hole with trend to infinite in mass density difficult to be formed by gravitation only is explored.By discussing the position hypothesis of fractionaldimension derivative about general function and the formula form the hypothesis of fractionaldimension derivative about power function,the concrete equation formulas of fractionaldimension derivative,differential and integral are described distinctly further,and the difference between the fractionaldimension derivative and the fractionalorder derivative are given too.Subsequently,the concrete forms of measure calculation equations of selfsimilar fractal obtaining by based on the definition of form in fractionaldimension calculus about general fractal measure are discussed again,and the differences with Hausdorff measure method or the covering method at present are given.By applying the measure calculation equations,the measure of selfsimilar fractals which include middlethird Cantor set,Koch curve,Sierpinski gasket and orthogonal cross star are calculated and analyzed.


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