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Keywords:
distribution function; g-discrepancy; sequence of points; center of mass; trajectory of two planets; solar system
distribution function; g-discrepancy; sequence of points; center of mass; trajectory of two planets; solar system
Summary:
In this paper we derive a sequence from a movement of center of~mass of arbitrary two planets in some solar system, where the planets circle on concentric circles in a same plane. A trajectory of center of mass of the planets is discussed. A sequence of points on the trajectory is chosen. Distances of the points to the origin are calculated and a distribution function of a sequence of the distances is found.
References:
[1] Dick, J., Pillichshammer, F.: Digital Nets and Sequences. 2010, Cambridge University Press, New York, MR 2683394
[2] Horák, Z., Krupka, F.: Fyzika. Příručka pro vysoké školy technického směru. 1981, Praha: Nakladatelství technické literatury,
[3] Kuipers, L., Niederreiter, H.: Uniform Distribution of Sequences. 1974, John Wiley, (reprint edition published by Dover Publications, Inc. Mineola, New York in 2006). MR 0419394 | Zbl 0281.10001
[4] Strauch, O., Porubský, Š.: Uniform Distribution of Sequences. 2005, Peter Lang, Frankfurt am Main, (Electronic revised version December 11, 2013) in: https://math.boku.ac.at/udt MR 2290224
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