Relaxed triangle inequality for the orbital similarity criterion by Southworth and Hawkins and its variants
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In this article, we prove the relaxed triangle inequality for Southworth and Hawkins, Drummond and Jopek orbital similarity criteria on the set of non-rectilinear Keplerian orbits with the eccentricity bounded above. We give estimates of the minimal coefficients in the inequality for each criterion and show that one of the calculated coefficients is exactly minimal. The obtained inequalities can be used for the acceleration of algorithms involving pairwise distances calculations between orbits. We present an algorithm for calculation of all distances not exceeding a fixed number in a quasi-metric space and demonstrate that the algorithm is faster than the complete calculation on the set of meteors orbits. Finally, we estimate the correlation dimensions of the set of main belt asteroids orbits and meteors orbits with respect to various orbital metrics and quasi-metrics.
KeywordsOrbital similarity criterion Space of Keplerian orbits Quasi-metric Relaxed triangle inequality Clustering algorithm Distance matrix Correlation integral Correlation dimension
This work is supported by the Russian Science Foundation, Grant 18-12-00050. We express our gratitude to the anonymous referee for useful and detailed comments, which improved the article.
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Conflict of interest
We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the paper submitted.
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