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Metric spaces of Keplerian orbits |
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| Authors: | Konstantin V Kholshevnikov |
| Institution: | (1) Astronomical Institute, St. Petersburg State University, Universitetsky pr. 28, Stary Peterhof, St. Petersburg, 198504, Russia;(2) Institute for Applied Astronomy, nab. Kutuzova 10, St. Petersburg, 191187, Russia |
| Abstract: | Several metric spaces of Keplerian orbits and a set of their most important subspaces, as well as a factor space (not distinguishing orbits with the same longitudes of nodes and pericentres) are constructed. Topological and metric properties of them are established. Simple formulae to calculate the distance are deduced. Applications to a number of problems of Celestial Mechanics are discussed. |
| Keywords: | Topological space Metric space Space of Keplerian orbits Manifold Embedding and imbedding in Euclidean space |
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