title: On local normability of spaces of Keplerian orbits
metadata.name: dc.contributor.author
metadata.value: Milanov, Danila V.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2019-09-05T18:37:00Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2019-09-05T18:37:00Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2019-09
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Milanov D.V. On local normability of spaces of Keplerian orbits. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2019, vol. 6 (64), issue 3, pp. 505– 518.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu01.2019.314
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/16327
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: Geometric properties of spaces of Keplerian orbits are of interest for problems of Celestial Mechanics related with the search of groups of celestial bodies whose orbits are close to each other. Those groups include asteroid families and meteoroid streams. Their study brings an important information about the evolution of the solar system, characteristics of a family members and their parent bodies. The local properties of a distance function between orbits are of main importance for the problems of search of families of genetically related celestial bodies, because orbits of a family members cluster together in a small region of the orbits space. In this article we consider several metrics on the set of Keplerian orbits H and its quotient spaces. For each of these metrics we solve the question: does there exist a normed space locally isometric to the orbits metric space? In two of considered cases, the answer turns out to be positive: the quotient space of H by the equivalence relation, neglecting the magnitude of pericentre argument of the orbit, can be isometrically embedded into R4. The embedding into R3 also exists for the quotient space by the pair of elements: the longitude of ascending node and the pericentre argument. It is shown in the article, that the answer to the stated question is negative for other metrics we considered. The possibility of an isometric embedding of orbits space or of its part into Euclidean space is useful in application to aforementioned problems of Celestial Mechanics. The isometric map helps to define the mean of orbits family in a natural way: the arithmetic mean of images corresponds to the orbit with the minimal square deviation of distances from orbits of the family.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: The work is supported by Russian Science Foundation (grant N18-12-00050).
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Mathematics. Mechanics. Astronomy;Volume 6 (64); Issue 3
metadata.lang: -
metadata.name: dc.subject
metadata.value: space of Keplerian orbits
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: orbital similarity criterion
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: local isometry
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: normability
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: asteroid family
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: meteor stream
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: mean orbit
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: On local normability of spaces of Keplerian orbits
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 505-518.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/16327/1/505-518.pdf
resources.format: Adobe PDF
resources.size: 330,97 kB