title: The determination of a preliminary orbit by Cauchy— Kuryshev—Perov method
metadata.name: dc.contributor.author
metadata.value: Kuznetsov, Vladimir B.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2022-02-17T11:44:29Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2022-02-17T11:44:29Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2021-12
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Kuznetsov V.B. The determination of a preliminary orbit by Cauchy— Kuryshev—Perov method. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2021, vol. 8 (66), issue 4, pp. 716–727.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/spbu01.2021.417
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/35141
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: The determination of preliminary orbits of celestial bodies is of interest for observational
  astronomy, from the point of the view of the discovery of new bodies or identification with
  already known ones. To solve this problem, the techniques are required that are not limited
  both by the values of eccentricity of the orbit and by the time intervals between observations.
  In this paper, we consider the geometric Cauchy—Kuryshev—Perov method for
  determining the preliminary orbit. It is shown how, within the framework of the two-body
  problem, proceeding only from geometric constructions, using five angular observations to
  determine an orbit that does not lie in the plane of the observer’s motion. This method
  allows us to reduce the problem of determining the preliminary orbit to an algebraic system
  of equations for two dimensionless variables, with a finite number of solutions. The
  method is suitable for determining both elliptical and hyperbolic orbits. Moreover, it has
  no restrictions on the length of the orbital arc of the observed body and is unlimited by the
  number of complete revolutions around the attracting center between observations. All possible
  combinations of body positions in orbit are divided into 64 variants and represented
  by the corresponding systems of equations. This article presents an algorithm for finding
  solutions to the problem without a priori information about the desired orbit. Solutions
  are sought in a limited area, in which triangulation is performed with ranking triangles for
  compliance with the search conditions, which makes it possible to exclude consideration of
  most of them at the initial stage. Solutions of the system are found by the Nelder—Mead
  method through the search for the minima of the objective function. The obtained orbits
  are compared, through the presentation of observations, and the best one is selected. An
  example of determining the orbit of comet Borisov 2I is given.
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 8 (66); Issue 4
metadata.lang: -
metadata.name: dc.subject
metadata.value: preliminary orbit determination
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: geometric method of Cauchy—Kuryshev— Perov
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: method of Nelder—Mead
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: algebraic equations
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: 2I/Borisov
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: The determination of a preliminary orbit by Cauchy— Kuryshev—Perov method
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 716-727.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/35141/1/716-727.pdf
resources.format: Adobe PDF
resources.size: 350,38 kB