### Abstract

In astronomical problems, we must estimate the proximity of celestial body orbits. This can serve as a criterion for common origin (usually of a parent body fragmentation). Several submetrics were proposed for this in the latter half of the 20th century. We call the submetric a function defined for each pair of Keplerian orbits, and, satisfying the first two axioms of metric space, but not making obligatory the third, triangle axiom. During the last decade, for each of the proposed submetrics, one can indicate an open set of orbital pairs that this key axiom violates. Recently, new metrics were constructed satisfying all axioms of mertric space, as well as metrics induced by them, widespread in celestial mechanics factor-spaces of the space of nonrectilinear Keplerian orbits. In the present paper, we extended the examination of considered submetrics and metrics propertie; calculated corresponding subdistances and distances between planetary orbits in the Solar System; calculated distances between all pairs of orbits of numbered asteroids (in the space of orbits as well as in its three subspaces); and calculated distances between the orbit of the Chelyabinsk body and orbits of all numbered asteroids.

Original language | English |
---|---|

Pages (from-to) | 305-316 |

Number of pages | 12 |

Journal | Vestnik St. Petersburg University: Mathematics |

Volume | 51 |

Issue number | 3 |

DOIs | |

State | Published - 1 Jul 2018 |

### Keywords

- asteroid
- distance between orbits
- Keplerian orbit
- metrics

### Scopus subject areas

- Mathematics(all)

### Cite this

}

**On Distances between Orbits of Planets and Asteroids.** / Kholshevnikov, K. V.; Shchepalova, A. S.

Research output: Contribution to journal › Article › Research › peer-review

TY - JOUR

T1 - On Distances between Orbits of Planets and Asteroids

AU - Kholshevnikov, K. V.

AU - Shchepalova, A. S.

PY - 2018/7/1

Y1 - 2018/7/1

N2 - In astronomical problems, we must estimate the proximity of celestial body orbits. This can serve as a criterion for common origin (usually of a parent body fragmentation). Several submetrics were proposed for this in the latter half of the 20th century. We call the submetric a function defined for each pair of Keplerian orbits, and, satisfying the first two axioms of metric space, but not making obligatory the third, triangle axiom. During the last decade, for each of the proposed submetrics, one can indicate an open set of orbital pairs that this key axiom violates. Recently, new metrics were constructed satisfying all axioms of mertric space, as well as metrics induced by them, widespread in celestial mechanics factor-spaces of the space of nonrectilinear Keplerian orbits. In the present paper, we extended the examination of considered submetrics and metrics propertie; calculated corresponding subdistances and distances between planetary orbits in the Solar System; calculated distances between all pairs of orbits of numbered asteroids (in the space of orbits as well as in its three subspaces); and calculated distances between the orbit of the Chelyabinsk body and orbits of all numbered asteroids.

AB - In astronomical problems, we must estimate the proximity of celestial body orbits. This can serve as a criterion for common origin (usually of a parent body fragmentation). Several submetrics were proposed for this in the latter half of the 20th century. We call the submetric a function defined for each pair of Keplerian orbits, and, satisfying the first two axioms of metric space, but not making obligatory the third, triangle axiom. During the last decade, for each of the proposed submetrics, one can indicate an open set of orbital pairs that this key axiom violates. Recently, new metrics were constructed satisfying all axioms of mertric space, as well as metrics induced by them, widespread in celestial mechanics factor-spaces of the space of nonrectilinear Keplerian orbits. In the present paper, we extended the examination of considered submetrics and metrics propertie; calculated corresponding subdistances and distances between planetary orbits in the Solar System; calculated distances between all pairs of orbits of numbered asteroids (in the space of orbits as well as in its three subspaces); and calculated distances between the orbit of the Chelyabinsk body and orbits of all numbered asteroids.

KW - asteroid

KW - distance between orbits

KW - Keplerian orbit

KW - metrics

UR - http://www.scopus.com/inward/record.url?scp=85052717222&partnerID=8YFLogxK

U2 - 10.3103/S1063454118030044

DO - 10.3103/S1063454118030044

M3 - Article

VL - 51

SP - 305

EP - 316

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 3

ER -