### Abstract

We examine intermediate perturbed orbits proposed by the first author previously, defined from the two position vectors and three angular coordinates of a small celestial body. It is shown theoretically, that at a small reference time interval covering the measurements the approximation accuracy of real movements by these orbits corresponds approximately to the third order of osculation. The smaller reference interval of time, the better this correspondence. Laws of variation of the methodical errors in constructing intermediate orbits subject to the length of reference time interval are deduced. According to these laws, the convergence rate of the methods to the exact solution (upon reducing the reference interval of time) is higher by two orders of magnitude than in the case of conventional methods using the Keplerian unperturbed orbit. The considered orbits are among the most accurate in set of orbits of their class determined by the order of osculation. The theoretical results are validated by numerical examples.

Original language | English |
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Pages (from-to) | 51-60 |

Number of pages | 10 |

Journal | Solar System Research |

Volume | 49 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2015 |

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### Keywords

- Gauss method of determining preliminary orbit
- initial orbit determination
- intermediate perturbed orbit
- superosculating orbit

### ASJC Scopus subject areas

- Astronomy and Astrophysics
- Space and Planetary Science

### Cite this

**On the accuracy of approximation of a small celestial body motion using intermediate perturbed orbits calculated from two position vectors and three observations.** / Shefer, V. A.; Shefer, O. V.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - On the accuracy of approximation of a small celestial body motion using intermediate perturbed orbits calculated from two position vectors and three observations

AU - Shefer, V. A.

AU - Shefer, O. V.

PY - 2015

Y1 - 2015

N2 - We examine intermediate perturbed orbits proposed by the first author previously, defined from the two position vectors and three angular coordinates of a small celestial body. It is shown theoretically, that at a small reference time interval covering the measurements the approximation accuracy of real movements by these orbits corresponds approximately to the third order of osculation. The smaller reference interval of time, the better this correspondence. Laws of variation of the methodical errors in constructing intermediate orbits subject to the length of reference time interval are deduced. According to these laws, the convergence rate of the methods to the exact solution (upon reducing the reference interval of time) is higher by two orders of magnitude than in the case of conventional methods using the Keplerian unperturbed orbit. The considered orbits are among the most accurate in set of orbits of their class determined by the order of osculation. The theoretical results are validated by numerical examples.

AB - We examine intermediate perturbed orbits proposed by the first author previously, defined from the two position vectors and three angular coordinates of a small celestial body. It is shown theoretically, that at a small reference time interval covering the measurements the approximation accuracy of real movements by these orbits corresponds approximately to the third order of osculation. The smaller reference interval of time, the better this correspondence. Laws of variation of the methodical errors in constructing intermediate orbits subject to the length of reference time interval are deduced. According to these laws, the convergence rate of the methods to the exact solution (upon reducing the reference interval of time) is higher by two orders of magnitude than in the case of conventional methods using the Keplerian unperturbed orbit. The considered orbits are among the most accurate in set of orbits of their class determined by the order of osculation. The theoretical results are validated by numerical examples.

KW - Gauss method of determining preliminary orbit

KW - initial orbit determination

KW - intermediate perturbed orbit

KW - superosculating orbit

UR - http://www.scopus.com/inward/record.url?scp=84921395907&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84921395907&partnerID=8YFLogxK

U2 - 10.1134/S0038094615010074

DO - 10.1134/S0038094615010074

M3 - Article

AN - SCOPUS:84921395907

VL - 49

SP - 51

EP - 60

JO - Solar System Research

JF - Solar System Research

SN - 0038-0946

IS - 1

ER -