### Abstract

Intermediate perturbed orbits, which were proposed earlier by the first author and are calculated based on three position vectors and three measurements of angular coordinates of a small celestial body, are examined. Provided that the reference time interval encompassing the measurements is short, these orbits are close in the accuracy of approximation of actual motion to an orbit with fourth-order tangency. The shorter the reference time interval is, the better is the approximation. The laws of variation of the errors of methods for constructing such intermediate orbits with the length of the reference time interval are formulated. According to these laws, the rate of convergence of the methods to an exact solution in the process of shortening of the reference time interval is, in general, three orders of magnitude higher than that of conventional methods relying on an unperturbed Keplerian orbit. The considered orbits are among the most accurate of their class that is defined by the order of tangency. The obtained theoretical results are verified by numerical experiments on determining the orbit of 99942 Apophis.

Original language | English |
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Pages (from-to) | 204-210 |

Number of pages | 7 |

Journal | Solar System Research |

Volume | 50 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1 May 2016 |

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### Keywords

- Herrick–Gibbs method
- 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 motion of a small celestial body by intermediate perturbed orbits calculated on the basis of three position vectors and three observations.** / Shefer, V. A.; Shefer, O. V.

Research output: Contribution to journal › Article

*Solar System Research*, vol. 50, no. 3, pp. 204-210. https://doi.org/10.1134/S0038094616030060

}

TY - JOUR

T1 - On the accuracy of approximation of motion of a small celestial body by intermediate perturbed orbits calculated on the basis of three position vectors and three observations

AU - Shefer, V. A.

AU - Shefer, O. V.

PY - 2016/5/1

Y1 - 2016/5/1

N2 - Intermediate perturbed orbits, which were proposed earlier by the first author and are calculated based on three position vectors and three measurements of angular coordinates of a small celestial body, are examined. Provided that the reference time interval encompassing the measurements is short, these orbits are close in the accuracy of approximation of actual motion to an orbit with fourth-order tangency. The shorter the reference time interval is, the better is the approximation. The laws of variation of the errors of methods for constructing such intermediate orbits with the length of the reference time interval are formulated. According to these laws, the rate of convergence of the methods to an exact solution in the process of shortening of the reference time interval is, in general, three orders of magnitude higher than that of conventional methods relying on an unperturbed Keplerian orbit. The considered orbits are among the most accurate of their class that is defined by the order of tangency. The obtained theoretical results are verified by numerical experiments on determining the orbit of 99942 Apophis.

AB - Intermediate perturbed orbits, which were proposed earlier by the first author and are calculated based on three position vectors and three measurements of angular coordinates of a small celestial body, are examined. Provided that the reference time interval encompassing the measurements is short, these orbits are close in the accuracy of approximation of actual motion to an orbit with fourth-order tangency. The shorter the reference time interval is, the better is the approximation. The laws of variation of the errors of methods for constructing such intermediate orbits with the length of the reference time interval are formulated. According to these laws, the rate of convergence of the methods to an exact solution in the process of shortening of the reference time interval is, in general, three orders of magnitude higher than that of conventional methods relying on an unperturbed Keplerian orbit. The considered orbits are among the most accurate of their class that is defined by the order of tangency. The obtained theoretical results are verified by numerical experiments on determining the orbit of 99942 Apophis.

KW - Herrick–Gibbs method

KW - initial orbit determination

KW - intermediate perturbed orbit

KW - superosculating orbit

UR - http://www.scopus.com/inward/record.url?scp=84970983731&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84970983731&partnerID=8YFLogxK

U2 - 10.1134/S0038094616030060

DO - 10.1134/S0038094616030060

M3 - Article

AN - SCOPUS:84970983731

VL - 50

SP - 204

EP - 210

JO - Solar System Research

JF - Solar System Research

SN - 0038-0946

IS - 3

ER -