Skip to main content
Log in

From Astrometry to Celestial Mechanics: Orbit Determination with Very Short Arcs

(Heinrich K. Eichhorn Memorial Lecture)

  • Published:
Celestial Mechanics and Dynamical Astronomy Aims and scope Submit manuscript

Abstract

Contemporary surveys provide a huge number of detections of small solar system bodies, mostly asteroids. Typically, the reported astrometry is not enough to compute an orbit and/or perform an identification with an already discovered object. The classical methods for preliminary orbit determination fail in such cases: a new approach is necessary. When the observations are not enough to compute an orbit we represent the data with an attributable (two angles and their time derivatives). The undetermined variables range and range rate span an admissible region of solar system orbits, which can be sampled by a set of Virtual Asteroids (VAs) selected by an optimal triangulation. The attributable results from a fit and has an uncertainty represented by a covariance matrix, thus the predictions of future observations can be described by a quasi-product structure (admissible region times confidence ellipsoid), which can be approximated by a triangulation with each node surrounded by a confidence ellipsoid. The problem of identifying two independent short arcs of observations has been solved. For each VA in the admissible region of the first arc we consider prediction at the time of the second arc and the corresponding covariance matrix, and we compare them with the attributable of the second arc with its own covariance. By using the penalty (increase in the sum of squares, as in the algorithms for identification) we select the VAs which can fit together both arcs and compute a preliminary orbit. Even two attributables may not be enough to compute an orbit with a convergent differential corrections algorithm. The preliminary orbits are used as first guess for constrained differential corrections, providing solutions along the Line Of Variations (LOV) which can be used as second generation VAs to further predict the observations at the time of a third arc. In general the identification with a third arc will ensure a least squares orbit, with uncertainty described by the covariance matrix.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • M. Carpino A. Milani S.R. Chesley (2003) ArticleTitle‘Error statistics of asteroid optical astrometric observations’ Icarus 166 248–270 Occurrence Handle10.1016/S0019-1035(03)00051-4

    Article  Google Scholar 

  • J.M.A. Danby (1989) Fundamentals of Celestial Mechanics Willmann-Bell Richmond

    Google Scholar 

  • Gauss C.F., (1809), Theory of the Motion of the Heavenly Bodies Moving about the Sun in Conic Sections, reprinted by Dover publications, 1963.

  • J.D. Goldader C. Alcock (2003) ArticleTitle‘Constraining recovery observations for Trans-Neptunian objects with poorly known orbits’ Publ. Astron. Soc. Pacific 115 1330–1339 Occurrence Handle10.1086/379218

    Article  Google Scholar 

  • A. Milani M.E. Sansaturio S.R. Chesley (2001) ArticleTitle‘The asteroid identi.cation problem IV: Attributions’ Icarus 151 150–159 Occurrence Handle10.1006/icar.2001.6594

    Article  Google Scholar 

  • A. Milani G.F. Gronchi M. de’Michieli Vitturi Z. Knezević (2004) ArticleTitle‘Orbit determination with Very Short Arcs. I Admissible Regions’ CMDA 90 59–87

    Google Scholar 

  • A. Milani M.E. Sansaturio G. Tommei O. Arratia S.R. Chesley (2005a) ArticleTitle‘Multiple solutions for asteroid orbits: computational procedure and applications’ Astron. Astrophys. 431 729–746 Occurrence Handle10.1051/0004-6361:20041737

    Article  Google Scholar 

  • Milani A., Gronchi G.F., Knezević Z., Sansaturio M.E., and Arratia O., (2005)b, ‘Orbit determination with Very Short Arcs. II Identi.cations’. Icarus, submitted.

  • D. Tholen R.J. Whiteley (2003) ArticleTitle‘Short Arc Orbit Computations’ Icarus 154 412–431

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Zoran Knežević.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Milani, A., Knežević, Z. From Astrometry to Celestial Mechanics: Orbit Determination with Very Short Arcs. Celestial Mech Dyn Astr 92, 1–18 (2005). https://doi.org/10.1007/s10569-005-3314-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10569-005-3314-7

Keywords

Navigation