Orbit Determination

  • Oliver Montenbruck
  • Thomas Pfleger


The classical aim of orbit determination is to obtain the orbital elements of a planet, comet, or minor planet from the smallest possible number of observed positions. This is therefore essentially the opposite to determining an ephemeris, where positions are obtained from known orbital elements. Any observation made from Earth at a specific time gives two spherical coordinates. We may chose whether these relate to the celestial equator (right ascension and declination) or to the ecliptic (ecliptic longitude and latitude). On the other hand, the distance cannot be measured, so knowledge of it cannot be used in orbit determination. To derive six orbital elements, the same number of independent observational values are required, so three observations must be available.


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  1. [40]
    C. F. Gauss; Theory of the Motion of the Heavenly Bodies Moving about the Sun in Conic Sections: Dover Publications; New York; English translation of Theoria motus corporum coelestium) in which Gauss describes his method of orbital determination. The book is mainly of historical interest, but it is less suitable as a textbook on orbital determination.Google Scholar
  2. [41]
    H. Bucerius; Bahnbestimmung als Randwertproblem I–V; Astronomische Nachrichten, vol. 278, 280, 281, 282 (1950–1955); A series of five papers, in which Gauss’ simplified and full methods of orbital determination are examined, amongst other subjects. Numerous examples illustrate possible problems that may occur in determining orbits.Google Scholar
  3. [42]
    D. L. Boulet; Methods of orbit determination for the micro computer: Willmann-Bell; Richmond, Virginia (1991). Principles and methods of ephemeris calculation and orbit determination, including special perturbations and the orbit determination methods of Laplace, Olbers and Gauss. The listed Basic programs are also available on floppy disk. An up-to-date introduction to orbital determination is also given by the corresponding chapter in Himmelsmechanik I by Bucerius and Schneider [2].Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Oliver Montenbruck
    • 1
  • Thomas Pfleger
    • 2
  1. 1.DLR-GSOCWeßlingGermany
  2. 2.HennefGermany

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