Laplacian Orbit Determination and Differential Corrections

Author: Branham, Richard

Source: Celestial Mechanics and Dynamical Astronomy, Volume 93, Numbers 1-4, September 2005 , pp. 53-68(16)

Publisher: Springer

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Abstract:

Laplace’s method is a standard for the calculation of a preliminary orbit. Certain modifications, briefly summarized, enhance its efficacy. At least one differential correction is recommended, and sometimes becomes essential, to increase the accuracy of the computed orbital elements. Difficult problems, lack of convergence of the differential corrections, for example, can be handled by total least squares or ridge regression. The differential corrections represent more than just getting better agreement with the observations, but a means by which a satisfactory orbit can be calculated. The method is applied to three examples of differing difficulty: to calculate a preliminary orbit of Comet 122/P de Vico from 59 observations made during five days in 1995; a more difficult calculation of a possible new object with a poor distribution of observations; Herget’s method fails for this example; and finally a really difficult object, the Amor type minor planet 1982 DV (3288 Seleucus). For this last object use of L₁ regression becomes essential to calculate a preliminary orbit. For this orbit Laplace’s method compares favorably with Gauss’s.

Keywords: Laplace’s method; L1 norm regression; orbit determination; ridge regression; total least squares

Document Type: Research article

DOI: http://dx.doi.org/10.1007/s10569-005-3242-6

Affiliations: 1: IANIGLA, C.C. 330, 5500, Mendoza, Argentina, Email: rlb@lanet.com.ar

Publication date: 2005-09-01