Laplacian Orbit Determination and Differential Corrections |
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| Authors: | Richard L Branham Jr |
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| Institution: | (1) IANIGLA, C.C. 330, 5500 Mendoza, Argentina |
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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. |
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| Keywords: | Laplace’ s method L1 norm regression orbit determination ridge regression total least squares |
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