Astronomy and Astrophysics – Astronomy
Scientific paper
Nov 2003
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2003ala..conf...85b&link_type=abstract
Astronomy in Latin America, Second Meeting on Astrometry in Latin America and Third Brazilian Meeting on Fundamental Astronomy,
Astronomy and Astrophysics
Astronomy
Scientific paper
Laplace's method is a standard for the calculation of a preliminary orbit. Certain modifications enhance its efficacy: reduce the observations, if necessary, by use of the L1 criterion; use a polynomial, whose order is determined by impersonal criteria, to calculate the first and second derivatives of observational quantities; combine the separate equations, one to determine the heliocentric distance of the object and the other its geocentric distance, into one polynomial equation for the heliocentric distance, whose roots are found by a standard algorithm; use recursion to calculate the f and g series. At least one differential correction is recommended 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 method is first applied to calculate a preliminary orbit of Comet P/ 1846 D1 (de Vico) from 59 observations made during five days in 1995 and then to a more difficult object, the Amor type minor planet 1982 DV (3288 Seleucus).
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