A New Method to Determine the Derivatives of the Laplace Coefficients

Details A New Method to Determine the Derivatives of the Laplace Coefficients A New Method to Determine the Derivatives of the Laplace Coefficients

Mar 2004

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2004cemda..88..259s&link_type=abstract

Celestial Mechanics and Dynamical Astronomy, v. 88, Issue 3, p. 259-268 (2004).

Astronomy and Astrophysics

Astronomy

1

Scientific paper

The determination of the secular variations of the orbital elements of objects in N-body systems is based on the literal development of the perturbing function. The development makes use of the Laplace coefficients and their derivatives. In this paper a new method is described for the analytical computation of the derivatives of the Laplace coefficients. It is an explicit formula in the sense that it only contains the Laplace coefficients and the parameter α on which the Laplace coefficients depend. The advantage of this method is that it is unnecessary to calculate all the derivatives up to the desired order. It is enough to calculate the Laplace coefficients. Easy coding is a further benefit of the method and it provides more accurate numerical results. The paper describes in detail the application of the method through an example and gives comparison with former methods.

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