Expansion of the planetary mutual distance raised to any negative power by the method of symbolic differential operators. (English) Zbl 0883.70009
Summary: We present an approach to evaluate \(\Delta^{-s}\) necessary for the construction of high-order planetary theories. This approach is valid to be applied on very large scale digital computers with standard Poisson series programs, for high-order and high-degree planetary theories. We apply the method of symbolic differential operators for single variable functions, and the binomial theorem expansions, for the evaluation of \(\Delta^{-s}\). We utilize Laplace coefficients and their derivatives to carry out the development, without dealing with Newcomb operators or Hansen’s coefficients.
MSC:
| 70F15 | Celestial mechanics |
Keywords:
planetary perturbations; high-order planetary theories; Poisson series programs; binomial theorem expansions; Laplace coefficientsReferences:
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