Tables for the Development of the Disturbing Function With Schedules for Harmonic Analysis (Classic Reprint)

Excerpt from Tables for the Development of the Disturbing Function With Schedules for Harmonic Analysis

These tables of the coefficients in the development of the disturbing function have been so constructed that for the great majority of problems which demand the calculation of general planetary perturbations, the values of the coefficients may be extracted by interpolation with first differences only. To achieve this within a reasonable compass, it was necessary to separate those factors of the coefficients which vary rapidly with the argument from those which vary slowly: the former are simple functions of the argument easily computed while the latter portions are tabulated. Since the product of four factors will, in general, be needed for the calculation of any term in the disturbing function or disturbing forces, it was advisable to tabulate the logarithms rather than the natural values.

While the tables are available for any mode of development of the planetary theory, the calculations of the disturbing forces can best be reduced to routine computation by the methods of harmonic analysis. To facilitate the work of carrying it out, schedules for the analysis are shown in detail with examples. Additional tables to aid in the calculation of the special values of the functions are also given.

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