Second-Order Planetary Theory. Part i: Outline of the Method

Details Second-Order Planetary Theory. Part i: Outline of the Method Second-Order Planetary Theory. Part i: Outline of the Method

Jul 1969

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1969saosr.302.....h&link_type=abstract

SAO Special Report #302 (1969)

Statistics

Computation

3

Scientific paper

The analytical procedure for computing second-order perturbations in rectangular coordinates, according to Brouwer's theory of planetary motion, is given. Single and double-harmonic analyses and the multiplication of Fourier series with numerical coefficients are used in the computations. In the series multiplication, a variable tolerance is considered, enabling us to avoid the difficulties arising from a small divisor. Also presented is an example computing that part of the second-order perturbation of Mars containing the masses of Jupiter and Saturn. The analytical solution of this perturbation is compared with the numerical integration of the differential equations defining this perturbation. The numerical integration covered the interval from 0 to 40,000 days. The comparison shows an agreement within 1 X 10-9.

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