First-Order Planetary Theory. Perturbations in Rectangular Coordinates Hansen's Variables, Longitude, and Distance

Details First-Order Planetary Theory. Perturbations in Rectangular Coordinates Hansen's Variables, Longitude, and Distance First-Order Planetary Theory. Perturbations in Rectangular Coordinates Hansen's Variables, Longitude, and Distance

Sep 1968

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1968saosr.285.....h&link_type=abstract

SAO Special Report #285 (1968)

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5

Scientific paper

Brouwer published a method of calculating perturbations in rectangular coordinates. It is the most convenient, streamlined method to be carried to higher orders on a digital computer. A general computer program to compute the first-order theory by this method has been constructed. Literal expansion of the various functions involved has been avoided, being replaced by single- and double-harmonic analysis techniques. The program's input consists of the sequence number of the perturbing and the perturbed planets and the number of points used in the harmonic analysis. The output is the Fourier series representation of the first-order perturbations in the rectangular coordinates. Two approaches for solving for the constants of integration have been incorporated into the program. The first assumes that the perturbations in position and velocity are equal to given quantities at the initial epoch. The second, following Brouwer and Clemence, assumes that the perturbations in the z coordinate do not contain sin l , cos l and that the perturbations in the longitude do not contain the terms C0, C1t, sin l, or cos l, where l is the mean anomaly of the disturbed planet, C0 and C1 are constants, and t is the time from epoch. The program has been applied to compute the first-order theory of Mars as perturbed by the other planets. The planetary elements employed by Clemence in his theory of Mars were used for a numerical check on our program. Our results agree almost exactly with those of Clemence.

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