A formulation to obtain semi-analytical planetary theories using true anomalies as temporal variables

Details A formulation to obtain semi-analytical planetary theories using true anomalies as temporal variables A formulation to obtain semi-analytical planetary theories using true anomalies as temporal variables

Jul 2007

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2007jcoam.204...77l&link_type=abstract

Journal of Computational and Applied Mathematics, vol. 204, no. 1, pp. 77-83

Statistics

Computation

1

Celestial Mechanics, Orbital Mechanics, Disturbing Function, Planetary Theory

Scientific paper

The main methods used to obtain analytical theories of perturbed motion in celestial mechanics are based on the expansion of the disturbing function in trigonometric series of the mean anomalies (or longitudes). In this paper a new method based on the double Fourier series expansion using the true anomalies (or longitudes) is developed. The method involves a semi-analytical technique to allow the expansion of the inverse of the distance with great accuracy, and a new integration technique using a linear combination of the true anomalies based on an iterative method to integrate each term of the expansion of the Lagrange planetary equations.

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