Efficient Orbit Integration by Orbital Longitude Methods with Sundmann Transformation on the Time Variable

Details Efficient Orbit Integration by Orbital Longitude Methods with Sundmann Transformation on the Time Variable Efficient Orbit Integration by Orbital Longitude Methods with Sundmann Transformation on the Time Variable

Feb 2005

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2005aj....129.1171f&link_type=abstract

The Astronomical Journal, Volume 129, Issue 2, pp. 1171-1177.

Astronomy and Astrophysics

Astronomy

3

Celestial Mechanics, Methods: Numerical

Scientific paper

We apply Sundmann's time transformation to two orbital longitude methods for numerical integration of perturbed two-body problems that we developed previously. The modified methods share many good features with the original orbital longitude methods. In addition, they are efficient enough in integrating highly eccentric orbits to be competitive with the quadruple scaling method with Kustaanheimo-Stiefel regularization, which we have found to have the best cost performance in integrating highly eccentric orbits. Moreover, the computational cost of the new methods is significantly less than that of the quadruple scaling method, in the sense that the number of components to be integrated for the perturbed two-body problem is reduced from 13 to seven. In the case of unperturbed orbits, the new orbital longitude methods reduce to the machine-epsilon level the errors in all the orbital elements except the mean longitude at epoch, which grows linearly with respect to the real time, independently of the precision of the numerical integration used. In the case of perturbed orbits, the orbital longitude methods with Sundmann transformation are significantly superior to the original ones when the eccentricity is large, and they show more robustness against oblateness perturbations than the quadruple scaling method. However, the quadruple scaling method remains the best when only the other types of perturbations are to be considered and the nominal eccentricity is extremely large.

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