Astronomy and Astrophysics – Astronomy
Scientific paper
Jun 2006
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006dda....37.1503f&link_type=abstract
American Astronomical Society, DDA meeting #37, #15.03; Bulletin of the American Astronomical Society, Vol. 38, p.677
Astronomy and Astrophysics
Astronomy
Scientific paper
We present a scheme to treat properly close encounters in a three-dimensional two-body problem under perturbations. It is a combination of Sundman's time transformation and Levi-Civita's spatial coordinate transformation applied to the two-dimensional components of the position and velocity vectors in the osculating orbital plane. We adopt a coordinate triad specifying the plane as a function of the orbital angular momentum vector only. Since the magnitude of the orbital angular momentum is explicitly computed from the in-the-plane components of the position and velocity vectors, only two components of the orbital angular momentum vector are to be determined. In addition to these, we select the total energy of the two-body system and the physical time as additional components of the new variables. The equations of motion of the new variables have no singularity even when the mutual distance is extremely small, and therefore, the new variables are suitable to deal with close encounters. As a result, the number of dependent variables in the new scheme becomes eight, which is significantly smaller than the existing schemes to avoid close encounters; by two than the Kustaanheimo-Stiefel and the Burdet-Ferrandiz regularizations, and by five than the Burdet-Heggie regularization.
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