Eccentricity-based invariant transformation of the two-body problem

Details Eccentricity-based invariant transformation of the two-body problem Eccentricity-based invariant transformation of the two-body problem

Dec 1985

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1985cemec..37..351e&link_type=abstract

Celestial Mechanics (ISSN 0008-8714), vol. 37, Dec. 1985, p. 351-358. In French.

Mathematics

2

Celestial Mechanics, Eccentricity, Two Body Problem, Comets, Many Body Problem, Transformations (Mathematics)

Scientific paper

For the non-circular two-body problem, having non-zero angular momentum a parametric transformation may be defined changing only the eccentricity and the time. This transformation is of homographic type, and it is an analytical expression depends on the value of the eccentricity with respect to unity. Therefore an hyperbolic or parabolic solution may be changed into an elliptic solution. The application and usefulness of this transformation is concerned with the capture of comets.

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