Coordinates in Keplerian motion as D'Alembertian functions

Details Coordinates in Keplerian motion as D'Alembertian functions Coordinates in Keplerian motion as D'Alembertian functions

May 1998

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1998arep...42..420k&link_type=abstract

Astronomy Reports, Volume 42, Issue 3, May 1998, pp.420-424

Astronomy and Astrophysics

Astronomy

1

Scientific paper

The article is a continuation of a series of studies connected with fundamental functions of Keplerian motion. The independent variables used in the two-body problem are the semi-major axis a, mean orbital longitude lambda, eccentricity r, longitude of pericenter phi, sine of half the inclination r_1, and longitude of the ascending node phi_1. It is shown that the Cartesian coordinates are D'Alembertian functions of the pairs (r, phi) and (r_1, phi_1) for real values of a and . Their D'Alembertian radii R and R_1 are equal to the Laplace limit R_0 and to unity, respectively. If a and lambda vary in the complex domain |a| <= a_bar,|lambda| <= c, it is necessary to set R = R_0e^-c and R_1 = 1.

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