COORDINATES IN KEPLERIAN MOTION AS DALEMBERTIAN FUNCTIONS

The article is a continuation of a series of studies connected with fu ndamental functions of Keplerian motion. The independent variables use d in the two-body problem are the semi-major axis a, mean orbital long itude lambda, eccentricity r, longitude of pericenter phi, sine of hal f the inclination r(1), and longitude of the ascending node phi(1). It is shown that the Cartesian coordinates are D'Alembertian functions o f the pairs (r, phi) and (r(1), phi(1)) for real values of a and lambd a. 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 do main \a\ less than or equal to (a) over bar, \F lambda\ less than or e qual to c, it is necessary to set R = R(0)e(-c) and R-1 = 1.