Universal procedures for conversion of orbital elements to and from position and velocity (unperturbed orbits)
Abstract
Universally applicable algorithms for converting from orbital elements to position and velocity, and vice versa are presented. Though the element set is universal, the algorithms distinguish internally between six types of orbit, three of them rectilinear, since this leads to maximum efficiency and accuracy. The element set is not free from singularity, but it is shown that this does not detract from the universal validity of the computing procedures that implement the algorithms. Because of the importance of singularities in other contexts, however, a convenient method of dealing with them, when necessary, is described. The algorithm that converts from elements to position and velocity requires the solution of Kepler's equation for elliptic orbits, and the analogous equation for hyperbolic orbits.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 June 1987
 Bibcode:
 1987STIN...8821184G
 Keywords:

 Orbital Elements;
 Orbital Mechanics;
 Orbital Position Estimation;
 Orbital Velocity;
 Algorithms;
 Singularity (Mathematics);
 Astrodynamics