Secondorder piterative solution of the Lambert/Gauss problem.
Abstract
An algorithm is presented for efficient piterative solution of the Lambert/Gauss orbitdetermination problem using secondorder Newton iteration. The algorithm is based on a universal transformation of Kepler's timeofflight equation and approximate inverse solutions of this equation for shortway and longway flight paths. The approximate solutions provide both good starting values for iteration and simplified computation of the secondorder term in the iteration formula. Numerical results are presented which indicate that in many cases of practical significance (except those having collinear position vectors) the algorithm produces at least eight significant digits of accuracy with just two or three steps of iteration.
 Publication:

Journal of the Astronautical Sciences
 Pub Date:
 December 1984
 Bibcode:
 1984JAnSc..32..475B
 Keywords:

 Iterative Solution;
 Kepler Laws;
 Orbit Calculation;
 Orbital Mechanics;
 Trajectory Analysis;
 Algorithms;
 Eccentric Orbits;
 Error Analysis;
 Flight Paths;
 Flight Time;
 Gauss Equation;
 Newton Theory;
 Astrodynamics;
 Celestial Mechanics:Orbit Determination;
 Orbit Determination:Celestial Mechanics