Universal trueanomaly time equations
Abstract
In a trueanomaly regularization of the twobody problem, time becomes a dependent variable governed by its own differential equation. Heretofore, that equation has not been integrated in a form which is valid for all kinds of orbits. However, a universal trueanomaly time equation would lead to new algorithms for the Kepler and Lambert problems, analogous to well known eccentricanomaly methods, but cast solely in terms of the orbital transfer angle. In this analysis it is shown that the direct relation between time and true anomaly can be developed in a variety of computationally useful forms which are valid for all kinds of orbits, including rectilinear ones. A Newtonian iteration for the Keplerian initialvalue problem is developed which requires only one transcendental function evaluation per cycle. Subsequently, the state vector and transition matrix can be computed in rational algebraic terms.
 Publication:

Astrodynamics 1989
 Pub Date:
 1990
 Bibcode:
 1990asdy.conf.1195S
 Keywords:

 Astrodynamics;
 Differential Equations;
 Kepler Laws;
 Transfer Orbits;
 Two Body Problem;
 Universal Time;
 Computer Programs;
 Iterative Solution;
 Orbital Mechanics;
 State Vectors;
 Transcendental Functions;
 Astrodynamics