Alternative solution of Kepler's equation
Abstract
Kepler's equation: M = Ee Sin E, is frequently solved for E(M) in order to determine v (where M is the mean anomaly, E the eccentric anomaly, e the eccentricity, and v the true anomaly). By introducing a new auxiliary angle F at the second focus of the ellipse, computations can be reduced. If E is near 0 or 180 deg, this method will always be more accurate than the conventional technique. The new solution is calculated and presented to the 5th order in e, and the resulting residuals are presented. In addition a new companion equation, using the 3 point, or H angle method is also presented, for values of E near 90 deg. These techniques are frequently faster and more accurate.
 Publication:

AAS and AIAA
 Pub Date:
 August 1991
 Bibcode:
 1991ads..confQ....V
 Keywords:

 Celestial Mechanics;
 Orbital Elements;
 Trigonometric Functions;
 Angles (Geometry);
 Angular Momentum;
 Bessel Functions;
 Conservation Laws;
 Lagrange Multipliers;
 Astrophysics