BOUNDS ON THE SOLUTION TO KEPLER'S EQUATION : II. UNIVERSAL AND OPTIMAL STARTING POINTS

Abstract

In this paper we find bounds on the solution to Kepler's equation for hyperbolic and parabolic motions. Two general concepts introduced here may be proved useful in similar numerical problems. Moreover, we give optimal starting points for Kepler's equation in hyperbolic and elliptic motions with particular attention to nearly parabolic orbits. It allows to expand the accepted earlier interval |e - 1| ≤ 0.01 for nearly parabolic orbits to the interval |e - 1| ≤ 0.05.