Abstract
We deal here with efficient starting points for Kepler's equation in a special case of nearly rectilinear hyperbolic orbits, that is these ones with the eccentricities e ≫ 1. These orbits appear in stellar dynamics when considering encounters of stars. We test efficiency of these starters for the method for successive approximation (MSA) in its two often applied variants, that is the Newton's method with the quadratic convergence (NM) and in the fixed point method (FPM). Moreover, we determine a dynamical domain of Kepler's equation for this motion.
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