On solving Kepler's equation for nearly parabolic orbits

Abstract

We deal here with the efficient starting points for Kepler's equation in the special case of nearly parabolic orbits. Our approach provides with very simple formulas that allow calculating these points on a scientific vest-pocket calculator. Moreover, srtarting with these points in the Newton's method we can calculate a root of Kepler's equation with an accuracy greater than 0″.001 in 0–2 iterations. This accuracy holds for the true anomaly |ϑ| ⩽ 135° and |e − 1| ⩽ 0.01. We explain the reason for this effect also.