ON SOLVING KEPLERS EQUATION FOR NEARLY PARABOLIC ORBITS

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 sci entific vest-pocket calculator. Moreover, srtarting with these points in the Newton's method we can calculate a root of Kepler's equation wi th an accuracy greater than 0.'' 001 in 0-2 iterations. This accuracy holds for the true anomaly \phi\ less than or equal to 135 degrees and \e - 1\ less than or equal to 0.01. We explain the reason for this ef fect also.