FUNCTION-THEORETIC ANALYSIS OF KEPLER'S EQUATION

Abstract : Kepler's equation M = E - e sin E is investigated from the function-theoretic standpoint. The complex representation leads to the conformal mapping of the complex E-plane onto the complex M-plane and shows the region of regularity of the function; that is, the region of validity. Single-valuedness of the mapping is shown by construction of a Riemann surface. (Author)