Theorem: Kepler Newton step from E = M gives (M e cos M - M - e sin M) / (e cos M - 1)

Theorem (Kepler single-Newton-step canonical): starting Newton-Raphson from initial guess E_0 = M applied to f(E) = E - e sin E - M gives exactly one iterate E_1 = M - f(M)/f'(M) which simplifies to (M e cos(M) - M - e sin(M)) / (e cos(M)…