Comparison between our analytical estimates (see Eqs. (24), (25), (33), (34)) and the expected values of the eccentricity (e), the mean longitude at the reference time (λ = M₀ + ω), the semi-amplitude K, and the argument of periastron (ω) (from top to bottom), as a function of ω and for e = 0.5, 0.8, 0.9, 0.95 (from left to right). We show the errors obtained on the parameters using the approximations C = 1/4, and (see Sect. 3.2). For the approximation , we also show the errors after one and two iterations of the Newton-Raphson correcting algorithm (see Sect. 3.4).