The mean radius vector of an elliptic orbit is equivalent to the semi-major axis.
If I sample the radius vector of an unperturbed elliptic orbit as a function of the eccentric anomaly with at a constant angular step, I get exactly the semi-major axis.
Given a value of the eccentric anomaly, I need to find the corresponding time since the TLE epoch.
While the solution is trivial for an unperturbed orbit, when I use TLE + SGP4 the algorithm is very complicated and critical (at least for the heavily perturbed very low Earth orbit satellites).
1) Is there any procedure (which works with TLE + SGP4) to calculate t as a function of E?
2) With some satellites, the eccentric anomaly is the same for different times, as showed by the following graph:
The graph could seem a bit confusing, but it simply shows the ambiguity within 1 orbit for E= -52.3 deg. Suppose that in my calculation of the semi-major axis, my current E to consider is -52.3 deg, should I take just one t (for example 18044.94) or should I take all the t’s with E= -52.3?