Just a (hopefully) quick qualitative question that I'm having a bit of trouble extracting from the literature: I've implemented a universal-variables Lambert's method in python, and it has been validated pretty darn extensively for both long and short-angle solutions. I'm using it for a school project in which we're looking at mission designs to intercept earth-threatening asteroids.
Thing is, when the asteroids get too close to Earth (around 40,000-60,000 km in altitude), at the characteristic average ECI hyperbolic velocity of somewhere between 13 and 17 km/s for solar-system bodies, the method seems to break down. Obviously for such a last-minute kind of intercept, long-angle solutions are not viable, and the necessary Delta-V could easily exceed technological feasibility.
However, going back through the derivation of the universal-variables Lambert's method derivation, I am not explicitly seeing anything that would mathematically bar the method from coming up with a solution even if the Delta-Vs were insanely high. I'm wondering if perhaps anybody's got any experience with this particular problem for high-Delta-V maneuvers and Lambert's Method.
For the record, I've gone through most of the potential error points that I, or my partners, can think of (i.e. Kepler's method for calculating mean anomalies breaking down at high eccentricities, updating equations for hyperbolic trajectories etc.) and replaced them with appropriate equations, more robust solvers, or even gone to numerical propagation in some TOF calculations.
I'm definitely not saying that it couldn't be a computational error or bug somewhere, but have been unable to positively determine that it might not be an issue with the method itself. Basically I would just like to see if I can put that possibility to bed or not.