  Lambert's problem is the orbital boundary-value problem constrained by two
points and elapsed time. It is one of the most extensively studied problems in
celestial mechanics and astrodynamics, and, as such, it has always attracted
the interest of mathematicians and engineers. Its solution lies at the base of
algorithms for, e.g., orbit determination, orbit design (mission planning),
space rendezvous and interception, space debris correlation, missile and
spacecraft targeting. There is abundancy of literature discussing various
approaches developed over the years to solve Lambert's problem. We have
collected more than 70 papers and, of course, the issue is treated in most
astrodynamics and celestial mechanics textbooks. From our analysis of the
documents, we have been able to identify six or seven main solution methods,
each associated to a number of revisions and variations, and many, so to say,
secondary research lines with little or no posterior development. We have
ascertained plenty of literature with proposed solutions, in many cases
supplemented by performance comparisons with other methods. We have reviewed
and organized the existing bibliography on Lambert's problem and we have
performed a quantitative comparison among the existing methods for its
solution. The analysis is based on the following issues: choice of the free
parameter, number of iterations, generality of the mathematical formulation,
limits of applicability (degeneracies, domain of the parameter, special cases
and peculiarities), accuracy, and suitability to automatic execution.
Eventually we have tested the performance of each code. The solvers that
incorporate the best qualities are Bate's algorithm via universal variables
with Newton-Raphson and Izzo's Householder algorithm. The former is the
fastest, the latter exhibits the best ratio between speed, robustness and
accuracy.
