  Lambert's problem has been long studied in the context of space operations;
its solution enables accurate orbit determination and spacecraft guidance. This
work offers an analytical solution to Lambert's problem using the Koopman
Operator (KO). In contrast to previous methods in the literature, the KO
provides the analysis of a nonlinear system by seeking a transformation that
embeds the nonlinear dynamics into a global linear representation. Our new
methodology to solve for Lambert solutions considers the position of the
system's eigenvalues on the phase plane, evaluating accurate state transition
polynomial maps for a computationally efficient propagation of the dynamics.
The methodology used and multiple-revolution solutions found are compared in
accuracy and performance with other techniques found in the literature,
highlighting the benefits of the newly developed analytical approach over
classical numerical methodologies.
