Solving the Lambert Problem

This function addresses the Lambert problem, which calculates the velocity vectors V1 and V2 at two specified position vectors R1 and R2 given the transfer time t between them (noting that this method may result in high impulse requirements). The core algorithm typically employs universal variables and iterative methods like Newton-Raphson to solve the orbital boundary value problem. Key computational steps include calculating the chord length between positions, determining the transfer angle, and solving Lagrange's coefficients through transcendental equations. The resulting velocity vectors enable determination of orbital elements and spacecraft state at any time along the trajectory. The Lambert solver accommodates various orbital scenarios including elliptical, parabolic, and hyperbolic trajectories. The implementation features robust convergence handling for different transfer angles and time constraints. Through this function, users can analyze orbital mechanics principles, spacecraft navigation maneuvers, and mission design parameters. The algorithm's application extends to interplanetary trajectory planning, rendezvous scenarios, and orbital transfer optimization studies in astrodynamics.