Abstract:
Lambert’s problem concerns determining an orbital transfer trajectory that connects two position vectors in a specified time, and multiple mathematical formulations exist to solve it efficiently across all orbit types. Key distinctions in transfer geometry include short-way versus long-way paths, low-energy versus high-energy solutions, and the presence of zero or multiple revolutions, yielding several valid trajectories for a single endpoint pair. Modern solution strategies such as universal variables, Battin’s method, and related iterative schemes aim to improve robustness, convergence, and computational speed, particularly for hyperbolic, high-energy, or multi-revolution cases. The study of solution spaces reveals how semimajor axis, time-of-flight, and perigee radius vary across different transfer families, enabling deeper insight into feasible orbital dynamics. Practical applications span rendezvous, intercept, stationkeeping, initial orbit determination, and debris cloud modeling, where Lambert solutions help characterize risk and fragment dispersal. Advances in analytical methods and numerical techniques continue to expand the reliability and utility of Lambert-based trajectory design within modern astrodynamics.
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Vallado, D.A., “Lambert’s Problem – not another one!,” University of Arizona guest lecture, AGI SSA Initiative Project CoSTAR - Commercial SSA Technology for Academic Research, 9 Nov 2019, accessible at https://comspoc.com/Resources/Content/Private/C-20220425T181322/Presentation/20191109_Lambert%e2%80%99s%20Problem%20%e2%80%93%20not%20another%20one%20-%20UA.show.pdf..
