Celestial Mechanics and Dynamical Astronomy

, Volume 121, Issue 1, pp 1–15

Revisiting Lambert’s problem

Original Article

DOI: 10.1007/s10569-014-9587-y

Cite this article as:
Izzo, D. Celest Mech Dyn Astr (2015) 121: 1. doi:10.1007/s10569-014-9587-y


The orbital boundary value problem, also known as Lambert problem, is revisited. Building upon Lancaster and Blanchard approach, new relations are revealed and a new variable representing all problem classes, under L-similarity, is used to express the time of flight equation. In the new variable, the time of flight curves have two oblique asymptotes and they mostly appear to be conveniently approximated by piecewise continuous lines. We use and invert such a simple approximation to provide an efficient initial guess to an Householder iterative method that is then able to converge, for the single revolution case, in only two iterations. The resulting algorithm is compared, for single and multiple revolutions, to Gooding’s procedure revealing to be numerically as accurate, while having a significantly smaller computational complexity.


Lambert’s problem Orbital boundary value problem  Interplanetary trajectories Time of flight Lambert solver Gooding algorithm 

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.ESTECNoordwijkThe Netherlands

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