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Some simple results about the Lambert problem

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Abstract

We give simple proofs of some simple statements concerning the Lambert problem. We first restate and reprove the known existence and uniqueness results for the Keplerian arc. We also prove in some cases that the elapsed time is a convex function of natural parameters. Our statements and proofs do not distinguish between the three types of Keplerian conic section, elliptic, parabolic and hyperbolic. We also prove non-uniqueness results and non-convexity results. We do not develop any algorithm of resolution, limiting ourselves to such obviously useful a priori questions: How many solutions should we expect? Can we be sure that the Newton method will converge?

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Authors and Affiliations

  1. IMCCE, CNRS-UMR8028 Observatoire de Paris, 77, Avenue Denfert-Rochereau, 75014, Paris, France

    Alain Albouy

  2. Departamento de Matematica Aplicada, Facultad de Ciencias, Campus Universitario de Fuentenueva, Universidad de Granada, 18071, Granada, Spain

    Antonio J. Ureña

Authors
  1. Alain Albouy
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  2. Antonio J. Ureña
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Correspondence to Alain Albouy or Antonio J. Ureña.

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Albouy, A., Ureña, A.J. Some simple results about the Lambert problem. Eur. Phys. J. Spec. Top. 229, 1405–1417 (2020). https://doi.org/10.1140/epjst/e2020-900198-x

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