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Lambert problem solution in the hill model of motion

Abstract

The goal of this paper is obtaining a solution of the Lambert problem in the restricted three-body problem described by the Hill equations. This solution is based on the use of pre determinate reference orbits of different types giving the first guess and defining the sought-for transfer type. A mathematical procedure giving the Lambert problem solution is described. This procedure provides step-by-step transformation of the reference orbit to the sought-for transfer orbit. Numerical examples of the procedure application to the transfers in the Sun–Earth system are considered. These examples include transfer between two specified positions in a given time, a periodic orbit design, a halo orbit design, halo-to-halo transfers, LEO-to-halo transfer, analysis of a family of the halo-to-halo transfer orbits. The proposed method of the Lambert problem solution can be used for the two-point boundary value problem solution in any model of motion if a set of typical reference orbits can be found.

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Correspondence to Alexander Sukhanov.

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Sukhanov, A., Prado, A.F.B.A. Lambert problem solution in the hill model of motion. Celestial Mech Dyn Astr 90, 331–354 (2004). https://doi.org/10.1007/s10569-004-1508-z

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Keywords

  • Lambert problem
  • three-body problem
  • Hill equations
  • Lagrange points
  • halo orbit