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Weierstrass elliptic and related functions have been recently shown to enableanalytical explicit solutions to classical problems in astrodynamics. Theseinclude the constant radial acceleration problem, the Stark problem and thetwo-fixed center (or Euler's) problem. In this paper we review the basictechnique that allows for these results and we discuss the limits and merits ofthe approach. Applications to interplanetary trajectory design are thendiscussed including low-thrust planetary fly-bys and the motion of anartificial satellite under the influence of an oblate primary including $J_2$and $J_3$ harmonics.

On the astrodynamics applications of Weierstrass elliptic and related functions