Closed-Form Conversion Between Mean and Osculating Elements in Vectorial Form

EasyChair Preprint 11801

Abstract

For the zonal part of Kaula's linear geopotential theory, the conversion between mean and osculating variables is derived from a generating function in closed form up to an arbitrary degree. While this scalar generator is naturally obtained in the canonical set of Delaunay variables, it is used in the construction of the short-period corrections in non-singular variables by the straightforward application of the chain rule. At difference from alternative solutions in the literature, the generating function is purely periodic in the mean anomaly, and is given in the form of a multivariate Fourier series based on the efficient Kaula recursions.

Keyphrases: Frozen orbits, Gravitational perturbations, Kaula's linear theory, Mean elements, Mean to osculating transformation, Vectorial elements, orbital motion

@booklet{EasyChair:11801,
  author    = {Martin Lara},
  title     = {Closed-Form Conversion Between Mean and Osculating Elements in Vectorial Form},
  howpublished = {EasyChair Preprint 11801},
  year      = {EasyChair, 2024}}