A semi-analytic theory for preliminary analysis of GARATÉA-L Brazilian lunar mission

Abstract

© 2025 COSPARThis work describes the development of a semi-analytic theory for a preliminary orbit analysis of the GARATÉA-L Brazilian lunar probe. The dynamical model includes the effects of the zonal harmonics J2 up to J12, the effects of second- and third-degree tesserals and sectorials, and the third-body perturbation due to the attraction of the Earth. The Hamiltonian describing the dynamics is implicitly expressed in Delaunay variables, and, Hori's method is applied to derive a semi-analytic solution which is expressed in closed form with respect to the eccentricity. Expressions for Keplerian orbital elements are obtained including short-period and medium-period terms. In order to avoid singularities in eccentricity, non-singular orbital elements are introduced to compute frozen orbit conditions considering several values of inclinations and semi-major axes. A preliminary analysis of the orbit of the GARATÉA-L Brazilian probe is conducted, and the results are compared to those provided by several models using Cowell's method. A realistic model based on ephemeris data is also used for comparison. The findings reveal that the probe's nominal orbit does not exhibit a frozen condition in terms of eccentricity. A new inclination is proposed to freeze the orbit without altering the pericenter and apocenter altitudes. However, orbital evolution results in a collision with the Moon, as revealed by the 50 × 50 models. A polar frozen orbit is then suggested, offering the advantage of gradually shifting the sub-pericenter point from the South Pole toward the center of the Aitken Basin region.

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