A Semi-Analytical Theory for Improved Orbit Design of the GARATÉA-L

This work proposes a semi-analytical theory for improving orbit design of the GARATÉA-L Brazilian lunar mission. The dynamical model incorporates the lunar gravitational potential up to degree 12 and order 3 harmonics and a third-body. The new analysis still awaits peer review, but it already lays out the central claim clearly.

This matters because cosmology operates at the edge of what current instruments can measure, where systematic errors and model assumptions are never trivial. Small discrepancies between independent measurements have historically pointed toward missing physics rather than simple calibration errors, and the ongoing tension in the Hubble constant is a live example of how a persistent disagreement between methods can reshape the theoretical landscape. Each new dataset that approaches this territory with independent systematics adds real information to a problem that has resisted easy resolution for more than a decade. The dynamical model incorporates the lunar gravitational potential up to degree 12 and order 3 harmonics and a third-body perturbation model accounting for the eccentricity and. Through Hori's method, short- and medium-period terms are eliminated from the Hamiltonian to derive a first-order theory in mean orbital elements.

It is demonstrated that nominal frozen orbits designed under simplified circular and equatorial assumptions for the motion of the third body are not maintained in this more. The inclusion of the third body's inclination and eccentricity breaks the system's axial symmetry, introducing the longitude of the ascending node into the double-averaged.

Consequently, the problem is addressed through a parametric study around the simplified model's frozen conditions to identify ``low-drift" states where eccentricity variations are. A new nominal orbit is proposed for GARATÉA-L.

Numerical validation against high-fidelity propagation and JPL ephemeris confirms that this new configuration maintains the ``low-drift" behaviour throughout the mission, ensuring. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy.

The relevance goes beyond one dataset because even small shifts in measured parameters can matter when the field is testing the limits of the standard cosmological model. The Lambda-CDM framework describes the observable universe with remarkable economy, but its success rests on two components, dark matter and dark energy, whose physical nature remains entirely unknown. Any credible measurement that tightens or loosens the constraints on those components moves the entire theoretical enterprise forward, regardless of whether the immediate result looks dramatic on its own terms.

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Because this is still a preprint, the result should be read with genuine interest and proportionate caution. Peer review is not a guarantee of correctness, but it is a process that forces authors to respond to technical criticism from specialists who have no stake in a particular outcome. Preprints that survive that process, often with substantive revisions, emerge with a stronger evidential base than the version that first appeared. Until that stage is complete, the responsible reading keeps uncertainty explicitly visible rather than treating the claims as established findings.

The next step is to see whether the effect survives when independent surveys, different calibration strategies and tighter control of systematic uncertainties enter the picture. Programmes such as Euclid, DESI and the Rubin Observatory will deliver datasets over the next several years that cover the same parameter space with largely independent methods. If the current signal persists through those tests, its theoretical implications will become impossible to set aside. Until peer review and independent follow-up address those open questions, skepticism is not a failure of appreciation for the work; it is part of how science decides what to keep.

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