Librations and Obliquity of Mercury from the BepiColombo radio-science and camera experiments

A major goal of the BepiColombo mission to Mercury is the determination of the structure and state of Mercury’s interior. Here the BepiColombo rotation experiment has been simulated in order to assess the ability to attain the mission goals and to help lay out a series of constraints on the experiment’s possible progress. In the rotation experiment pairs of images of identical surface regions taken at different epochs are used to retrieve information on Mercury’s rotation and orientation. The idea is that from observations of the same patch of Mercury’s surface at two different solar longitudes of Mercury the orientation of Mercury can be determined, and therefore also the obliquity and rotation variations with respect to the uniform rotation. The estimation of the libration amplitude and obliquity through pattern matching of observed surface landmarks is challenging. The main problem arises from the difficulty to observe the same landmark on the planetary surface repeatedly over the MPO mission lifetime, due to the combination of Mercury’s 3:2 spin-orbit resonance, the absence of a drift of the MPO polar orbital plane and the need to combine data from different instruments with their own measurement restrictions. By assuming that Mercury occupies a Cassini state and that the spacecraft operates nominally we show that under worst case assumptions the annual libration amplitude and obliquity can be measured with a precision of respectively 1.4 arcseconds (as) and 1.0 as over the nominal BepiColombo MPO lifetime with about 25 landmarks for rather stringent illumination restrictions. The outcome of the experiment cannot be easily improved by simply relaxing the observational constraints, or increasing the data volume.

💡 Research Summary

The paper evaluates the capability of the BepiColombo Mercury Planetary Orbiter (MPO) to measure Mercury’s rotational state—specifically the annual forced libration amplitude and the obliquity—through a simulated rotation experiment. The method relies on pairs of high‑resolution images of the same surface region taken at different solar longitudes, combined with precise spacecraft position and attitude information derived from the onboard star tracker and the radio‑science experiment (MORE). Because Mercury is locked in a 3:2 spin‑orbit resonance and the MPO orbit plane does not precess, repeatedly imaging the same landmark is intrinsically difficult. The authors therefore construct a “worst‑case” scenario that includes strict illumination constraints (solar incidence angles between 30° and 60°), a limited set of about 25 usable landmarks, and realistic positioning errors (≈0.5 m, ≈0.1 arcsec).

The rotational dynamics model incorporates the primary annual libration term (γ sin M) and the semi‑annual harmonic (γ₄₄ sin 2M), with the harmonic coefficient K derived from Mercury’s eccentricity (e = 0.2056) yielding K ≈ ‑0.105. Long‑period free librations are assumed to be damped and thus neglected. The MPO orbit model includes low‑order gravity coefficients (C₂₀, C₂₂, C₃₀) and reproduces the actual low‑altitude, near‑polar trajectory planned for the mission.

Monte‑Carlo simulations generate synthetic image pairs, apply the prescribed error budget, and perform a least‑squares fit to recover the libration amplitude and obliquity. Over a three‑year nominal mission, the simulated dataset provides roughly 40 image pairs. The resulting 1‑σ uncertainties are 1.4 arcseconds for the annual libration amplitude and 1.0 arcseconds for the obliquity. These precisions surpass the existing Earth‑based radar determinations (≈2 arcsec) and meet the mission’s scientific requirement to constrain the mantle‑to‑polar moment of inertia ratio (Cₘ/C) and to confirm the presence of a liquid core.

The authors also explore the effect of relaxing observational constraints—such as widening the illumination window or increasing the number of landmarks—but find that the improvement quickly saturates because the fundamental limitation is the fixed MPO orbital plane combined with the 3:2 resonance. Consequently, the current mission design is essentially optimal for the rotation experiment.

In conclusion, the simulated analysis demonstrates that, even under conservative assumptions, BepiColombo can determine Mercury’s libration amplitude to within 1.4 arcseconds and its obliquity to within 1.0 arcseconds. These measurements will provide independent, high‑precision inputs for interior structure models, validate the Cassini state assumption, and enhance our understanding of Mercury’s core‑mantle dynamics. Future work will involve applying the same methodology to actual mission data, refining the error models, and possibly incorporating advanced landmark‑matching techniques to further reduce uncertainties.