Mercury’s librations from self-registration of MESSENGER laser profiles

Mercury is locked in a 3:2 spin-orbit resonance. Moreover, the combination of its non-spherical shape and eccentric orbit lead to reversing torques that produce small periodic changes in its spin rate, a motion referred to as forced (physical) libration. The annual (88-day) libration of Mercury has been determined independently based on observations from Earth-based radar (Margot et al., 2012), camera and/or laser altimeter (Stark et al., 2015; Bertone et al., 2021), and radio tracking (Mazarico et al., 2014; Genova et al., 2019; Konopliv et al., 2020). Unfortunately, the precision of such annual libration measurements does not allow the detection of a large solid inner core (Van Hoolst et al., 2012). Additional long-period forced librations due to the non-Keplerian characteristics of Mercury’s orbits could be amplified by resonances if their periods are close to that of a libration eigenperiod (Yseboodt et al., 2013). Constraints on the amplifications of these additional librations would inform us about the free libration periods, which can be related to the interior structure of Mercury. Currently, these long-period librations remain largely unknown.

We devise an alternative approach based on the self-registration of laser altimetric profiles (Xiao et al., 2022; Xiao et al., 2025a) to maximize their self-consistency, while precisely tracking temporal variations of the rotation angle of the prime meridian. This allows us to simultaneously measure the annual libration and the long-period librations. We also take advantage of the fact that mismodelings in the rotation angle and external error sources would shift the laser profiles in different ways. The orbit, pointing, and timing errors are typically slow-varying and thus lead to near-constant shifts. In contrast, offsets in the rotation angles would rotate the profiles around Mercury’s spin axis. We apply our approach to MESSENGER’s Mercury Laser Altimeter (MLA) data to constrain Mercury’s librations (Xiao et al., 2025b). 

Figure 1. Rotation angle variation, with respect to Mercury’s resonant rotation, using IAU2015 model values as priors. Each dot represents the measurement from an individual MLA profile. Results using other a priori values feature similar trends.

Simulations using realistic synthetic profiles verify that there is negligible bias associated with the proposed approach. In terms of the actual profiles, we have experimented with various a priori rotation and orientation values, i.e., Stark2015, IAU2015 (Archinal et al., 2018), Genova2019, and Bertone2021. An example of the obtained temporal variation of the rotation angle is shown in Figure 1. In addition, Figure 2 shows the amplitudes of  our measured mean rotation rate and annual libration. The obtained annual libration converges to 37.53±0.56 as, which is significantly smaller than the existing estimates and indicative for a slightly smaller outer core and a larger inner core. The amplified long-period libration is clearly visible in Figure 1 with its amplitude constrained to be 18.50±1.12 as. The captured long-period libration features a period of around 6 years, and is either induced by Venus (5.66 y), Jupiter (5.93 y), or the Earth (6.57 y).  

For interpretation, we have performed libration modelling taking into account the gravitational coupling between layers (Dumberry et al., 2013) and different core compositions to investigate the insights these measurements provide into Mercury's interior (Rivoldini et al., this meeting; Yseboodt et al., this meeting). Preliminary models favor an inner core size larger than 1,000 km.  These findings will critically enhance our understanding of Mercury’s thermal evolution and magnetic dynamo. Further improvements can be expected from data by the upcoming BepiColombo Laser Altimeter (BELA) onboard ESA/JAXA’s BepiColombo mission to Mercury (Thomas et al., 2021).

Figure 2. Rotation rates and annual libration amplitudes estimated from various a priori values, in comparison with existing estimates. The 3-σ errors for our weighted mean rotation rate and annual libration are 0.53×10^-6 °/day and 0.56 as, respectively.

References

Archinal et al., 2018. Celest. Mech. Dyn. Astron., 130. https://doi.org/10.1007/s10569-017-9805-5.
Bertone et al., 2021. JGR: Planets, 126(4). https://doi.org/10.1029/2020JE006683.
Dumberry et al., 2013. Icarus, 225(1), 62-74.  https://doi.org/10.1016/j.icarus.2013.03.001.
Genova et al., 2019. GRL, 46(7). https://doi.org/10.1029/2018GL081135.
Konopliv et al., 2020. Icarus, 335, 113386. https://doi.org/10.1016/j.icarus.2019.07.020.
Margot et al., 2012. JGR: Planets, 117(E12). https://doi.org/10.1029/2012JE00416.
Mazarico et al., 2014. JGR: Planets, 119(12). https://doi.org/10.1002/2014JE004675.
Stark et al., 2015. GRL, 42(19). https://doi.org/10.1002/2015GL065152.
Thomas et al., 2021. SSR, 217, 1-62. https://doi.org/10.1007/s11214-021-00794-y.
Van Hoolst et al., 2012. EPSL, 333. https://doi.org/10.1016/j.epsl.2012.04.014.
Xiao et al., 2022. PSS, 214, 105446. https://doi.org/10.1016/j.pss.2022.105446.
Xiao et al., 2025a. GRL, 52(7), e2024GL112266. https://doi.org/10.1029/2024GL112266.
Xiao et al., 2025b. Lunar and Planetary Science Conference. https://www.hou.usra.edu/meetings/lpsc2025/pdf/1980.pdf. E-poster available at https://lpsc2025.ipostersessions.com/Default.aspx?s=6F-4E-28-F7-3A-45-58-51-CB-5C-5D-57-69-39-F5-9B.
Yseboodt et al., 2013. Icarus, 226(1). https://doi.org/10.1016/j.icarus.2013.05.011.