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Spin state and deep interior structure of Mars from InSight radio tracking


Knowledge of the interior structure and atmosphere of Mars is essential to understanding how the planet has formed and evolved. A major obstacle to investigations of planetary interiors, however, is that they are not directly accessible. Most of the geophysical data provide global information that cannot be separated into contributions from the core, the mantle and the crust. The NASA InSight mission changed this situation by providing high-quality seismic and lander radio science data1,2. Here we use the InSight’s radio science data to determine fundamental properties of the core, mantle and atmosphere of Mars. By precisely measuring the rotation of the planet, we detected a resonance with a normal mode that allowed us to characterize the core and mantle separately. For an entirely solid mantle, we found that the liquid core has a radius of 1,835 ± 55 km and a mean density of 5,955–6,290 kg m−3, and that the increase in density at the core–mantle boundary is 1,690–2,110 kg m−3. Our analysis of InSight’s radio tracking data argues against the existence of a solid inner core and reveals the shape of the core, indicating that there are internal mass anomalies deep within the mantle. We also find evidence of a slow acceleration in the Martian rotation rate, which could be the result of a long-term trend either in the internal dynamics of Mars or in its atmosphere and ice caps.

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Fig. 1: Estimates of the main rotation parameters.
Fig. 2: Interpretation of nutation parameters in terms of interior structure.
Fig. 3: Density jump at the core–mantle boundary as a function of FCN period.
Fig. 4: Fraction of light elements in the core of Mars.

Data availability

The RISE data that support the findings of this study are available on the Planetary Data system: Doppler data for Viking are in the REDUCED directories: DSN media calibration files are given in the RISE PDS archives: The full correlation matrix is available as source data for Extended Data Fig. 3bSource data are provided with this paper.

Code availability

Distribution of the MONTE navigation code is restricted by the Export Administration Regulations of the US Department of Commerce. Eligible readers may request a copy of MONTE, under a licence that does not permit redistribution, at GINS software is the property of CNES. It can be used for research only; any other commercial or non-commercial uses are strictly prohibited. CNES grants to the GINS Licensee (natural person) a free non-exclusive licence.


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This is InSight Contribution Number 211. The research done at the Royal Observatory of Belgium was supported by the Belgian PRODEX programme managed by the European Space Agency in collaboration with the Belgian Federal Science Policy Office, contract numbers PEA4000129361 and PEA4000140326. A.C. was supported by the French Community of Belgium within the frame of a FRIA grant. The work performed at the Jet Propulsion Laboratory, California Institute of Technology, was under contract with NASA. J.-C.M., D.A., J.B., M.D., H.S., M.W., P.L. acknowledge support from CNES and ANR (ANR-19-CE31-0008-08), and J.B., H.S. and P.L. thank IdEx Université de Paris (ANR-18-IDEX-0001). D.A. received funding from the European Research Council under the European Union’s Horizon 2020 research and innovation programme (grant agreement 724690). Those authors computing BSL models were given access to the HPC resources of IDRIS under the allocation A011041317 made by GENCI. J.B. acknowledges support from the European Research Council under the European Union’s Horizon 2020 research and innovation programme (grant agreement 101019965—ERC advanced grant SEPtiM).

Author information

Authors and Affiliations



Writing the original draft: S.L.M., A.R., M.B., A.C., M.Y., R.-M.B., T.V.H., M.D. and H.S. Writing, review and editing: M.W. and D.A. Formal analysis: S.L.M. and A.C. Validation: D.B., A.K. and M.-J.P. Software: J.-C.M., S.L.M. and A.C. Data curation: D.K., D.B., S.L.M. and A.C. Methodology: A.R., M.Y., R.-M.B., M.B., T.V.H., D.A., J.B., M.D., A.-C.P., H.S. and N.T. Investigation: S.L.M., A.R., W.M.F., D.K. and D.B. Conceptualization: W.M.F., V.D. and P.L. Project administration: W.B.B., S.S. and M.P.

Corresponding author

Correspondence to Sébastien Le Maistre.

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Extended data figures and tables

Extended Data Fig. 1

RISE Doppler residuals and signature of the liquid core. Post-fit Doppler residuals and their histogram distributions for RISE (a) and Viking 1 lander (b) as a function of the mission time after landing and of the DSN facilities location. (c) Pre-fit Doppler residuals of RISE data as a function of time computed with the latest rotation models of Konopliv et al. (2020)10 (in blue) and Kahan et al. (2021)44 (in orange). (d) Pre-fit residuals with nominal values of the classical rotation model parameters coming from converged RISE solution using only the first 24 months of data (blue) and only the last 24 months of data (orange). This shows that the classical model fails at matching RISE full arc data since a clear trend is observed in the regions not covered by the corresponding nominal solution. (e) Theoretical signature of the liquid core for the RISE timing, separated in red for the East antenna and in green for the West antenna tracking. The FCN parameters are \(F=0.06\) and FCN period of −243 days. The orange envelope shows the signature when the FCN period is slightly different (between −238 and −248 days). The pink box is the interval where the SEP angle is smaller than 15° (conjunction) while the grey boxes are the intervals where the Earth declination is close to 0°. The signature of a parameter in the Doppler observable is the difference between the observable computed using a nominal/non-zero value for this parameter and that obtained when the parameter is set to 060.

Extended Data Fig. 2

RISE data calibrations. (a) Correction for media delays as applied to the RISE data points. On the left, the corrections due to the Earth’s atmosphere as a function of the elevation at the DSN, on the right those due to Mars’ troposphere, as a function of their elevation at Mars. (b) RISE Doppler residuals: only the red points are processed, i.e. used in our analysis. Points acquired at low elevation above the DSN station (orange diamonds) are affected by large noise from the Earth’s atmosphere. They are still part of our analysis thanks to our accurate Earth noise calibration. The rest of the points are eliminated due to low SEP (blue squares), or high residual value (green crosses). (c) Estimated wet troposphere bias parameter per pass, classified by DSN station identifier. Shaded area is the a priori uncertainty.

Extended Data Fig. 3 Mars rotation and orientation angles and their correlations.

(a) Reference frames and Mars orientation angles (orange and green) for conversion between the Earth mean equator of J2000 (in blue) and Mars body-fixed coordinates (in red). (b) Correlation matrix between MONTE solved parameters (GINS correlation matrix is equivalent) using the full set of RISE data (see Supplementary Table S1 for symbol definition). Values smaller than 0.3 are set to 0 for readability.

Source Data

Extended Data Fig. 4 Comparison between the classical model of rotation of Mars and the one proposed in this study.

Temporal evolution of the 30-months solutions for the FCN period (a), the core amplification factor (b), and the precession rate (c), with the classical spin model (orange) and with the model with corrections on the rotation rate for the post-dust-storm period (blue). Shaded envelopes are \(1\sigma \) uncertainty bounds.

Extended Data Table 1 2-way Doppler data at 60 s of integration time considered in this study
Extended Data Table 2 Best solution of the main Mars rotation parameter estimates corresponding to an average of the GINS and MONTE sets of full arc solutions reported in Supplementary Table S1

Supplementary information

Supplementary Information

This file contains sections 1–13, Supplementary Figs. 1–16, Supplementary Tables 1–5 and references.

Source data

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Le Maistre, S., Rivoldini, A., Caldiero, A. et al. Spin state and deep interior structure of Mars from InSight radio tracking. Nature 619, 733–737 (2023).

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