Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

A low-density ocean inside Titan inferred from Cassini data

Nature Astronomy (2024)Cite this article

Subjects

An Author Correction to this article was published on 14 May 2024

This article has been updated

Abstract

The Cassini mission has provided measurements of the gravity of several moons of Saturn as well as an estimate of the tidal response, which is expressed as the degree 2 Love number k2 of its largest moon, Titan. The first estimates of Titan’s Love number were larger than pre-Cassini expectations. Interior modelling suggested it may be explained with a dense ocean, but the interpretation remains unclear. We analysed Cassini tracking data to determine Titan’s gravity field and its Love number. Our gravity results are consistent with earlier studies, but we find a lower Love number for Titan of k2 = 0.375 ± 0.06. This lower value follows from an elaborate investigation of the tidal effects. We show that a dense ocean is not implied by the obtained Love number; instead, a water or ammonia ocean is more probable. A lower density ocean can increase the likeliness of contact between the silicate core and ocean, which can leach minerals into the ocean and could promote its habitability.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Titan’s gravity expressed as radial accelerations.
Fig. 2: RMS power for Titan’s gravity.
Fig. 3: Properties of Titan’s core.
Fig. 4: Ocean density versus Love number k2 for Titan.

Similar content being viewed by others

Data availability

Cassini radio tracking data and ancillary information can be found at the Planetary Data System’s Atmospheres node (https://pds-atmospheres.nmsu.edu/data_and_services/atmospheres_data/Cassini/inst-rss.html). Results from our analysis such as the gravity field models and output from our MCMC modelling are available via NASA’s Planetary Geodesy Data Archive at https://pgda.gsfc.nasa.gov/products/91 or https://doi.org/10.60903/gsfcpgda-titank2.

Code availability

We used the open source software TidalPy to analyse Titan’s Love number (https://doi.org/10.5281/zenodo.7017474 (ref. 43)) and the emcee open source software32 for our MCMC analysis (https://emcee.readthedocs.io/en/stable/). We also used the PlanetProfile software44 (https://github.com/vancesteven/PlanetProfile) to compute the self-consistent interior models for Titan used in our modelling. The input data for the MCMC analysis are the results presented in this work; additional input parameters for TidalPy are discussed in the text and listed in Supplementary Table 4. We also used the Python package corner45 for the distribution plot in Supplementary Information. We cannot provide the software used for the analysis of the Cassini tracking data, but the methods have long been established and are described in detail in Methods. All figures (apart from the distribution plot in Supplementary Fig. 5) were drawn with the free software GMT (https://www.generic-mapping-tools.org/)46.

Change history

References

  1. Iess, L. et al. Gravity field, shape, and moment of inertia of Titan. Science 327, 1367–1369 (2010).

    Article  ADS  Google Scholar 

  2. Tortora, P. et al. Rhea gravity field and interior modeling from Cassini data analysis. Icarus 264, 264–273 (2016).

    Article  ADS  Google Scholar 

  3. Durante, D., Hemingway, D. J., Racioppa, P., Iess, L. & Stevenson, D. J. Titan’s gravity field and interior structure after Cassini. Icarus 326, 123–132 (2019).

    Article  ADS  Google Scholar 

  4. Zannoni, M., Hemingway, D., Gomez Casajus, L. & Tortora, P. The gravity field and interior structure of Dione. Icarus 345, 113713 (2020).

    Article  Google Scholar 

  5. Iess, L. et al. Measurement and implications of Saturn’s gravity field and ring mass. Science 364, aat2965 (2019).

    Article  ADS  Google Scholar 

  6. Iess, L. et al. The tides of Titan. Science 337, 457–459 (2012).

    Article  ADS  Google Scholar 

  7. Lunine, J. I. & Stevenson, D. J. Clathrate and ammonia hydrates at high pressure: application to the origin of methane on Titan. Icarus 70, 61–77 (1987).

    Article  ADS  Google Scholar 

  8. Grasset, O. & Sotin, C. The cooling rate of a liquid shell in Titan’s interior. Icarus 123, 101–112 (1996).

    Article  ADS  Google Scholar 

  9. Grasset, O., Sotin, C. & Deschamps, F. On the internal structure and dynamics of Titan. Planet. Space Sci. 48, 617–636 (2000).

    Article  ADS  Google Scholar 

  10. Sohl, F., Hussmann, H., Schwentker, B., Spohn, T. & Lorenz, R. D. Interior structure models and tidal Love numbers of Titan. J. Geophys. Res. Planets 108, 5130 (2003).

    Article  ADS  Google Scholar 

  11. Rappaport, N., Bertotti, B., Giampieri, G. & Anderson, J. D. Doppler measurements of the quadrupole moments of Titan. Icarus 126, 313–323 (1997).

    Article  ADS  Google Scholar 

  12. Rappaport, N. J. et al. Can Cassini detect a subsurface ocean in Titan from gravity measurements? Icarus 194, 711–720 (2008).

    Article  ADS  Google Scholar 

  13. Sohl, F. et al. Structural and tidal models of Titan and inferences on cryovolcanism. J. Geophys. Res. Planets 119, 1013–1036 (2014).

    Article  ADS  Google Scholar 

  14. Sotin, C., Kalousová, K. & Tobie, G. Titan’s interior structure and dynamics after the Cassini–Huygens mission. Annu. Rev. Earth Planet. Sci. 49, 579–607 (2021).

  15. Stiles, B. W. et al. Determining Titan’s spin state from Cassini RADAR images. Astron. J. 135, 1669–1680 (2008).

    Article  ADS  Google Scholar 

  16. Zebker, H. A. et al. Size and shape of Saturn’s moon Titan. Science 324, 921–923 (2009).

    Article  ADS  Google Scholar 

  17. Mitri, G. et al. Shape, topography, gravity anomalies and tidal deformation of Titan. Icarus 236, 169–177 (2014).

    Article  ADS  Google Scholar 

  18. Baland, R.-M., Tobie, G., Lefèvre, A. & Van Hoolst, T. Titan’s internal structure inferred from its gravity field, shape, and rotation state. Icarus 237, 29–41 (2014).

    Article  ADS  Google Scholar 

  19. Beuthe, M. Tidal Love numbers of membrane worlds: Europa, Titan, and co. Icarus 258, 239–266 (2015).

    Article  ADS  Google Scholar 

  20. Iess, L. et al. The gravity field and interior structure of Enceladus. Science 344, 78–80 (2014).

    Article  ADS  Google Scholar 

  21. Murray, C. & Dermott, S. Solar System Dynamics (Cambridge Univ. Press, 1999).

  22. Meriggiola, R., Iess, L., Stiles, B. W., Lunine, J. I. & Mitri, G. The rotational dynamics of Titan from Cassini RADAR images. Icarus 275, 183–192 (2016).

    Article  ADS  Google Scholar 

  23. Fortes, A. D. Titan’s internal structure and the evolutionary consequences. Planet. Space Sci. 60, 10–17 (2012).

    Article  ADS  Google Scholar 

  24. Gao, P. & Stevenson, D. J. Nonhydrostatic effects and the determination of icy satellites’ moment of inertia. Icarus 226, 1185–1191 (2013).

    Article  ADS  Google Scholar 

  25. Coyette, A., Baland, R.-M. & Van Hoolst, T. Variations in rotation rate and polar motion of a non-hydrostatic Titan. Icarus 307, 83–105 (2018).

    Article  ADS  Google Scholar 

  26. Zharkov, V. N., Leontjev, V. V. & Kozenko, V. A. Models, figures, and gravitational moments of the Galilean satellites of Jupiter and icy satellites of Saturn. Icarus 61, 92–100 (1985).

    Article  ADS  Google Scholar 

  27. Asmar, S. W., Armstrong, J. W., Iess, L. & Tortora, P. Spacecraft Doppler tracking: noise budget and accuracy achievable in precision radio science observations. Radio Sci. 40, RS2001 (2005).

    Article  ADS  Google Scholar 

  28. Ermakov, A. I., Park, R. S. & Bills, B. G. Power laws of topography and gravity spectra of the Solar System bodies. J. Geophys. Res. Planets 123, 2038–2064 (2018).

    Article  ADS  Google Scholar 

  29. Eanes, R., Schutz, B. & Tapley, B. Earth and ocean tide effects on Lageos and Starlette. In Proc. 9th International Symposium on Earth Tides (ed. Kuo, J. T.) 239–249 (E. Schweizerbart, 1983).

  30. McCarthy, D. D. & Petit, G. IERS Conventions (2003) Technical Note 32 (IERS, 2004).

  31. Vance, S. D. et al. Geophysical investigations of habitability in ice-covered ocean worlds. J. Geophys. Res. Planets 123, 180–205 (2018).

    Article  ADS  Google Scholar 

  32. Foreman-Mackey, D., Hogg, D. W., Lang, D. & Goodman, J. emcee: The MCMC hammer. Publ. Astron. Soc. Pac. 125, 306 (2013).

    Article  ADS  Google Scholar 

  33. Pavlis, D. E. & Nicholas, J. B. GEODYN II system description (vols. 1–5). Contractor report, (SGT Inc., 2017); https://earth.gsfc.nasa.gov/geo/data/geodyn-documentation

  34. Bertotti, B., Iess, L. & Tortora, P. A test of general relativity using radio links with the Cassini spacecraft. Nature 425, 374–376 (2003).

    Article  ADS  Google Scholar 

  35. Archinal, B. A. et al. Report of the IAU Working Group on Cartographic Coordinates and Rotational Elements: 2015. Celest. Mech. Dyn. Astron. 130, 22 (2018).

    Article  ADS  MathSciNet  Google Scholar 

  36. Bellerose, J., Roth, D. & Criddle, K. in Space Operations: Inspiring Humankind’s Future (eds Pasquier, H. et al.) 575–588 (Springer, 2019); https://arc.aiaa.org/doi/10.2514/6.2018-2646

  37. Barbaglio, F., Armstrong, J. W. & Iess, L. Precise Doppler measurements for navigation and planetary geodesy using low gain antennas: test results from Cassini. In Proc. 23rd International Symposium on Space Flight Dynamics (German Aerospace Center, 2012); https://issfd.org/ISSFD_2012/ISSFD23_OD1_4.pdf

  38. Montenbruck, O. & Gill, E. Satellite Orbits (Springer-Verlag, 2000).

  39. Tapley, B. D., Schutz, B. E. & Born, G. H. Statistical Orbit Determination (Elsevier, 2004).

  40. Kusche, J. Noise variance estimation and optimal weight determination for GOCE gravity recovery. Adv. Geosci. 1, 81–85 (2003).

    Article  Google Scholar 

  41. Běhounková, M., Souček, O., Hron, J. & Čadek, O. Plume activity and tidal deformation on Enceladus influenced by faults and variable ice shell thickness. Astrobiology 17, 941–954 (2017).

    Article  ADS  Google Scholar 

  42. Hemingway, D. J. & Mittal, T. Enceladus’s ice shell structure as a window on internal heat production. Icarus 332, 111–131 (2019).

    Article  ADS  Google Scholar 

  43. Renaud, J. P. TidalPy (0.4.1). Zenodo https://doi.org/10.5281/zenodo.7017474 (2023).

  44. Styczinski, M. J., Vance, S. D. & Melwani Daswani, M. Planetprofile: self-consistent interior structure modeling for ocean worlds and rocky dwarf planets in Python. Earth Space Sci. 10, e2022EA002748 (2023).

    Article  ADS  Google Scholar 

  45. Foreman-Mackey, D. corner.py: scatterplot matrices in Python. J. Open Source Softw. 1, 24 (2016).

    Article  ADS  Google Scholar 

  46. Wessel, P., Smith, W. H. F., Scharroo, R., Luis, J. & Wobbe, F. Generic Mapping Tools: improved version released. Eos Trans. Am. Geophys. Union 94, 409–410 (2013).

    Article  ADS  Google Scholar 

  47. Kaula, W. M. Theory of Satellite Geodesy, Applications of Satellites to Geodesy (Blaisdell Publishing Company, 1966).

Download references

Acknowledgements

This work was funded by NASA’s Cassini Data Analysis Program (S.G., B.v.N. and E.M.). We thank T. Sabaka (NASA/GSFC), S. Bertone (NASA/GSFC, University of Maryland, Baltimore County, and CRESST II), W. Henning and J. Renaud (NASA/GSFC, University of Maryland and CRESST II), G. Cascioli (NASA/GSFC and University of Maryland, Baltimore County), and D. Durante and L. Iess (Sapienza University of Rome, Italy) for discussions.

Author information

Author notes

  1. Bob van Noort

    Present address: Faculty of Civil Engineering and Geosciences, Delft University, Delft, The Netherlands

  2. Alfonso Mateo

    Present address: Universidad Politécnica de Madrid, Madrid, Spain

Authors and Affiliations

  1. NASA Goddard Space Flight Center, Greenbelt, MD, USA

    Sander Goossens & Erwan Mazarico

  2. Southeastern Universities Research Association, Washington DC, USA

    Bob van Noort

  3. Center for Research and Exploration in Space Science and Technology (CRESST) II, College Park, MD, USA

    Bob van Noort

  4. Faculty of Aerospace Engineering, Delft University of Technology, Delft, The Netherlands

    Bob van Noort, Alfonso Mateo & Wouter van der Wal

Authors
  1. Sander Goossens
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bob van Noort
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Alfonso Mateo
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Erwan Mazarico
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Wouter van der Wal
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

S.G. and E.M. conceived and designed the study. S.G., B.v.N. and A.M. analysed the Cassini tracking data. E.M. supported the analysis of the Cassini tracking data. W.v.d.W. provided theoretical support. All authors contributed to the discussion and interpretation of the results. S.G. wrote the first draft of the paper. All authors contributed to subsequent drafts.

Corresponding author

Correspondence to Sander Goossens.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature Astronomy thanks Sebastien Le Maistre, Marzia Parisi and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Supplementary Figs. 1–13, Tables 1–4 and references.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Goossens, S., van Noort, B., Mateo, A. et al. A low-density ocean inside Titan inferred from Cassini data. Nat Astron (2024). https://doi.org/10.1038/s41550-024-02253-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1038/s41550-024-02253-4

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing