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.

The peculiar shapes of Saturn’s small inner moons as evidence of mergers of similar-sized moonlets

Nature Astronomy volume 2, pages 555–561 (2018)Cite this article

Subjects

Abstract

The Cassini spacecraft revealed the spectacular, highly irregular shapes of the small inner moons of Saturn1, ranging from the unique 'ravioli-like' forms of Pan and Atlas2,3 to the highly elongated structure of Prometheus. Closest to Saturn, these bodies provide important clues regarding the formation process of small moons in close orbits around their host planet4, but their range of irregular shapes has not been explained yet. Here, we show that the spectrum of shapes among Saturn’s small moons is a natural outcome of merging collisions among similar-sized moonlets possessing physical properties and orbits that are consistent with those of the current moons. A significant fraction of such merging collisions take place either at the first encounter or after 1–2 hit-and-run events, with impact velocities in the range of 1–5 times the mutual escape velocity. Close to head-on mergers result in flattened objects with large equatorial ridges, as observed on Atlas and Pan. With slightly more oblique impact angles, collisions lead to elongated, Prometheus-like shapes. These results suggest that the current forms of the small moons provide direct evidence of the processes at the final stages of their formation, involving pairwise encounters of moonlets of comparable size4,5,6. Finally, we show that this mechanism may also explain the formation of Iapetus’ equatorial ridge7, as well as its oblate shape8.

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

Access options

Rent or buy this article

Prices vary by article type

from$1.95

to$39.95

Learn more

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

Fig. 1: Shapes of small moons of Saturn compared to model outcomes.
Fig. 2: Impact probability distribution and collision regimes.
Fig. 3: Shapes resulting from merging collisions.
Fig. 4: Ridge formation on Iapetus.

References

  1. Thomas, P. C. Sizes, shapes, and derived properties of the saturnian satellites after the Cassini nominal mission. Icarus 208, 395–401 (2010).

    Article  ADS  Google Scholar 

  2. Charnoz, S., Brahic, A., Thomas, P. C. & Porco, C. C. The equatorial ridges of Pan and Atlas: terminal accretionary ornaments? Science 318, 1622–1624 (2007).

    Article  ADS  Google Scholar 

  3. Porco, C. C., Thomas, P. C., Weiss, J. W. & Richardson, D. C. Saturn’s small inner satellites: clues to their origins. Science 318, 1602–1607 (2007).

    Article  Google Scholar 

  4. Charnoz, S., Salomon, J. & Crida, A. The recent formation of Saturn’s moonlets from viscous spreading of the main rings. Nature 465, 752–754 (2010).

    Article  ADS  Google Scholar 

  5. Hyodo, R. & Ohtsuki, K. Saturn’s F ring and shepherd satellites a natural outcome of satellite system formation. Nat. Geosci. 8, 686–689 (2015).

    Article  ADS  Google Scholar 

  6. Crida, A. & Charnoz, S. Formation of regular satellites from ancient massive rings in the Solar System. Science 338, 1196–1199 (2012).

    Article  Google Scholar 

  7. Porco, C. C. et al. Cassini Imaging Science: Initial results on Phoebe and Iapetus. Science 307, 1237–1242 (2005).

    Article  ADS  Google Scholar 

  8. Thomas, P. C. et al. Shapes of the saturnian icy satellites and their significance. Icarus 190, 573–584 (2007).

    Article  ADS  Google Scholar 

  9. Goldreich, P. & Tremaine, S. Disk-satellite interactions. Astrophys. J. 241, 425–441 (1980).

    Article  ADS  MathSciNet  Google Scholar 

  10. Karjalainen, R. Aggregate impacts in Saturn’s rings. Icarus 189, 523–537 (2007).

    Article  ADS  Google Scholar 

  11. Jutzi, M. & Asphaug, E. The shape and structure of cometary nuclei as a result of low velocity collisions. Science 348, 1355–1358 (2015).

    Article  ADS  Google Scholar 

  12. Wisdom, J. The resonance overlap criterion and the onset of stochastic behavior in the restricted three-body problem. Astron. J. 85, 1122–1133 (1980).

    Article  ADS  Google Scholar 

  13. Deck, K. M., Payne, M. & Holman, M. J. First-order resonance overlap and the stability of close two-planet systems. Astrophys. J. 774, 129 (2013).

    Article  ADS  Google Scholar 

  14. Poulet, F. & Sicardy, B. Dynamical evolution of the Prometheus–Pandora system.Mon. Not. R. Astron.Soc. 322, 343–355 (2001).

    Article  ADS  Google Scholar 

  15. Benz, W. & Asphaug, E. Simulations of brittle solids using smooth particle hydrodynamics. Comput. Phys. Commun. 87, 253–265 (1995).

    Article  ADS  MATH  Google Scholar 

  16. Jutzi, M., Benz, W. & Michel, P. Numerical simulations of impacts involving porous bodies. I. Implementing sub-resolution porosity in a 3D SPH hydrocode. Icarus 198, 242–255 (2008).

    Article  ADS  Google Scholar 

  17. Jutzi, M. SPH calculations of asteroid disruptions: the role of pressure dependent failure models. Planet. Space Sci. 107, 3 (2015).

    Article  ADS  Google Scholar 

  18. Hyodo, R. & Ohtsuki, K. Collisional disruption of gravitational aggregates in the tidal environment. Astrophys. J. 787, 56 (2014).

    Article  ADS  Google Scholar 

  19. Asphaug, E., Agnor, C. B. & Williams, Q. Hit-and-run planetary collisions. Nature 439, 155–160 (2006).

    Article  Google Scholar 

  20. Richardson, D. C. Tree code simulations of planetary rings. Mon. Not. R. Astron. Soc. 269, 493–511 (1994).

    Article  ADS  Google Scholar 

  21. Thomas, P. C. Sizes, shapes, and derived properties of the saturnian satellites after the Cassini nominal mission. Icarus 208, 395–401 (2010).

    Article  ADS  Google Scholar 

  22. Hamilton, D. P., Proctor, A. L. & Rauch, K. P. An explanation for the high inclinations of Thebe and Amalthea. Bull. Am. Astron. Soc. 33, 1085 (2001).

    ADS  Google Scholar 

  23. Castillo-Rogez, J. C. et al. Iapetus’ geophysics: rotation rate, shape, and equatorial ridge. Icarus 190, 179–202 (2007).

    Article  ADS  Google Scholar 

  24. Singer, K. N. & McKinnon, W. B. Tectonics on Iapetus: despinning, respinning, or something completely different? Icarus 216, 198–211 (2011).

    Article  ADS  Google Scholar 

  25. Ip, W.-H. On a ring origin of the equatorial ridge of Iapetus. Geophys. Res. Lett. 33, L16203 (2006).

    Article  ADS  Google Scholar 

  26. Levison, H. F., Walsh, K. J., Barr, A. C. & Dones, L. Ridge formation and de-spinning of Iapetus via an impact-generated satellite. Icarus 214, 773–778 (2011).

    Article  ADS  Google Scholar 

  27. Dombard, A. J., Cheng, A. F., McKinnon, W. B. & Kay, J. P. Delayed formation of the equatorial ridge on Iapetus from a subsatellite created in a giant impact. J. Geophys. Res. 117, E03002 (2012).

    Article  ADS  Google Scholar 

  28. Stickle, A. M. & Roberts, J. H. Modeling an exogenic origin for the equatorial ridge on Iapetus. Icarus 307, 197–206 (2018).

    Article  ADS  Google Scholar 

  29. Asphaug, E. & Reufer, A. Late origin of the Saturn system. Icarus 223, 544–565 (2013).

    Article  ADS  Google Scholar 

  30. Murray, C. D. & Dermott, S. F. Solar System Dynamics (Cambridge Univ. Press, Cambridge, UK, 1999).

  31. El Moutamid, M., Sicardy, B. & Renner, S. Coupling between corotation and Lindblad resonances in the presence of secular precession rates. Celest. Mech. Dyn. Astron. 118, 235–252 (2014).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  32. Leleu, A., Robutel, P. & Correia, A. C. M. On the coplanar eccentric non-restricted co-orbital dynamics. Celest. Mech. Dyn. Astron. 130, 3 (2018).

    Article  MathSciNet  MATH  Google Scholar 

  33. Petit, A. C., Laskar, J. & Boué, G. AMD-stability in presence of first order mean motion resonances. Astron. Astro. 607, A35 (2017).

    Article  ADS  Google Scholar 

  34. Benz, W. & Asphaug, E. Simulations of brittle solids using smooth particle hydrodynamics. Comput. Phys. Commun. 87, 253–265 (1995).

    Article  ADS  MATH  Google Scholar 

  35. Jutzi, M., Holsapple, K. A., Wuenneman, K. & Michel, P. in Asteroids IV (eds Michel, P., DeMeo, F. & Bottke, W. F.) 679–699 (Univ. Arizona, Tucson, USA, 2015).

  36. Collins, G. S., Melosh, H. J. & Ivanov, B. A. Modeling damage and deformation in impact simulations. Meteorit. Planet. Sci. 39, 217–231 (2004).

    Article  ADS  Google Scholar 

  37. Jutzi, M., Michel, P., Hiraoka, K., Nakamura, A. M. & Benz, W. Numerical simulations of impacts involving porous bodies: II. Comparison with laboratory experiments. Icarus 201, 802–813 (2009).

    Article  Google Scholar 

  38. Wisdom, J. & Tremaine, S. Local simulations of planetary rings. Astron. J. 95, 925–940 (1988).

    Article  ADS  Google Scholar 

  39. Jutzi, M., Benz, W., Toliou, A., Morbidelli, A. & Brasser, R. How primordial is the structure of comet 67 P/C-G? Astron. Astro. 597, A61 (2017).

    Article  ADS  Google Scholar 

  40. Jutzi, M. & Benz, W. Formation of bi-lobed shapes by sub-catastrophic collisions. Astron. Astro. 597, A62 (2017).

    Article  ADS  Google Scholar 

  41. Collins, G. S. Numerical simulations of impact crater formation with dilatancy. J. Geophys. Res. Planets 119, 2600–2619 (2014).

    Article  ADS  Google Scholar 

  42. Leinhardt, Z. M. & Richardson, D. C. & Quinn, T. Direct N-body simulations of rubble pile collisions. Icarus 164, 133–151 (2000).

    Article  ADS  Google Scholar 

  43. Shoemaker, E. M. in Physics and Astronomy of the Moon Ch. 8 (Academic Press, New York, 1962).

  44. Spitale, J. N., Jacobson, R. A., Porco, C. C. & Owen, W. M. Jr The orbits of Saturn’s small satellites derived from combined historic and Cassini imaging observations. Astron. J. 132, 692–710 (2006).

    Article  ADS  Google Scholar 

  45. Dombard, A. J., Cheng, A. F., McKinnon, W. B. & Kay, J. P. Delayed formation of the equatorial ridge on Iapetus from a subsatellite created in a giant impact. J. Geophys. Res. 117,E03002 (2012).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

The authors acknowledge support from the Swiss NCCR PlanetS and the Swiss National Science Foundation.

Author information

Authors and Affiliations

  1. Physics Institute, Space Research and Planetary Sciences, Center for Space and Habitability - NCCR PlanetS - University of Bern, Bern, Switzerland

    A. Leleu, M. Jutzi & M. Rubin

  2. IMCCE, Observatoire de Paris - PSL Research University, UPMC Univ. Paris 06, Univ. Lille 1, CNRS, Paris, France

    A. Leleu

Authors
  1. A. Leleu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Jutzi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. Rubin
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

A.L. performed the dynamical modelling and analysed the results. M.J. performed the collision modelling and analysed the results. M.R. contributed initial ideas for the study. All authors contributed to interpretation of the results and the preparation of the manuscript.

Corresponding author

Correspondence to A. Leleu.

Ethics declarations

Competing interests

The authors declare no competing interests.

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 Figures 1–9.

Rights and permissions

Reprints and Permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Leleu, A., Jutzi, M. & Rubin, M. The peculiar shapes of Saturn’s small inner moons as evidence of mergers of similar-sized moonlets. Nat Astron 2, 555–561 (2018). https://doi.org/10.1038/s41550-018-0471-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41550-018-0471-7

This article is cited by

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