Skip to main content
SpringerLink
Log in

Web of resonances and possible path of evolution of the small Uranian satellites

  • Original Article
  • Published:
Astrophysics and Space Science Aims and scope Submit manuscript

Abstract

Satellite systems around giant planets are immersed in a region of complex resonant configurations. Understanding the role of satellite resonances contributes to comprehending the dynamical processes in planetary formation and posterior evolution. Our main goal is to analyse the resonant structure of small moons around Uranus and propose different scenarios able to describe the current configuration of these satellites. We focus our study on the external members of the regular satellites interior to Miranda, namely Rosalind, Cupid, Belinda, Perdita, Puck, and Mab, respectively. We use N-body integrations to perform dynamical maps to analyse their dynamics and proximity to two-body and three-body mean-motion resonances (MMR). We found a complicated web of low-order resonances amongst them. Employing analytical prescriptions, we analysed the evolution by gas drag and type-I migration in a circumplanetary disc (CPD) to explain different possible histories for these moons. We also model the tidal evolution of these satellites using some crude approximations and found possible paths that could lead to MMRs crossing between pairs of moons. Finally, our simulations show that each mechanism can generate significant satellite radial drift leading to possible resonant capture, depending on the distances and sizes.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

Data Availability

The research done in this project made use of the Astroquery (Ginsburg et al. 2019), a community-developed core Python package for Astronomy (Astropy Collaboration et al. 2013, 2018). The data presented in this paper is original from the authors, and it is available upon reasonable request.

Notes

  1. For a detailed discussion see Sect. 3.3.

  2. Ariel and Umbriel were both discovered by Lassell in 1851, Titania and Oberon by Herschel in 1787 and lastly Miranda in 1948 by Kuiper. See https://planetarynames.iau.

  3. The Voyager 2 team (Smith et al. 1986) discovered 10 of the 13 moons of the inner regular satellites. Perdita was first reported by Karkoschka (2001), while Mab and Cupid were detected by Showalter and Lissauer (2006).

  4. Maps with different masses (\(m_{i} = 10^{-11}, 10^{-13}\), and \(10^{-15}~\mbox{m}_{\odot}\)) show the same structure with both the \(\mathrm{max}(\Delta a)\) and \(\mathrm{max}(\Delta e)\) indicators.

  5. The choice of the integration timescale was reduced from that of Fig. 2 since at least one secular period of the eccentricity is covered, and we can shorten computational time.

  6. For reference, the orbital period of Perdita is \(\sim0.640~\mbox{days}\), while Puck’s is \(\sim0.76~\mbox{days}\).

References

Download references

Acknowledgements

We thank both Y. Chen and the anonymous reviewer for their reports that helped us improve our manuscript.

Funding

CC has been supported by the Fonds de la Recherche Scientifique – FNRS under Grant No. F.4523.20 (DYNAMITE MIS-project). CC and CG received research grants from CONICET, and Secyt – Universidad Nacional de Córdoba and used computational resources from CCAD – UNC which are part of SNCAD (https://ccad.unc.edu.ar), – MinCyT, República Argentina. OMG is partially supported by the PICT 2018-0934 from ANPCyT, Argentina, and by ANID – Millennium Science Initiative Program – NCN19_171.

Author information

Authors and Affiliations

  1. naXys, Department of Mathematics, University of Namur, Rue de Bruxelles 61, 5000, Namur, Belgium

    C. Charalambous

  2. Observatorio Astronómico - IATE, Universidad Nacional de Córdoba, Laprida 854, 5000, Córdoba, Argentina

    C. Charalambous & C. A. Giuppone

  3. Instituto de Astrofísica de La Plata, CONICET-UNLP, Paseo del Bosque S/N, 1900, La Plata, Argentina

    O. M. Guilera

  4. Núcleo Milenio de Formación Planetaria (NPF), Av. Vicuña Mackenna 4860, Macul-Santiago, 8970117, Chile

    O. M. Guilera

Authors
  1. C. Charalambous
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. C. A. Giuppone
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. O. M. Guilera
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

The dynamical analysis was made by C. Charalambous and C.A. Giuppone. The analysis about migration was performed by C. Charalambous, the section about gas drag was made by O.M. Guilera and the tidal contribution was made by C.A. Giuppone.

Ethics declarations

Conflict of Interest

The authors declare that they have no conflict of interest.

Additional information

Publisher’s Note

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Charalambous, C., Giuppone, C.A. & Guilera, O.M. Web of resonances and possible path of evolution of the small Uranian satellites. Astrophys Space Sci 367, 54 (2022). https://doi.org/10.1007/s10509-022-04083-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10509-022-04083-0

Keywords

Search

Navigation