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Tides in Planetary Systems

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Tides in Astronomy and Astrophysics

Part of the book series: Lecture Notes in Physics ((LNP,volume 861))

Abstract

The Solar system is the seat of many interactions between the Sun, the planets and their natural satellites. Moreover, since 1995, a large number of extrasolar planetary systems has been discovered where planets orbit around other stars, sometimes very close to them. Therefore, in such systems, tidal interactions are one of the key mechanisms that must be studied to understand the celestial bodies’ dynamics and evolution. Indeed, tides generate displacements and flows in planetary (and in the host star) interiors. The associated kinetic energy is then dissipated into heat because of internal friction processes. This leads to secular evolution of orbits and of spins with characteristic time-scales that are intrinsically related to the properties of dissipative mechanisms, those latters depending both on the internal structure of the studied bodies and on the tidal frequency. This lecture is aimed to review the must advanced theories to study tidal dynamics in planetary systems and the different tidal flows or displacements that can be excited by a perturber, the conversion of their kinetic energy into heat, the related exchanges of angular momentum, and the consequences for systems evolution.

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Notes

  1. 1.

    They are driven by two types of deformation. The first one is those induced by internal dynamical processes such that rotation (through the centrifugal acceleration) and magnetic field (through the volumetric Lorentz force). The second one is the axisymmetric permanent tidal oval shape due to a companion in close binary or multiple systems.

  2. 2.

    The denomination of \(V_{\mathrm{A-B}}\) as a potential is not very pertinent since it has the dimension of the product of a mass by a potential. However, we keep it to stay coherent with [44].

  3. 3.

    Note that each tidal Fourier’s mode have its own dissipation rate as it as been shown by Zahn (1966–1977).

  4. 4.

    The tidal multipole moments of B due to A can be derived using the same methodology and substituting A to B for the perturber and vice-versa.

  5. 5.

    See also the lecture in this volume on stellar tides by J.-P. Zahn.

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Acknowledgements

We thank the CNRS/INSU for the support given to this Thematic School. This work was supported in part by the Programme National de Planétologie (CNRS/INSU), the Programme National de Physique Stellaire (CNRS/INSU), the EMERGENCE-UPMC project EME0911, and the CNRS Physique théorique et ses interfaces program.

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Authors and Affiliations

  1. Laboratoire AIM Paris-Saclay, CEA/DSM-CNRS-Université Paris Diderot, CEA, 91191, Gif-sur-Yvette, France

    Stéphane Mathis & Françoise Remus

  2. LESIA, Observatoire de Paris-CNRS-Université Paris Diderot-Université Pierre et Marie Curie, Observatoire de Paris, 5 place Jules Janssen, 92195, Meudon, France

    Stéphane Mathis

  3. Syrte, Observatoire de Paris, CNRS UMR8630, Université Pierre et Marie Curie, Observatoire de Paris, 77 avenue Denfert-Rochereau, 75014, Paris, France

    Christophe Le Poncin-Lafitte

  4. LUTH, Observatoire de Paris-CNRS-Université Paris Diderot, Observatoire de Paris, 5 place Jules Janssen, 92195, Meudon Cedex, France

    Françoise Remus

  5. IMCCE, Observatoire de Paris-UMR 8028 du CNRS-Université Pierre et Marie Curie, Observatoire de Paris, 77 avenue Denfert-Rochereau, 75014, Paris, France

    Françoise Remus

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  1. Stéphane Mathis
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  1. Dépt. Astronomie Fondamental, Observatoire de Paris, avenue de l Observatoire 61, Paris, 75014, France

    Jean Souchay

  2. IRFU/SAP Centre de Saclay, Laboratoire AIM Paris Saclay Diderot, Bat. 709, Gif-sur-Yvette, 91191, France

    Stéphane Mathis

  3. University of Cambridge, Trinity Hall, Cambridge, CB2 1TJ, United Kingdom

    Tadashi Tokieda

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Mathis, S., Le Poncin-Lafitte, C., Remus, F. (2013). Tides in Planetary Systems. In: Souchay, J., Mathis, S., Tokieda, T. (eds) Tides in Astronomy and Astrophysics. Lecture Notes in Physics, vol 861. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32961-6_7

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