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In this lecture opening the session focused on tides in stellar and planetary systems, I will review the Jean-Paul Zahn's key contributions to the theory of tidal dissipation in stars and fluid planetary layers. I will first recall the general principles of tidal friction in celestial bodies. Then, I will focus on the theories of the stellar equilibrium and dynamical tides founded by Jean-Paul and their predictions for the evolution of binary stars. I will underline their essential legacy for ongoing studies of tidal dissipation in stars hosting planets and in fluid planetary regions. I will also discuss his pioneering work on the turbulent friction applied on tidal flows by stellar convection and the corresponding still unsolved challenging problems. Next, I will present the results we obtained on tidal dissipation in the potential dense rocky/icy core of gaseous giant planets such as Jupiter and Saturn within the Encelade international team. This mechanism provides important keys to interpret the high-precision astrometric measurements of the rates of tidal orbital migration of the moons of these planets, which are found to be larger than expected. This corresponds to a Jovian and Saturnian tidal frictions which are higher by one order of magnitude than the usually used values calibrated on formation scenarios. Finally, I will review the work done by Jean-Paul and Michel Rieutord on potential Ekman boundary layers associated to tidal flows. As a consequence, a coherent physical modeling of tides is now mandatory to understand the properties and the evolution of stellar and planetary systems. To progress on this forefront research subject, we are walking on the path first drawn by Jean-Paul.

Tidal dissipation in stars and giant planets: Jean-Paul Zahn's pioneering work and legacy