1. IMCCE-Observatoire de Paris, UMR 8028 du CNRS, 77 Avenue Denfert-Rochereau, 75014 Paris, France
2. Royal Observatory of Belgium, Avenue Circulaire 3, Uccle, 1180 Bruxelles, Belgium

Correspondence to: Valéry Lainey¹ Correspondence and requests for materials should be addressed to V.L. (Email: lainey@imcce.fr).

Io is the volcanically most active body in the Solar System and has a large surface heat flux^{1, 2, 3}. The geological activity is thought to be the result of tides raised by Jupiter⁴, but it is not known whether the current tidal heat production is sufficiently high to generate the observed surface heat flow^{5, 6}. Io's tidal heat comes from the orbital energy of the Io–Jupiter system (resulting in orbital acceleration), whereas dissipation of energy in Jupiter causes Io's orbital motion to decelerate. Here we report a determination of the tidal dissipation in Io and Jupiter through its effect on the orbital motions of the Galilean moons. Our results show that the rate of internal energy dissipation in Io (k ₂/Q = 0.015  0.003, where k ₂ is the Love number and Q is the quality factor) is in good agreement with the observed surface heat flow^{5, 6}, and suggest that Io is close to thermal equilibrium. Dissipation in Jupiter (k ₂/Q = (1.102  0.203)  10^-5) is close to the upper bound of its average value expected from the long-term evolution of the system⁷, and dissipation in extrasolar planets may be higher than presently assumed⁸. The measured secular accelerations indicate that Io is evolving inwards, towards Jupiter, and that the three innermost Galilean moons (Io, Europa and Ganymede) are evolving out of the exact Laplace resonance.

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