Io is the volcanically most active body in the Solar System and has a large surface heat flux1,2,3. 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 flow5,6. 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 (k2/Q = 0.015 ± 0.003, where k2 is the Love number and Q is the quality factor) is in good agreement with the observed surface heat flow5,6, and suggest that Io is close to thermal equilibrium. Dissipation in Jupiter (k2/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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We thank D. Pascu for sharing his unpublished observations.
Author Contributions All authors contributed to the writing of the manuscript. V.L. developed and fitted to the observations the full numerical model presented in this work. J.-E.A. fitted to the observations the secular accelerations using L1 astrometric residuals (Supplementary Information). Theoretical calculations of the energy dissipation and Fig. 2 were made by Ö.K. T.V.H. and Ö.K. contributed to the geophysical interpretations of the secular accelerations.
This file provides a detailed description of the dynamical model, a Supplementary Discussion, Supplementary Notes including references, Supplementary Tables 1-5 and Supplementary Figures 1-3 with Legends. (PDF 555 kb)
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Lainey, V., Arlot, JE., Karatekin, Ö. et al. Strong tidal dissipation in Io and Jupiter from astrometric observations. Nature 459, 957–959 (2009). https://doi.org/10.1038/nature08108
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