Tides in the Jovian System

Tidal interaction is presumed to play a crucial role in the long term evolution
of the orbits of the Galilean satellites. Io's active volcanism and associated
heat flow are probably driven by tidal dissipation within the satellite. It is
of high interest to determine whether Io is spiraling toward or away from
Jupiter. If the former is true, Io is losing more energy through internal
dissipation than it is gaining from the torque on the tidal bulge that it raises
on Jupiter. Lainey et al. (2009 Nature 459, 957) published an investigation
of tidal effects in the Jovian system based on an analysis of astrometric
observations through 2007 and mutual events through 2003. Their modelling
included the tide raised on Jupiter by each Galilean satellite and the tide
raised on Io by Jupiter. Subsequently, we extended their analysis adding
additional astrometry through through 2013, mutual events through 2009, Galilean
satellite eclipse timings, and data acquired by the Voyager, Cassini, Galileo,
and New Horizons spacecraft (Jacobson and Folkner, 2014 AAS/Division for
Planetary Sciences Meeting Abstracts 46 418.03). With the inclusion of
the spacecraft data, we found that the tidal effects became barely dectectable
if at all.

On 2021 June 07 the Juno spacecraft flew by Ganymede at an altitude 1046 km.
Unlike our previous work, when we added the Juno tracking data to our data set
(also extended to astrometry through 2018 and mutual events in 2015), we were
able to obtain a strong determination of the dissipation, k2/Q (k2 is the love
number, Q is the tidal quality factor), of both Jupiter and Io. Our analysis
incorporated the Jupiter love number recently reported by Wahl et al. (2020 
Astrophys. J. 891, 42) from Juno tracking data. Our Jupiter Q falls within
the bounds postulated by Peale (1999 Ann. Review Astron. Astrophys. 37,
533). The heat flux computed with our k2/Q for the tide raised on Io is within
the estimated range based on the observed heat radiated by Io (McEwen et al.
2004, Jupiter, Cambridge Univ. Press, 281). As a consequence of the tidal
forces, our orbit for Io is spiraling inward confirming the significant internal
energy loss. Our orbit for Europa is also spiraling inward as it attempts to
maintain its orbital resonance with Io despite the tidal force acting on it from
Jupiter. Ganymede, on the other hand, is on an outward spiral, moving out of its
resonance with Europa. The tidal force appears to be too small to detectably
alter Callisto's orbit.