  Tidal effects in planetary systems are the main driver in the orbital
migration of natural satellites. They result from physical processes occurring
deep inside celestial bodies, whose effects are rarely observable from surface
imaging. For giant planet systems, the tidal migration rate is determined by
poorly understood dissipative processes in the planet, and standard theories
suggest an orbital expansion rate inversely proportional to the power 11/2 in
distance, implying little migration for outer moons such as Saturn's largest
moon, Titan. Here, we use two independent measurements obtained with the
Cassini spacecraft to measure Titan's orbital expansion rate. We find Titan
migrates away from Saturn at 11.3 $\pm$ 2.0 cm/year, corresponding to a tidal
quality factor of Saturn of Q $\simeq$ 100, and a migration timescale of
roughly 10 Gyr. This rapid orbital expansion suggests Titan formed
significantly closer to Saturn and has migrated outward to its current
position. Our results for Titan and five other moons agree with the predictions
of a resonance locking tidal theory, sustained by excitation of inertial waves
inside the planet. The associated tidal expansion is only weakly sensitive to
orbital distance, motivating a revision of the evolutionary history of Saturn's
moon system. The resonance locking mechanism could operate in other systems
such as stellar binaries and exoplanet systems, and it may allow for tidal
dissipation to occur at larger orbital separations than previously believed.
