Orbital acceleration and the energy budget in the galilean satellite system

Prodigious amounts of heat are generated in Jupiter's satellite Io, as evidenced by its spectacular volcanism¹ and infrared heat flux ^2-6 (∼7.6×l0¹³ W (ref. 7)). Such heating had been predicted from tidal flexing of Io due to the eccentricity of its orbit⁸, which is maintained by its resonant gravitational interaction with the satellites Europa and Ganymede. The energy for tidal heating must come from Io's orbit, but due to the resonance the energy loss is shared among the three satellites' orbits^9,10. This effect modifies the rate at which Io's semi-major axis would be expected to decrease, and also tends to drive the system out of resonance. Yoder⁹ suggested that the resonance is maintained by tides raised on Jupiter by Io, which act to transfer planetary rotational energy and angular momentum into Io's orbit, but the jovian torque may be insufficient for this purpose. Greenberg¹⁰ proposed that with smaller jovian torque the system may be evolving away from resonance, and that measurement of Io's orbital acceleration could show whether the evolution is in fact dominated by heating in Io. An acceleration value n.₁/n ₁=4.6×10^-l0 yr^-1±20%, where n ₁ is Io's mean motion, derived¹¹ from historical records of Io's motion, is in accord with the expected value n.₁/n ₁=3.2×10^-10±28% based on the measured thermal radiation and the assumption of negligible jovian torque. A much smaller negative acceleration has been determined by Lieske^12,13, which would imply significant jovian torque, but not enough to maintain the equilibrium proposed by Yoder, unless the average tidal disruption in Io is much less than is indicated by the thermal flux.