Consideration is given to the energy-momentum balances within the Jupiter-Galilean moons system. It is noted that the level of dissipation is set by the masses of the resonant satellites Io, Europa, Ganymede, and Callisto, and the power supply from Jupiter is independent of the internal structure of Io. Energy balances are calculated for two satellites raising tides on the planet, receiving a feedback, then transferring some of the dissipated energy to the outer two moons. The orbits of the Jovian moons are found to have dissipated 1.15 x 10 to the 27th J over a period of 1,500,000 yr, with corresponding orbit increases of 0.003%. The energetics of a steady tidal evolution are analyzed, as is the melting of Io after entering resonance with Europa.