GRAVITATIONAL TIDES IN THE OUTER PLANETS .2. INTERIOR CALCULATIONS AND ESTIMATION OF THE TIDAL DISSIPATION FACTOR

The theory of excitation of tidal oscillations in a fluid planetary body is formulated, and separable equations are derived that extend the results of the classical theory of tides to the nonhydrostatic interiors of planets. The theory is applied to the example of the gravitational tidal response of Jupiter to forcing by Io. The tidal response is found to crucially depend on the static stability in the interior of the planet, the response of the planet being as much as two to three orders of magnitude greater than the response with a neutral interior. The tidal dissipation factor Q is calculated for Jupiter and found to agree with the values required by the astronomical arguments only if the interior has finite (though small static stability. We are led to the conclusion that the interior of Jupiter must have regions which are stably stratified.