From: sylvia@email.invalid   
      
   On 30-Oct-24 12:53 pm, Sylvia Else wrote:   
   > NASA has a mission to the Jovian system, to study Europa. That moon is   
   > interesting because it appears to have liquid water under an icy   
   > surface. The heat need to keep the water liquid comes from the   
   > stretching and compression Europa experiences during its orbit around   
   > Jupiter, the orbit not been exactly circular.   
   >   
   > So much, so simple.   
   >   
   > Some thought made me realise that although the tidal forces on Europa   
   > mean that it is not exactly spherical, its two bulges cannot remain   
   > perfectly aligned with Jupiter, because Europa's angular velocity   
   > relative to Jupiter is higher at periapsis than at apoapsis. The result   
   > is that the nearer bulge is sometimes ahead, and sometimes behind,   
   > relative to Europa's orbital motion, resulting in a net force backwards   
   > along the orbit, or forward along the orbit.   
   >   
   > Again, certainly stuff that's already well known.   
   >   
   > As far as I can see, the energy that is being dissipated as heat inside   
   > Europa has to come from changes to Europa's orbit. Further, if Europa   
   > were either perfectly rigid, or perfectly elastic, there would be no   
   > energy transfer, and consequently no change to the orbit.   
   >   
   > It would make no difference if Jupiter itself were perfectly rigid, so   
   > the transfer cannot involve tides on Jupiter generated by Europa.   
   >   
   > So the existence of the orbital energy transfer depends on Europa being   
   > neither perfectly rigid nor perfectly elastic.   
   >   
   > What escapes me is the mechanism.   
   >   
   > Any thoughts?   
      
   Perhaps I was naive to think anyone would address the essence of my   
   post, rather than going off at massive tangent.   
      
   Sylvia.   
      
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